DMOL3 GUIDEMATERIALS STUDIO

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ContentsDMol3 1Introduction 1Further Information 1

Tasks in DMol3 2Energy 3Setting up the calculation 3

Dynamics 4Selecting the thermodynamic ensemble 4Defining the time step 4Controlling the thermostat 4Constraints during dynamics 4

Transition state searching 5Transition state optimization 6Transition state searching by synchronoustransit methods 6Verifying a transition state 7Transition state searching via synchronoustransit methods 7Input to a synchronous transit calculation 8Restarting a QST calculation 9

Transition state searching via eigenvectorfollowing 9Calculation parameters 9Use of the Hessian 9

Geometry optimization 9Following a reaction path 10Elastic constants 11Reaction kinetics 11Electron Transport 12Electrodes 12

Properties 13Setting up DMol3 calculations 13Setting up electronic options 14Integration accuracy 14SCF tolerance 14k-points 14Core treatment 14Real space cutoff 15Harris approximation 17Solvation scheme 17Performance tips 18

Setting up k-points 18Setting up a geometry optimization 19Algorithms for the optimization 20Parameters for the optimization 20

Setting up a molecular dynamics calculation20Choosing an ensemble 21Defining the time step 21Defining the thermostat control 21Constraints during dynamics 21

Setting up a transition state calculation 22Which method to use? 22Verifying a transition state 22

Setting up a TS confirmation calculation 23Setting up a work function calculation 23Setting up an elastic constants calculation 24Parameters for the optimization 24

Setting up a reaction kinetics calculation 24Transition state search 25Hessian calculation 25Reaction rate calculation 25

Setting up an electron transport calculation 25Requesting electronic and structuralproperties 26Setting up electron densities 27Setting up electrostatics 27Setting up vibrational frequencies 28Setting up Raman intensities 28Setting up Fukui functions 28Setting up molecular orbital analysis 29Setting up a population analysis 29Setting up band structures 30Setting up density of states 30Setting up Fermi surfaces 31Setting up COSMO Sigma profilecalculation 31Setting up an optics calculation 31

Manipulating files 32Input files 32Output files 33Restarting a DMol3 calculation 33Importing a Hessian file 35

Analyzing DMol3 results 35Updating structure 36Displaying trajectory and chart data 37Creating a trajectory and chart 37Animating the trajectory 38Chart Viewer point selection 38

Visualizing volumetric data 38Electron density 38

Electrostatic potential 39Fukui functions 40Molecular orbitals 40Field visualization 41

Visualizing Fermi surfaces 42Displaying population analysis results 42Displaying computed charges, spins, andbond orders 43

Displaying band structure charts 43Displaying density of states charts 44Full density of states 45Partial density of states 45

Calculating elastic constants 46Displaying the averaged potential chart forwork function calculations 46Analyzing optical properties 47Displaying Raman spectra 48Calculating reaction kinetics 48Displaying solvation properties 49Analyzing current and transmissionproperties 50

DMol3 jobs 51Using DMol3 job control 51Remote DMol3 jobs 51A sample DMol3 run 51If a remote DMol3 job fails 53Running DMol3 in standalonemode 54DMol3 file formats 57DMol3 file formats - ARC 58DMol3 file formats - BANDS 58DMol3 file formats - CAR and MDF 58DMol3 file formats - COSMO 58DMol3 file formats - GRD 59DMol3 file formats - HESSIAN 59DMol3 file formats - HESSWK 59DMol3 file formats - INPUT 60DMol3 file formats - OCCUP 60DMol3 file formats - OUTMOL 60DMol3 file formats - PDOS_WEIGHTS 61DMol3 file formats - TPVEC 61DMol3 file formats - TPDENSK 61

Reaction Kinetics Study Table 61Theory in DMol3 62Density functional theory (DFT) in DMol3 62Functionals in DMol3 62Local functionals 62Nonlocal functionals 62Hybrid functionals 62

Meta-GGA functionals 63Numerical basis sets 63Atomic basis sets are generatednumerically 63Advantages of numerically derived basissets 63Additional basis functions, includingpolarization 63

Numerical integration 65Atomic and molecular integration grids 65Integration points, atomic size, precision,and computational cost 65Atomic shells 66Assuring consistent precision duringintegration 66Partition functions improve convergenceand avoid nuclear cusps 66

Pseudopotentials 67Norm-conserving pseudopotentials 68Evaluating the Coulombic potentialnumerically 69

Themodel charge density 70Effect of angular truncation on precisionofmodel charge density 70The Coulombic potential 70The total potential 70

Computational self-consistent fieldprocedure 70Interpolating the numerical atomic basesonto themolecular grid 70Constructing the initial molecular electrondensity 71Additional computational costs 71Reducing the computational cost 71Damping and convergence 71Efficiently calculating the electrostaticpotential 71Effect of auxiliary density approximationon accuracy of calculated total energy 72SCF convergence acceleration by DIIS 72

Energy gradients 73Predicting chemical structure 73First derivative of total energy withrespect to change in nuclear position 73Derivative of the basis function 74Derivation of other terms 74The final equation for the derivative of theenergy 75Computational costs 75Potential problems 75

Minimization algorithms; molecularsymmetry 75

Electronic excitations with TD-DFT 75Predicting UV-Vis spectra 75Computational costs 76Accuracy of excitation energies and orbitaloverlap 77TD-DFT in combination with hybridfunctionals in DMol3 77

Molecular dynamics 77Ensembles 77NVE ensemble 78NVT dynamics 78

Constraints 79Point group symmetry 80COSMO-solvation effects 80DMol3/COSMO 82Determination of the cavity surface (orsolvent-accessible surface) 83Determination of non-electrostaticcontributions to the free energy ofsolvation 83COSMO-SAC model 83COSMO sigma profile 84

Electric field gradients 84Thermodynamic calculations 86Enthalpy 86Entropy 87Heat capacity 87Using the results 88

Fitting atomic point charges to theelectrostatic potential (ESP) 88Mulliken and Mayer bond orders 89Hirshfeld charge analysis 90Fukui functions 91Raman spectra 92Basis set superposition error 93Converging SCF 93

Challenging systems 94Checklist 94

Dialogs in DMol3 96DMol3 Calculation dialog 96Setup tab 96DMol3 Energy dialog 99DMol3 Geometry Optimization dialog 100DMol3 Dynamics dialog 101Dynamics tab 102Thermostat tab 102

DMol3 Transition State Search dialog 103

DMol3 TS Optimization dialog 105DMol3 TS Confirmation dialog 105DMol3 Elastic Constants dialog 106DMol3 Reaction Kinetics dialog 107DMol3 Transport dialog 109Setup tab 110

Density Mixing 110Electrode 111

DMol3 Transmission dialog 111DMol3 Current/Voltage dialog 111Electrodes tab 111Electrostatics tab 112DMol3 Poisson Boundary Conditionsdialog 112

Electronic tab 113DMol3 Electronic Options dialog 115SCF tab 116k-points tab 117Orbital Cutoff tab 118Solvent tab 119DFT-D tab 120

Properties tab 121Band structure selection 122Density of states selection 122DMol3 Density of States Optionsdialog 123

Electron density selection 124Electrostatics selection 125Frequency selection 125Partial Hessian dialog 126

Fukui function selection 127Optics selection 127DMol3 Optics Options dialog 128

Orbitals selection 129Population analysis selection 129DMol3 Grid Parameters dialog 130

Job Control tab 131DMol3 Job Control Options dialog 132

DMol3 Job Files dialog 133DMol3 Analysis dialog 133Band structure selection 134Current/Voltage selection 135Density of states selection 136DMol3 DOS Analysis Options dialog 137

Elastic constants selection 138Electron density selection 138Energy evolution selection 139

Fermi surface selection 139Fukui function selection 140Optics selection 141DMol3 Optics Analysis Options dialog 141

Orbitals selection 142Population analysis selection 143Potentials selection 144Raman spectrum selection 144Reaction kinetics selection 145Solvation properties selection 146Choose COSMO File dialog 146

Structure selection 147Thermodynamic properties selection 147Transmission selection 148

DMol3 keywords 149DMol3 References 150

DMol3

IntroductionDMol3 allows you to model the electronic structure and energetics ofmolecules, solids, and surfacesusing density functional theory (DFT). This produces highly accurate results, while keeping thecomputational cost fairly low for an ab initio method. You can study a broad range of systems usingDMol3, including organic and inorganic molecules, molecular crystals, covalent solids, metallic solids,and surfaces of a material. With DMol3, you can predict structure, reaction energies, reaction barriers,thermodynamic properties, and optics and vibrational spectra.DMol3 uses DFT to produce highly accurate results, while keeping the computational cost fairly low foran ab initio method. You can learn more about howDMol3works in the Theory in DMol3 section.

Note: DMol3 is suitable for molecules and 3D periodic solids, but will not work for 1D or 2D periodicstructures. To model such systems, you must build a 3D structure with a vacuum between periodiccopies.

Further InformationFor more information about theMaterials Studio and other Accelrys software products, visit BIOVIASupport on theWeb: https://community.accelrys.com/index.jspa

DMol3  | Page 1

Tasks in DMol3

The DMol3module allows you to model the electronic structure and energetics of organic and inorganicmolecules, molecular crystals, covalent solids, metallic solids, and infinite surfaces. DMol3 can currentlyperform several different tasks:n Single-point energy calculationn Geometry optimizationn Molecular dynamicsn Transition-state searchn Transition-state optimizationn Following a reaction pathn Elastic constants calculationsn Reaction kinetics calculationsn Electron transport calculationsEach of these calculations can be set up so that it generates specified chemical and physical properties.An additional task, known as a properties calculation, allows you to restart a completed job to computeadditional properties that were not calculated as part of the original run.There are a number of steps involved in running a DMol3 calculation, which can be grouped as follows:n Structure definition: A 3D Atomistic document containing the system of interest must be specified.

There are a number of ways to prepare a structure:n Molecules can be built using the sketching tools in theMaterials Visualizern Polymers can be constructed using the Polymer Builder in theMaterials Visualizern 3D periodic structures can be built using the tools available in theMaterials Visualizer for building

crystalsn Nanostructures can be prepared using the tools available in the Nanostructure Builder in the

Materials Visualizern Existing structures can bemodified using theMaterials Visualizer sketching toolsn Structures can be imported from an existing structure fileIn the case of a transition-state calculation, a 3D Atomistic Trajectory document containing a reactionsequence is required as the input document. You should define the structures of the reactants andthe products in two separate 3D Atomistic documents via themethods listed above and then use theReaction Preview tool to generate the trajectory.

Note: DMol3 can only be used to perform calculations on molecules and 3D periodic structures(crystals). Structures with 2D periodicity (surfaces) cannot be used in DMol3.

n Calculation setup: Once a suitable 3D structure document has been defined, then it is necessary toselect the type of calculation to be performed and set the associated parameters. For example, in thecase of a transition-state search, these parameters include the search protocol and the convergencethreshold. Finally, the server on which the calculation is to be run should be selected and the jobinitiated.

n Analysis of the results:When the calculation is complete, the files related to that job are returned tothe client and, where appropriate, displayed in the Project Explorer. The tools on the DMol3 Analysisdialog may be used to visualize the results of the calculation.

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To select a DMol3 task1. ChooseModules | DMol3 | Calculation from themenu bar to display the DMol3 Calculation dialog.2. Select the Setup tab.3. Select the required DMol3 task from the Task dropdown list.

EnergyThe "total energy" of a molecule or crystal refers to the energy of a specific arrangement of atoms ascalculated using Eq. DFT-8 or Eq. DFT-12.The zero of energy is taken to be the infinite separation of all electrons and nuclei, so the total energy isgenerally negative, corresponding to a bound state. This quantity should not be confused with the"binding energy", which is the energy required to separate the individual atoms.Both of these quantities appear in the DMol3 output file.The default unit of energy in DMol3 is the Hartree (Ha) or atomic unit (au), equivalent to 627.5 kcal/mol.By comparing total energies of different systems you can computemany properties of chemicalsignificance such as:n heats of reactionn energy barriersn conformational energy differencesn bond strengthsn adsorption energies

Setting up the calculationThe energy computed by DMol3 for a particular molecular or crystalline geometry depends upon anumber of computational parameters. When comparing energies, it is necessary that you use the sameparameters for each system. When you set up a calculation using the DMol3 Calculation dialogs,Materials Studio selects reasonable defaults for you, so it is not absolutely necessary to choose newvalues for these parameters.1. ChooseModules | DMol3 | Calculation from theMaterials Studio menu bar.2. Open the Setup tab.3. Set the Task to Energy.4. Set the charge and spin state of the system.5. Set the exchange-correlation functional. This specifies the DFT functional that will be used in the

calculation. In general, LDA functionals provide quicker calculations, but GGA functional providemore reliable results. For any calculations involving comparison of energies, GGA functionals arerecommended.

6. If a basis set superposition error (BSSE) calculation is required, click theMore... to open the DMol3Energy dialog and prepare the appropriate atom sets.

7. Select the electronic parameters for the calculation on the Electronic tab. Themost importantoptions are discussed in Setting up electronic options.

8. Set the basis set. This controls the number of atomic orbitals used to describe each molecularorbital. The numerical basis sets used in DMol3 provide a means of balancing the cost and accuracyof a calculation.

9. Select appropriate options on the Job Control tab. Themost important option to specify is theGateway location, or the name of the compute server.

10. Click the Run button.

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DynamicsMolecular dynamics in DMol3 allows you to simulate how the atoms in a structure will move as afunction of time under the influence of computed forces by solving Newton's classical equations ofmotion, modified, where appropriate, to take account of the effects of temperature on the system.Before performing a DMol3molecular dynamics calculation, you should select a thermodynamicensemble and set the associated parameters, specify the simulation time, and enter the temperature atwhich the simulation is to be carried out.

Selecting the thermodynamic ensembleIntegrating Newton's equations ofmotion allows you to explore the constant energy surface (NVEdynamics) of a system. However, most natural phenomena occur under conditions where a systemexchanges heat with the environment. These conditions can be simulated using NVT ensembles(Gaussian, Nosé-Hoover, or (massive) generalized Gaussian moments).

Defining the time stepAn important parameter in the integration algorithm is the time step. To make the best use ofcomputation time, a large time step should be used. However, if the time step is too large, it may lead toinstability and inaccuracy in the integration process. Typically, this is manifested as a systematic drift inthe constant ofmotion, but it can also lead to the job failing unexpectedly due to a large energydeviation between steps.

Controlling the thermostatA second important parameter for NVT ensembles is the definition of the thermostat mass or relaxationtime step. For Nosé-type thermostats, this is done by defining a ratio between the thermostat mass andthe desired kinetic energy of the system. For the two generalized Gaussian moments thermostats, this isdone by defining a time scale, τ, which must be significantly larger than the time step.

Constraints during dynamicsDMol3 supports two types of constraints during molecular dynamics simulations via Materials Studiointerface:n Internal coordinates can be fixed (distances, angles, and torsions)n Individual atom positions can be fixed

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To perform a molecular dynamics calculation1. Either import the structure from a pre-existing file or construct a new system using the sketching

tools or the tools for building crystals and nanostructures in theMaterials Visualizer.2. ChooseModules | DMol3 | Calculation from themenu bar to display the DMol3 Calculation dialog.3. Select the Setup tab and choose Dynamics from the Task dropdown list.4. Set theQuality of the calculation.5. If you wish to customize any of the job settings, click heMore... button to display the DMol3

Dynamics dialog and alter the parameters accordingly.6. Select the exchange-correlation functional from the Functional dropdown lists. This specifies the DFT

functional that will be used in the calculation. In general, LDA functionals produce faster calculations,but GGA functionals yield more reliable results. For any calculations involving comparison ofenergies, GGA functionals are recommended.

7. If you wish to carry out a spin-unrestricted calculation, check the Spin unrestricted checkbox, theneither check theUse formal spin as initial checkbox or select a particular spin state that thecalculation will be carried out on from theMultiplicity dropdown list. Specify the charge of thesystem.

8. Select the Electronic tab. Set the electronic parameters for the calculation. Themost importantoptions are discussed in the Setting up electronic options topic.

9. Select a basis set. This controls the number of atomic orbitals used to describe each molecularorbital. The numerical basis sets used in DMol3 provide a means of balancing the cost and accuracyof a calculation.

10. Select the Properties tab. If you wish to compute any additional properties of the system as part ofthe DMol3 run, check the appropriate checkboxes in the list and set the associated parameters asrequired.

11. Select the Job Control tab and choose a server on which to run the DMol3 job from theGatewaylocation dropdown list. If necessary, specify theQueue to which the job will be submitted. DMol3will automatically assign a name to the job based on the name of the 3D structure documentcontaining the system being studied. If you wish to specify an alternative name, uncheck theAutomatic checkbox and enter the new name in the Job description text box.

12. Specify the number of cores on which to run the job in the Run in parallel on field.13. Click theMore... button to display the DMol3 Job Control Options dialog. Select the documents to

be used for live updates and set the behavior of DMol3 on job completion.14. Click the Run button.15. If you wish, you can examine the intermediate results to ensure that the calculation parameters are

reasonable.16. After the job has finished, view the output files. You can then analyze the results.

Note: When starting an MD simulation a geometry optimization should be performed on a systemstudied, with the same parameters (basis set, functional etc.). If the system is not in its equilibriumgeometry, large fluctuations and/or lack ofMD convergencemay be expected.

Transition state searchingWhen a molecular or crystal structure is built, it usually needs to be refined to bring it to a stablegeometry. The refinement process is known as optimization (or minimization) and is an iterativeprocedure in which the coordinates of the atoms are adjusted so that the energy of the structure isbrought to a stationary point, i.e., one in which the forces on the atoms are zero. A transition state is a

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stationary point that is an energy maximum in one direction (the direction of the reaction coordinate)and an energy minimum in all other directions.During the course of chemical reaction, the total energy naturally changes. Starting from the reactants,the energy increases to a maximum and then decreases to the energy of the products. Themaximumenergy along the reaction pathway is known as the activation energy; the structure corresponding tothis energy is called the transition state.You can also perform an optimization to a transition state by setting the Task to TS Optimization or toTS Search. By performing geometry optimization you can predict barriers to chemical reactions anddetermine reaction pathways.

Note: When a transition state search is performed on a periodic system the unit cell is fixed.

DMol3 offers two different methods for locating a transition state.

Transition state optimizationWhen you use the TS Optimization task, DMol3 starts from a reasonable guess for the transition stateand performs a Newton-Raphson search on the potential energy surface. This uses techniques similar toa search for an energy minimum but searches instead for an energy maximum along one normal mode.Because this method follows one of the Hessian eigenvectors to an energy maximum, themethod isoften referred to as "eigenvector following" (EF).You must have a Hessian associated with themodel in order to perform transition state optimization.Before proceeding, generate a Hessian by requesting a frequency calculation on the starting geometry.The transition state setup will automatically detect whether or not you have a Hessian, and it will notallow you to submit a transition state optimization without one.See the section on Transition state searching via eigenvector following for additional information.To perform a transition state optimization1. ChooseModules | DMol3 | Calculation from themenu bar.2. Open the Setup tab and set the Task to TS Optimization.3. Select Vibrational Analysis from the Toolsmenu. This dialog is used to specify the vibrational

frequencies and normal modes. Select the frequency of the normal mode that corresponds to thereaction coordinate by clicking on the frequency in the tabulated list. This mode is used by thetransition state optimization to search for a maximum.

4. If desired, set additional options by selecting theMore... button to bring up the DMol3 TSOptimization dialog.

5. Click the Run button.

Transition state searching by synchronous transit methodsStarting from reactants and products, the synchronous transit methods interpolate a reaction pathwayto find a transition state. Thesemethods alternate searching for an energy maximum with constrainedsearches for a minimum in order to refine the transition state to a high degree. See the section onTransition state searching via synchronous transit methods for background information.

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To perform a transition state search1. Construct or import onemodel representing reactants and a second for products.2. Determine the correspondence between atoms in the two documents using the Find Equivalent

Atoms tool. The synchronous transit method works by performing a geometric interpolationbetween the atomic coordinates of the atoms in the reactants with the atoms in the products. Inorder to accomplish this, it is necessary that the program understand which atom matches to which.

3. Generate a trajectory that converts reactants into products using the Reaction Preview. You cananimate this document to verify that the reactants are converted correctly to products. If you aresatisfied with thematch, proceed with the calculation. If not, use the Find Equivalent Atoms tool toedit the atom correspondence and try again.

4. ChooseModules | DMol3 | Calculation from theMaterials Studio menu bar.5. Set the Task to TS Search on the Setup tab.6. If desired, click theMore... button to open the DMol3 Transition State Search dialog where you can

set additional options (such as Optimize reactants and products).7. Click the Run button.

Tip: For best results you should optimize the structures of the reactants and products beforegenerating the trajectory in step 3.

Verifying a transition stateAt the conclusion of a successful transition state calculation by either method, you will have a stationarypoint. It is more difficult to prove that the stationary point actually corresponds to a transition state. Todo this, you must perform a vibrational analysis. A true transition state will have one imaginaryvibrational frequency whose normal mode corresponds to the reaction coordinate; all other eigenvalueswill be real. A structure with two or more imaginary frequencies is not a true transition state. In suchcases, it will be possible to locate a lower energy barrier by following one of themodes.

Tip: You can request that a vibrational frequency calculation be performed automatically following asuccessful transition state optimization or transition state search. Simply select Frequency on theProperties tab.

Transition state searching via synchronous transit methodsSynchronous transit methods are used to find a transition state (TS) when reasonable structures for thereactants and products exist, but the location of the TS is unknown. You can perform this type ofcalculation by setting the Task to TS Search.Starting from reactants and products, the synchronous transit methods interpolate a reaction pathwayto find a transition state. The Linear Synchronous Transit (LST)method performs a single interpolationto a maximum energy. The Quadratic Synchronous Transit (QST)method alternates searches for anenergy maximum with constrained minimizations in order to refine the transition state to a high degree.The options available through DMol3 include:

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n LSTMaximum performs a single LST maximization, bracketing themaximum between the reactantsand product. This is the quickest but least accurate of the options. The TS structure determined bythis method generally requires further refinement.

n LST/Optimization performs an LST maximization, followed by an energy minimization in directionsconjugate to the reaction pathway. This yields a structure lower in energy and closer to the true TSthan a simple LST. Minimization steps continue until an energy minimum is reached or the number ofconjugate directions is exhausted.

n Halgren-Lipscomb is a kind of limited LST/Optimization, and is designed to reproduce the algorithmpopularized by Halgren and Lipscomb. After determining the LST maximum, this method performs aconjugate gradient minimization, but only in a single direction.

n Complete LST/QST begins by performing an LST/Optimization calculation. The TS approximationobtained in that way is used to perform a QSTmaximization. From that point, another conjugategradient minimization is performed. The cycle is repeated until a stationary point is located or thenumber of allowed QST steps is exhausted. This is considerably more accurate than the othermethods, yielding results close to those obtainable using eigenvector following methods.

Input to a synchronous transit calculationThere are few parameters for these sorts of calculations, and they are discussed on the DMol3 TransitionState Search - Setup topic.The synchronous transit calculations are always performed in Cartesian coordinates. There is no optionto override this.Unlike other methods, the synchronous transit calculations require a trajectory rather than a singlemodel. Follow this procedure to set up a calculation.To set up a synchronous transit calculation1. Begin by constructing two separate documents, one for the reactants and a second for the

products.2. Determine the correspondence between atoms in the two documents using the Find Equivalent

Atoms tool. The synchronous transit method performs a geometric interpolation between theatomic coordinates of the atoms in the reactants and the atoms in the products. In order toaccomplish this, it is necessary that the program understand which atom matches to which.

3. Generate a trajectory that converts reactants into products using the Reaction Preview tool. You cananimate this document to check that the reactants are converted correctly to products. If you aresatisfied with thematch, proceed with the calculation. If not, use the Find Equivalent Atoms tool toedit the atom correspondence and try again.

4. Using the document that was created by the Reaction Preview tool, select your options for the TSSearch calculation and submit the DMol3 calculation by pressing the Run button.

Note: Problems may arise when the reactant and product structures have high symmetry but thetransition state does not. In these cases, the interpolation proceduremay be unable to breaksymmetry. It is recommended in such cases that you manually break the symmetry of the structureby a small amount.

For example, consider the HNC to CNH rearrangement. If the reactant and product are both perfectlylinear, then interpolated geometries will always put the H colinear with C and N. Bending the HCNangle even by 0.1° solves this problem and allows the procedure to locate the correct transition state.

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Restarting a QST calculationOne further option is available on the TS Search dialog: QST/Optimization. This option allows you to usethe results of a DMol33 synchronous transit calculation as the starting point for a QST calculation. In thisway, you can further refine the results of any of the four different types of calculations mentionedabove.The result of any of these calculations is a trajectory document. Provided you have such a trajectory,simply use it as input to DMol3: open the document, select QST/Optimization on the DMol3 TransitionState Search dialog, and submit the job to DMol3. In principle, this proceduremay be repeatedindefinitely; in practice, little refinement will be generated after the first five cycles of a QST.

Transition state searching via eigenvector followingSearching for a transition state (TS) by eigenvector following (EF) is similar to performing a geometryminimization. Many of the options are the same, and the setup dialogs are similar. Whereas theminimization will automatically choose from among several algorithms for theminimization, the TSoptimization in DMol3 always uses a Newton-Raphson method. Like theminimization, the TSoptimization can proceed in Cartesian, internal, or redundant internal coordinates. DMol3 chooses themost efficient method to perform the calculation.Starting from a reasonable guess for the TS, DMol3 performs a Newton-Raphson search on the potentialenergy surface. This searches for an energy maximum along one normal mode and a minimum along allother nodes. This method requires the presence of a Hessian matrix in order to compute the normalmodes. Generate a Hessian by performing a frequency calculation on the starting geometry.

Calculation parametersPerform an EF calculation by setting the Task to TS Optimization on the Setup tab of the DMol3Calculation dialog. Themost important setup parameter is Quality.TheQuality control specifies how close to a minimum you want to get. As described in the DMol3 TSOptimization dialog topic, the quality setting controls the convergence thresholds for energy change,maximum force, and maximum geometry displacement between optimization cycles. The optimizationwill stop when at least two of these criteria are satisfied.

Use of the HessianIf you have computed a Hessian using Materials Studio, it will be imported automatically when you openthe job for analysis. To import a Hessian file from another calculation see the HESSIAN file format topic.Select the normal mode that the EF method will follow. This should be themode corresponding mostclosely to the reaction coordinate. Generally, this will be themode of the only imaginary frequency, orthe imaginary frequency largest in magnitude. To specify themode, use controls on the VibrationalAnalysis dialog to compute the vibrational frequencies.On the tabulated list of frequencies, select the frequency you wish to follow by clicking on the row. TheEF method will use the this modewhen you start the calculation.

Geometry optimizationAfter a molecular or crystal structure is built, it usually needs to be refined to bring it to a stablegeometry. The refinement process is known as optimization, and is an iterative procedure in which thecoordinates of the atoms are adjusted so that the energy of the structure is brought to a stationarypoint, i.e., one in which the forces on the atoms are zero.You can request an energy minimization, a search for a relativeminimum on the energy hypersurface.The geometry corresponding to this structure should have a close resemblance to an actual physical

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structure of the system at equilibrium. You can also perform an optimization to a transition state.Searching for a transition state is covered elsewhere. In this section, "geometry optimization" is taken tomean "geometry minimization".To perform a geometry optimization (minimization)1. ChooseModules | DMol3 | Calculation from themenu bar.2. Open the Setup tab.3. Set the Task to Geometry Optimization.4. If desired, set additional options by selecting theMore... button to bring up the DMol3 Geometry

Optimization dialog. Normally, the default options will yield adequate results.5. Click the Run button.

Tip: When high accuracy is required in geometry optimization, set theQuality to Fine on theGeometry Optimization dialog. In addition, it is recommended that you set both Integration accuracyand SCF tolerance to Fine on the Electronic tab.

Tip: Optimization using delocalized internals may fail if angles close to 180 degrees occur duringoptimization. In such cases, specify a value using the Opt_Bend_Lin keyword. This sets a threshold, indegrees, that limits the number of linear bends. The default value is 0.01, and can be increasedsignificantly to improve the robustness of the optimization procedure.

Note: The Hessian file resulting from a DMol3 geometry optimization run should not be used toobtain the vibrational spectrum.

Following a reaction pathThe LST and QST tools locate a maximum energy structure along the reaction path, but this maximummay not, in fact, be the transition state that you are looking for. You can use the TS confirmation tool toconfirm that the transition state found does indeed connect your presumed reactant and product.To perform a Transition State Confirmation1. First perform a TS Search using LST or QST. The trajectory computed by this method is used as input

to the TS Confirmation. Make sure this trajectory document is in focus when you set up the TSConfirmation.

2. ChooseModules | DMol3 | Calculation from theMaterials Studio menu bar.3. Open the Setup tab.4. Set the Task to TS Confirmation.5. If desired, set additional options by selecting theMore... button to bring up the DMol3 TS

Confirmation dialog. Normally, the default options will yield adequate results.6. Click the Run button.Users should be aware that TS Confirmation jobs can take a long time to complete. These jobs perform aseries of geometry optimizations along the reaction pathway, requiring quite a lot of computer time.

Tip: At the end of the calculation, you can select any geometry on the reaction pathway using thechart/trajectory tools and perform subsequent calculations. In this way you could, for example,perform further geometry optimization on an interesting structure.

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Elastic constantsIn DMol3, themechanisms responsible for optimizing the unit cells of periodic systems can also be usedto calculate themechanical properties (for example, the elastic constants) of thesematerials. This isachieved by obtaining the stress tensor of a given unit cell by applying finite displacement distortions.For each distortion, the energy is minimized using a standard geometry optimization procedure. Theelastic constant tensor is then calculated from the energies corresponding to each finite displacement.The analysis section for elastic constants in DMol3 also calculates common mechanical properties thatcan be derived from the elastic constants tensor.

Note: Elastic constants should only be calculated on periodic structures with optimized latticeconstants. Use Periodicity (Materials) and then Property Range Filter to assess and filter periodic datarecords.

Reaction kineticsReaction rate coefficients can be estimated from transition state theory. Canonical transition statetheory assumes that the energy distribution of the reacting species does not vary significantly from theBoltzmann distribution. This allows the rate coefficient to be calculated in terms of the canonicalpartition functions of the reactant(s) and transition state, the reaction threshold energy, and the heat ofreaction.To calculate a reaction rate coefficient1. Perform a TS Search using LST or QST.

The 3D Atomistic Collection document generated will be used as input for the Reaction Kinetics task.You must ensure that it is in focus when you set up Reaction Kinetics.

Tip: LST/QST search often produces only an approximate transition state which should beoptimized further. To make this step easier it is advisable to request frequency calculations at endof the successful transition state search (see DMol3 Properties for more details).

2. In order to calculate the correct rate coefficient, the Reaction Kinetics task needs to determine thetype of reaction - whether it is an isomerization reaction, an association/dissociation reaction, or anexchange reaction. Reaction Kinetics does this by attempting to assign motion groups to thereactive fragments, however, if desired, motion groups on the reactant(s) and product(s) can beexplicitly set using theMotion Groups dialog.

3. SelectModules | DMol3 | Calculation from theMaterials Studio menu bar to open the DMol3Calculation dialog.

4. On the Setup tab, choose Reaction Kinetics from the Task dropdown list.5. Click theMore... button to open the DMol3 Reaction Kinetics dialog and specify more advanced

options if required.Normally, the default options will yield adequate results.

6. If theOptimize transition state checkbox is checked you should ensure a Hessian matrix is present.

Tip: You can check whether a Hessian matrix is available using the Vibrational Analysis dialog, thisalso allows you to inspect which eigenvectors will be followed during the transition stateoptimization phase of the Reaction Kinetics run.

7. Click the Run button.

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When Reaction Kinetics calculation has successfully completed a new 3D Atomistic Collection documentcontaining optimized structures of the reactant(s), product(s), and transition state with their Hessiansand total energies will be generated.The Reaction kinetics analysis option in DMol3 can now be used to calculate and fit the reaction ratecoefficient.

Electron TransportThe DMol3 Electron Transport task allows you to calculate electron transport properties, such astransmission and current, using non-equilibrium Green's function theory. For a structure to be valid forthe transport task it must contain two electrodes.Electrodes and complete devices can be constructed using the Transport Device Builder tools.

Note: The DMol3 Electron Transport task cannot be run under certain circumstances, if:n On the Setup tab of the DMol3 Calculation dialog:n Use method for DFT-D correction checkbox is checkedn Functional is set to B3LYP or m-GGA optionn Spin unrestricted checkbox is checkedn Charge is set to any non-zero value

n On the Electronic tab of the DMol3 Calculation dialog:n Core treatment is not set to DFT Semi-core Pseudopots when there is an element with Z > 20n Use solvation model checkbox is checked

n On the Properties tab of the DMol3 Calculation dialog, any of the following are selected:n Density of statesn Electron densityn Electrostaticsn Frequencyn Fukui functionn Opticsn Orbitalsn Population analysis

ElectrodesElectrodes are represented by semi-periodic structures that are connected to a central region of thedevice. The electrode comprises two regions; a wire and a tip. The wire region is a repeat unit that will beused to define the semi-periodic part of the contact. The tip region defines a section of the electrodethat is part of the central device region. When the electrode is translated or rotated using the editingtools the operation will apply to the atoms in both regions.The setup of electron transport calculations requires a buffer region between the electrode and devicethat has exactly the same periodically continued structure as the electrode. Materials Studioautomatically determines theminimal necessary buffer size from the atomic radial cutoff and insertsthese atoms into the entire system. This automatic insertion means that there will bemore atoms in theelectrode than shown in the visual displays. Nevertheless, it is still recommended that you shouldconverge the size of their electrodes and add additional electrode atoms to the boundary region ifpossible.

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PropertiesUse the Properties tab on the DMol3 Calculation dialog to request that electronic or structuralproperties be calculated as part of the DMol3 run. You can view the results using the DMol3 Analysisdialog. Each time that you want to computemore properties, you must submit another DMol3calculation.The properties that can be requested through the Properties tab are:n Electron densitiesn Electrostaticsn Vibrational frequenciesn Fukui functionsn Molecular orbitalsn Atomic populationsn Band structuren Density of states (DOS)n OpticsTo include properties as part of your DMol3 calculation1. ChooseModules | DMol3 | Calculation from theMaterials Studio menu bar.2. Select the Properties tab.3. Check the checkbox next to the desired property, for example Electron density.4. In most cases, checking the checkbox will provide you with additional options. For example,

checking the Electron density checkbox presents you with the option of computing any or all of thetotal density, deformation density, and spin density. Check the appropriate checkboxes to computethe desired properties.

5. Repeat for all desired properties.6. Click the Run button.If you uncheck the checkbox next to one of themajor property headings, then all the associatedproperties will become inaccessible. For example, if you uncheck the Electron density checkbox, thennone of the three types of densities can be computed.

Setting up DMol3 calculationsThe topics in this section describe how to set up DMol3 calculations of various types, as well as the waysin which the job control facility can be used.There are a number of options that are understood by DMol3which are not currently accessible via theMaterials Studio interface. Such options can be utilized by manually editing the DMol3 input files.Information about how to do this is also presented in this section.A convenient way to select DMol3 options is to specify the overall quality of calculations by using theQuality option on the Setup tab of the DMol3 Calculation dialog. Testing confirms that the overallaccuracy of calculations, as measured by the total energy, depend on the choice ofQuality option asfollows:n Coarse - 1.0 × 10-4 Han Medium - 1.0 × 10-5 Han Fine - 1.0 × 10-6 Ha

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Tip: Use the Coarse quality setting for qualitative and approximate calculations. TheMedium and Finesettings are designed to produce accurate quantitative results.

For structure optimizations, it is often best to use a Fine numerical integration grid for both Mediumand Fine quality calculations.

Setting up electronic optionsThe electronic options control the details of the way that DMol3 solves the SCF equations.To set electronic options1. ChooseModules | DMol3 | Calculation from themenu bar to display the DMol3 Calculation dialog.2. Select the Electronic tab. Most of the important parameters can be set using the controls on this

tab.3. Click theMore... button to display the DMol3 Electronic Options dialog. This dialog allows finer

control over some of the electronic parameters and offers additional settings.

Integration accuracyThe integration accuracy controls the precision with which Hamiltonian matrix elements are computed,as described in the Numerical integration topic.Generally, you should not need to change this parameter from the default. You could use a Coarse gridfor performing fast calculations of limited accuracy. A Fine integration grid is recommended when youwish to converge geometry optimizations to high accuracy.To set the integration accuracy, choose Coarse, Medium, or Fine from the Integration accuracydropdown list.

SCF toleranceThe SCF tolerance control specifies the accuracy to which the SCF equations are converged. Normally,the default accuracy ofMedium is sufficient. When you need to converge a geometry optimization tohigh accuracy, then the Fine setting is recommended.

k-pointsThe k-point set control specifies the number of wave vectors used to describe the band structure ofperiodic systems. When studying large nonsymmetrical systems, it is often sufficient to use the so-calledΓ-point. In other cases, the default setting should be adequate.To set the number of k-points choose Gamma, Coarse, Medium, or Fine from the k-point set dropdownlist. For more details on controlling the number of k-points, see Setting up k-points.

Core treatmentThe Core treatment parameter controls how electrons in the lowest lying atomic orbitals are treated.The default setting, All Electron, treats these in the samemanner as valence electrons, and isappropriate for atoms up to about atomic number 36 (Kr).With heavier elements, relativistic effects become important in the core electrons. Onemethod ofincorporating these effects is to use the All Electron Relativistic option. As the name implies, the coreelectrons are still included in the calculation, but scalar relativistic effects are included (Koelling andHarmon, 1977; Douglas and Kroll, 1974). This yields a more accurate calculation, but increases thecomputational cost.An alternative to all-electron calculations is to use DFT Semi-core Pseudopots (DSPP; Delley, 2002) orEffective Core Potentials (ECP; Dolg et al., 1987; Bergner et al., 1993). These replace the effects of core

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electrons with a simple potential. Because the core electrons are dropped, the calculation is lesscomputationally expensive, but because these core potentials include some degree of relativistic effects,they can be very useful approximations for heavier elements.You cannot restrict the use of ECPs or DSPPs to specific elements. Whenever you use either option,DMol3 examines a data file that contains the potentials. If DSPP or ECP data are found for an element,then the core electrons for that element are replaced; if the data are not found for an element, then allits electrons are retained. Currently, DSPPs and ECPs are provided beginning with element number 21,Sc. For example, in a system containing H, O, Al, Cu, and Au, if you opt to use ECPs or DSPPs, only thecore electrons for Cu and Au will be replaced; H, O, and Al will be treated as in the all-electron case.When it is necessary to use one of these approximations, Accelrys recommends that you use DSPPsrather than ECPs. The former have been developed specifically for DMol3 calculations, whereas the latterare Hartree-Fock potentials.To set the type of core treatment, choose All Electron, Effective Core Potential, All Electron Relativistic, orDFT Semi-core Pseudopots from the Core treatment dropdown list.

Real space cutoffIn principle, when performing numerical integrations, the charge density and functionals must beintegrated over all space. Because the density drops off quickly as the distance from an atomic nucleusincreases, in practice, it is possible to limit the range of the integrations. This serves to reducecomputation timewith little impact on the accuracy of the results. This cutoff is actually applied to thegeneration of the numerical basis sets.A global real space cutoff is selected for every system as a maximum value of the cutoffs specific forevery element of that system. Earlier versions of DMol3 applied the same default value for real spacecutoffs to all systems.

Real space cutoffs for elements were optimized by considering total energies of atoms at various qualitylevels of DMol3 calculations. For every quality level, the chosen Cutoff_Element values lead to theatomic energies, which differ from the reference energy within the accuracy thresholds defined for thequality levels:n Coarse - 1.0 eV atom-1

n Medium - 0.3 eV atom-1

n Fine - 0.1 eV atom-1

The reference energy is assumed to be that calculated using the Fine quality setting and with a real spacecutoff of 6.5 Å.The tables below specify Cutoff_Element values, in Å, for each quality level. Typically the cutoff valuesincrease within a column and decrease within the row of the Periodic Table. The current implementationassumes the values for the lanthanides are the same as for La and those for the actinides are the sameas for Ac.

Tasks in DMol3  | Page 15

Default Cutoff_Element values (Å) for Coarse quality calculations

H3.0

He3.0

Li3.6

Be3.3

B3.1

C3.0

N3.0

O3.0

F3.0

Ne3.0

Na3.8

Mg3.7

Al3.5

Si3.5

P3.4

S3.3

Cl3.3

Ar3.2

K4.2

Ca4.2

Sc4.0

Ti3.9

V3.7

Cr3.6

Mn3.5

Fe3.5

Co3.4

Ni3.4

Cu3.4

Zn3.4

Ga3.5

Ge3.5

As3.4

Se3.3

Br3.3

Kr3.3

Rb4.3

Sr4.4

Y4.2

Zr4.0

Nb3.8

Mo3.7

Tc3.6

Ru3.6

Rh3.4

Pd3.4

Ag3.4

Cd3.5

In3.6

Sn3.6

Sb3.6

Te3.6

I3.5

Xe3.4

Cs4.5

Ba4.6

La4.3

Hf4.0

Ta3.8

W3.7

Re3.7

Os3.6

Ir3.4

Pt3.4

Au3.4

Hg3.5

Tl3.7

Pb3.7

Bi3.7

Po3.7

At3.6

Rn3.6

Fr4.6

Ra4.7

Ac4.5

Default Cutoff_Element values (Å) for Medium quality calculations

H3.0

He3.0

Li4.4

Be3.9

B3.4

C3.3

N3.2

O3.2

F3.2

Ne3.2

Na4.5

Mg4.3

Al4.2

Si4.0

P3.7

S3.6

Cl3.4

Ar3.3

K4.9

Ca4.8

Sc4.7

Ti4.5

V4.4

Cr4.4

Mn4.4

Fe4.3

Co4.1

Ni4.0

Cu4.0

Zn3.9

Ga4.2

Ge4.1

As3.9

Se3.8

Br3.7

Kr3.5

Rb5.0

Sr5.0

Y4.8

Zr4.6

Nb4.5

Mo4.4

Tc4.4

Ru4.3

Rh4.2

Pd4.0

Ag4.0

Cd4.0

In4.4

Sn4.3

Sb4.2

Te4.1

I3.9

Xe3.8

Cs5.1

Ba5.2

La5.0

Hf4.7

Ta4.6

W4.5

Re4.4

Os4.3

Ir4.2

Pt4.0

Au4.0

Hg4.1

Tl4.5

Pb4.4

Bi4.3

Po4.2

At4.1

Rn4.0

Fr5.2

Ra5.3

Ac5.1

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Default Cutoff_Element values (Å) for Fine quality calculations

H3.1

He3.0

Li5.1

Be4.4

B4.1

C3.7

N3.4

O3.3

F3.2

Ne3.2

Na5.2

Mg4.9

Al4.8

Si4.6

P4.2

S4.0

Cl3.8

Ar3.5

K5.6

Ca5.5

Sc5.4

Ti5.2

V5.0

Cr4.8

Mn4.7

Fe4.6

Co4.5

Ni4.5

Cu4.4

Zn4.4

Ga4.8

Ge4.7

As4.4

Se4.2

Br4.0

Kr3.8

Rb5.8

Sr5.8

Y5.6

Zr5.3

Nb5.0

Mo4.9

Tc4.8

Ru4.7

Rh4.6

Pd4.5

Ag4.5

Cd4.5

In5.0

Sn4.9

Sb4.7

Te4.6

I4.4

Xe4.2

Cs6.1

Ba6.1

La5.8

Hf5.3

Ta5.1

W4.9

Re4.8

Os4.7

Ir4.6

Pt4.5

Au4.5

Hg4.6

Tl5.1

Pb5.0

Bi4.8

Po4.7

At4.6

Rn4.4

Fr6.2

Ra6.2

Ac5.9

Increasing the Fine Cutoff_Element values rarely has an impact on the results. Reducing this value willsignificantly decrease the computation time for periodic systems, but has little effect on molecularcalculations, except for extended polymer-typemolecules. Generally, the absolute energy computedwith a reduced cutoff will change a bit, while the relative energy (for example reactants-products)changes very little with cutoff. The smallest allowed value is 2.5 Å.These are the general rules, and there are exceptions, depending on the system choice and computationtask. For example, anions may require larger cutoffs, while for the bulk solids, smaller cutoffs may beacceptable. You can specify a value for the cutoff in theGlobal orbital cutoff field on the Orbital Cutofftab of the DMol3 Electronic Options dialog.

Note: Using too small or too large a cutoff may result in failure to converge during SCF or geometryoptimization calculations. The smallest recommended values for the cutoff are those in the table ofCoarse quality values. The largest value should not exceed 20 Å.

Harris approximationNormally, the evaluation of the energy requires the solution of the self-consistent DFT equations. Thiscan take about a dozen iterations for an organic molecule and can take well over 100 iterations in thecase ofmetallic systems with low lying virtual orbitals. The Harris approximation is an alternative to theiterative solution of the SCF DFT equations. In this procedure, the density from the first SCF iteration isused to compute the energy and forces on the atoms. This density, composed of the superimposedcharge density from isolated atoms, is a remarkably good approximation when you need reasonablegeometries. Although themethod yields reasonable structures, the relative energies are not reliable(Harris, 1985). The Harris method is limited to closed-shell systems and LDA functionals.To activate this option, check theHarris approximation checkbox.

Solvation schemeDMol3 allows you to simulate a solvent environment using the COSMO (conductor-like screening model)scheme. COSMO allows you to include the effects of a solvent in a DMol3 calculation. This is acontinuum solvation model where the solutemolecule forms a cavity within the dielectric continuum of

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permittivity that represents the solvent. The charge distribution of the solute polarizes the dielectricmedium. The response of the dielectric medium is described by the generation of screening (orpolarization) charges on the cavity surface.It is frequently important to include solvent effects in a DFT calculation, sincemany properties arestrongly influenced by the solvent medium. This includes heats of formation, heats of reaction, dipolemoments, and other electronic properties.To simulate solvation in a DMol3 calculation, check theUse COSMO checkbox on the Solvent tab of theDMol3 Electronic Options dialog and select a solvent from the Solvent dropdown list. If you wish, youcan specify the dielectric constant of the solvent in theDielectric constant field.For all calculations using the COSMO solvation model a COSMO Sigma Profile plot, named <seedname>Sigma Profile.xcd, is returned.

Performance tipsDMol3 uses a localized numeric basis set and very efficient density fitting technique, making the codeparticularly suitable for performing accurate DFT calculations for extended molecular, solid, and surfacesystems. Better computational performance can be achieved using the following guidelines:n If the system has low symmetry, for example C

sor C

2, it is better to perform calculations without

symmetry (C1).

n Use a small confinement on the atomic basis set by choosing Medium, or even Coarse, quality.n In the case of structure optimization, it may be better to maintain a Fine numerical integration grid,

useMedium SCF tolerance, and use Coarse orbital cutoff quality, initially. After the structure isconverged, only a few cycles may be needed to converge the structure with a better orbital cutoffquality.

n Real space cutoff can be set as low as 2.5 Å for Coarse quality calculations, typically without asignificant loss in total or binding energy. The performance gain is particularly significant for solidcalculations with k-points. Using too small a cutoff valuemay cause a failure to converge.

n Slow SCF convergencemay become a bottleneck for systems that have degenerate levels close to theFermi level. Typically, these are systems including metal atoms or systems in which dissociationprocesses are being studied. Using the smearing option with a small value for the smearing factor(0.001 Hartree)may be very beneficial here.

n A potential way to improve convergence for coarse k-point sets without introducing thermalsmearing is to switch off the tetrahedra integration algorithm with the defeat_tetrahedra keyword.

n The performance of geometry optimization calculations may suffer if the system has near-linearbends. Eliminating these bends will typically shorten optimization cycles.

n You should use sufficiently accurate integration grid and SCF tolerance to calculate accurate gradientsfor use in optimizations and TS searches.

Setting up k-pointsThe k-point set used in a calculation defines the accuracy of the Brillouin zone sampling. TheMonkhorst-Pack k-points used in DMol3 are characterized by divisions along three reciprocal space axes and by anoptional origin shift. However, it is not recommended that the origin shift is used. Thus, the k-pointssetup procedure simply involves selecting three integer divisions.The quality of the k-point set can be quantified in a number of ways; DMol3 uses the distance betweenthe points in reciprocal space as a numerical measure. The simplest way to define the set is thefollowing:

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Simple method for setting the k-points1. ChooseModules | DMol3 | Calculation from theMaterials Studio menu bar.2. Select the Electronic tab.3. Choose the desired k-point set from dropdown list.This method creates either a Monkhorst-Pack set of the selected quality (Coarse, Medium, or Fine) orinstructs DMol3 to use only one Γ-point (the origin in reciprocal space).

Note: Explicit selection of Γ-point sampling is not recommended. DMol3will automatically use thisoption if the cell is very large in real space, so that the Brillouin zone is small and no sampling isrequired.

In all other cases, the Γ-point is the least representative of all Brillouin zone points and using it as theonly sampling point can distort the results severely.Puska (2000) showed, for example, that there is a 1-2 eV error in the vacancy formation energy insilicon when the Γ-point is used for cells containing up to 128 atoms.

Finer control over k-point sets can be exercised by using the k-points tab on the DMol3 ElectronicOptions dialog. This tab allows you to enter the actualMonkhorst-Pack mesh parameters by selectingthe Custom grid parameters option.Materials Studio automatically optimizes themesh parameters according to the point group symmetryof the 3D model. For example, in a cubic crystal the even mesh parameters, N, will generate the set withas many k-points as the one with the odd mesh parameters, N-1. Since the former set provides bettersampling, it will be selected automatically when either Quality or k-point separation is used to define thek-point set.Custom grid parameters is the only option which allows you to specify a suboptimal mesh with odddivisions.The quality of the k-point sampling is particularly important for metallic systems, where rapid changes inelectronic structuremay occur along the energy band that crosses the Fermi level. Insulators orsemiconductors, even when they are treated using variable occupation numbers for electronic states,are less sensitive to the quality of k-point sampling.The default settings used by DMol3 are designed to give accurate sampling for metallic systems. Thismeans that you can get good results for insulators and semiconductors with a slightly less fine k-pointmesh than the default.

Note: The total energy is not guaranteed to decrease as more k-points are added. Therefore, whencarrying out convergence testing, you should strive to find a set such that further improvements to itdo not alter the total energy beyond the tolerance level you require. However, the energy is not likelyto converge smoothly and oscillations are to be expected.

Setting up a geometry optimizationWhen a molecular or crystal structure is built, it usually needs to be refined to bring it to a stablegeometry. The refinement process is known as optimization, and is an iterative procedure in which thecoordinates of the atoms are adjusted so that the energy of the structure is brought to a stationarypoint, i.e., one in which the forces on the atoms are zero.When you set the Task to Geometry Optimization on the Setup tab, you actually request an energyminimization, a search for a relativeminimum on the energy hypersurface. The geometry correspondingto this structure should have a close resemblance to an actual physical structure.

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You can also perform an optimization to a transition state by setting the Task to TS Optimization. SeeTransition state searching for additional information.By performing geometry optimization (minimizations) you can:n Predict the structure ofmolecules and crystalsn Determine the optimum binding site of a molecule on a surfacen Predict the lowest energy conformation or isomerto list just a few examples.

Algorithms for the optimizationDMol3 can use several different algorithms for performing the optimization. These include steepestdescent, conjugate gradient, and Newton-Raphson methods. These are not under user control. DMol3will choose the appropriatemethod automatically.Optimization can be performed using Cartesian coordinates, internal coordinates, or in redundantinternal coordinates (using linear combinations of internals). These are also not under user control.Optimizations will use redundant internals whenever possible, since these aremost efficient. If there is aproblem with the internals, then the program will print a message and switch to Cartesian coordinates.Both the Cartesian and redundant internal optimization methods are available for both molecular andcrystalline systems.

Note: DMol3 supports atom positions fixed in Cartesian space, and partial constraints on the x, y, or zcomponents of Cartesian atom positions, but ignores constraints on fractional positions and latticeparameters. In addition, fixed interatomic distances, angles, and torsions are supported fornonperiodic structures only.

Parameters for the optimizationThe parameters that control the accuracy of an energy calculation are still relevant for a geometryoptimization, since each step of the optimization requires an energy calculation. Other importantparameters include:n Quality - controls how close to a minimum you want to get. The Quality setting controls the

convergence thresholds for energy change, maximum force, and maximum geometry displacementbetween optimization cycles. The optimization will stop when at least two of these criteria aresatisfied. If the calculated initial gradients are below the threshold, the optimization will successfullystop without making a single step and without comparing displacements and energies.

n Use starting Hessian - whenever you have generated a Hessian (a matrix of second derivatives) youcan use this to speed up the geometry optimization. Simply check the box on the DMol3 GeometryOptimization dialog. This box is accessible only if there is a valid Hessian matrix already associatedwith the document. For information on generating a Hessian, see the vibrational calculation sectionin the Properties topic. To import a Hessian file from a calculation see the topic on the Hessian file.

Setting up a molecular dynamics calculationADMol3molecular dynamics calculation allows you to simulate how the atoms in a molecule will moveas a function of time under the influence of forces arising from the effects of temperature on the system.In most cases, a molecular dynamics calculation should be preceded by geometry optimization. It mayalso be desirable to perform minimizations on several of the conformations that are generated duringthe dynamics run.

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Choosing an ensembleYou can control the temperature of a DMol3molecular dynamics calculation in order to simulate asystem that exchanges heat with the environment. Under these conditions, the total energy of thesystem is no longer conserved and extended forms ofmolecular dynamics are required.You can simulate two different thermodynamics ensembles with a constant number of particles inDMol3.

Ensemble Conditions Description

NVE Constantvolume/constantenergy dynamics

The Newtonian equations ofmotion, which conserve the total energy,are used. The temperature is allowed to vary. Energy is the constant ofmotion - it can fluctuate slightly, but there should be no systematicdrift.

NVT Constantvolume/constanttemperaturedynamics

The dynamics aremodified to allow the system to exchange heat withthe environment at a controlled temperature. A range of thermostatsfor scaling or controlling the temperature are available:n Gaussiann Simple Nosé-Hoovern Nosé-Hoover chainn Massive Nosé-Hoovern Generalized Gaussian momentsn Massive generalized Gaussian moments

Defining the time stepA key parameter in the integration algorithms is the integration time step. A common rule-of-thumbused to set the time step is that the highest frequency vibration should be sampled between 15 and 20times in one cycle. For example, if the highest frequency is 20 THz, a typical optical mode frequency, atime step of 2.5-3.3 fs is appropriate (period = 1/frequency = 50 fs). In water, the stretching frequenciesare around 110 THz, indicating that a time step of 0.45-0.6 fs is required. You will probably be able to usea time step that samples themotion as few as 10 times in a cycle. However, you must check your choiceof time step by monitoring energy conservation in the NVE ensemble. A thermostat in the NVT ensemblecan completely mask inadequate integration.

Defining the thermostat controlFor NVT ensembles, it is important to define the thermostat control. For Nosé-Hoover thermostats, thisis done using the Nosé Q ratio value. The generalized Gaussian moment thermostats use a relaxationtime, τ, which defines a time scale over which the temperature control is implemented. For a stablemolecular dynamics run, it is important to chose a relaxation time that is large enough, for example, atleast between 10 and 100 times the size of the integration time step.

Constraints during dynamicsDMol3 dynamics respects atoms that have been fixed in Cartesian space, i.e., the x, y, and z coordinatesof any atom that is fixed in all three planes using the controls on the Atom tab of the Edit Constraintsdialog will remain constant during a calculation. Fixed atoms still contribute to the energy expressionthat is used to calculate the forces on atoms, so fixed atoms influence themotion of themovable atoms.DMol3 also allows you to define constraints in terms of the geometric relationship between atoms, i.e.,by fixing distances, angles, and/or torsion angles using the controls on theMeasurement tab of the EditConstraints dialog.

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Setting up a transition state calculationWhen a molecular or crystal structure is built, it usually needs to be refined to bring it to a stablegeometry. The refinement process is known as optimization and is an iterative procedure in which thecoordinates of the atoms are adjusted so that the energy of the structure is brought to a stationarypoint, i.e., one in which the forces on the atoms are zero. A transition state is a stationary point that isan energy maximum in one direction (the direction of the reaction coordinate) and an energy minimumin all other directions.During the course of chemical reaction, the total energy naturally changes. Starting from the reactants,the energy increases to a maximum and then decreases to the energy of the products. Themaximumenergy along the reaction pathway is known as the activation energy; the structure corresponding tothis energy is called the transition state.You can perform an optimization to a transition state by setting the Task to TS Optimization or to TSSearch. By performing geometry optimization (minimizations) you can predict barriers to chemicalreactions and determine reaction pathways.DMol3 offers two different methods for locating a transition state.n Transition state optimization: Starting from a reasonable guess for the transition state, DMol3

performs a Newton-Raphson search on the potential energy surface. This uses techniques similar to asearch for an energy minimum but searches instead for an energy maximum along one normal mode.Because this method follows one of the Hessian eigenvectors to an energy maximum, themethod isoften referred to as "eigenvector following" (EF). See the section on Transition state searching viaeigenvector following for additional information.

n Synchronous transit methods: Starting from reactants and products, the synchronous transitmethods interpolate a reaction pathway to find a transition state. Thesemethods alternate searchingfor an energy maximum with constrained searches for a minimum in order to refine the transitionstate. See the section on Transition state searching via synchronous transit methods for additionalinformation.

Which method to use?The synchronous transit methods are best employed when you know the product and reactant but donot have good guess for the transition state. The EF methods are best employed when have areasonably good guess for the transition state, say from chemical intuition or another calculation. A"good guess" means one in which the atomic forces are less than about 0.02 Hartree/Å.The EF will generally yield a more accurate result, meaning one with smaller atomic forces. However, theEF is also considerably more expensive since it requires you generate a Hessian matrix before you canstart the calculation.

Verifying a transition stateAt the conclusion of a successful transition state calculation by either method, you will have a stationarypoint. It is more difficult to prove that the stationary point actually corresponds to a transition state. Todo this, you must perform a vibrational analysis. A true transition state will have one imaginaryeigenvalue whose vibrational mode corresponds to the reaction coordinate; all other eigenvalues will bereal. A structure with two or more imaginary frequencies is not a true transition state: in such cases, itwill be possible to locate a lower energy barrier by following one of themodes.

Tip: You can request that a vibrational frequency calculation be performed automatically following asuccessful transition state optimization or transition state search. Simply select Frequency on theProperties tab.

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Setting up a TS confirmation calculationThe TS Confirmation tool verifies that a TS calculated by an LST or QST search connects the reactant andproduct as expected. See Following a reaction path for more details on themechanics of this method.Materials Studio automatically determines the reactant, TS and product from the given LST or QSTtrajectory document.Select and display the trajectory file. On the Setup tab of the DMol3 Calculation dialog, change the Taskto TS Confirmation. Click theMore... button to display the DMol3 TS Confirmation dialog.Use the controls on this dialog to specify the convergence criteria for each individual geometryoptimization (microiteration), and to specify the number of frames to use in the TS confirmationtrajectory.

Note: That this is the upper limit for the number of frames. Structures that are too similar will bedropped during the calculation.

The output of a TS confirmation calculation is another trajectory document. This one follows theIntrinsic Reaction Path (IRP) as discussed in Reaction pathways. Each successive refinement to thepathway is displayed as a graph in Materials Studio. Use the chart selection tools to choose any point onthe graphs and display the corresponding geometry.In most cases, no minima will be found on the IRP other than your reactant and product. If so, the TSconfirmation calculation verifies that the TS does connect your presumed reactant and product.On the other hand, any other minima located by the TS confirmation are the structures that are actuallyconnected by the TS. These are identified with an asterisk (*). You should perform a geometryoptimization to refine the geometry of theseminima. Select the structures as described in the topicDisplaying trajectory and chart data.You can generate a detailed map of the entire reaction by repeating TS Search and TS Confirmation forall minima on the IRP.

Setting up a work function calculationThe work function is theminimum energy (usually measured in electron Volts) required to remove anelectron from a solid to a point immediately outside the solid surface (or the energy needed to move anelectron from the Fermi energy level into a vacuum). This energy depends on the orientation of thecrystal, different crystallographic surfaces have different work function values. The typical range ofvalues of work function for all crystalline elements is from 2 to 6 eV, and the orientational dependence ofthe work function is of the order of 1 eV.A practical way of evaluating work function is to compare the values of the Fermi energy and that of theelectrostatic potential in a vacuum away from the surface. DMol3 calculations for crystal surfaces arecarried out on slabs with a region of vacuum. Effectively, an infinite array of 2D-periodic slabs ofmaterialis separated by wide vacuum spacings. DMol3 produces the Fermi energy for such systems, and thespatial distribution of the electrostatic potential. Materials Studio averages the electrostatic potential inthe planes parallel to the surface. This approach allows the value of electrostatic potential in vacuum,and hence the work function, to be determined.The work function can have a large dependence on the crystal structure and surface orientation. It isrecommended that the structure is carefully prepared before calculation of the work function, asdescribed in the steps below. The recommended sequence of steps includes the geometry optimizationof the bulk structure, preparation of the surface followed optionally by optimization of atomiccoordinates in the surface and bulk layers. It is possible to perform work function calculations withoutthis optimization, so that the effects of surface relaxation on the work function can be investigated. It is

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reasonable to keep the structure of themiddle of the slab as close to the perfect bulk structure aspossible, for example by imposing fixed atom constraints on some inner atoms of the slab.It is important to have a fair representation of the bulk material, by including at least 8-10 Å ofmaterialin the slab calculation. It is equally important to provide enough vacuum between layers ofmaterials sothat the electrostatic interactions between two sides of a slab are negligible and electrostatic potentialreaches its asymptotic value; there should be at least 30 Å of vacuum in the cell.To set up a work function calculation1. Either import a structure of the bulk material from a pre-existing file or construct a new structure

using the sketching and crystal building tools in theMaterials Visualizer.2. Geometry optimize the bulk structure using DMol3.3. Cleave the required crystallographic surface using the Cleave Surface dialog so that the thickness

provides a meaningful representation of the bulk.4. Build a slab using the Build Vacuum Slab Crystal dialog, you should ensure that the distance

between the surface and the end of the vacuum is great enough that there can be no potentialinteractions between the surface and the next layer.

5. ChooseModules | DMol3 | Calculation from themenu bar.6. Select the Setup tab.7. Choose the Geometry Optimization task.8. Select a Functional from the dropdown list (see the theory section for more information on

functionals).9. On the Properties tab select and check the Electrostatics checkbox and ensure that the Electrostatic

potential checkbox is checked.10. Ensure that theWork function checkbox is checked.11. Fix Cartesian atomic positions of some atoms in themiddle of the slab using the Edit Constraints

dialog, accessible from theModifymenu.12. Click the Run button.13. Follow the steps in the Displaying the averaged potential chart for work function calculations topic.The result of this procedure is a chart of the electrostatic potential as a function of position along thesurface normal, with Fermi energy and the vacuum energy level marked as two horizontal lines. Thework function value is reported in the chart caption.

Setting up an elastic constants calculationThe calculation of elastic constants enables you to predict some of the following properties: n mechanical hardness and strengths for crystals and polycrystallinematerialsn shear strengthn Poisson ratio, which determines the change in the crystal's cross-sectional area perpendicular to an

applied strain.

Parameters for the optimizationMost of the parameters involved in setting up geometry optimizations are also necessary for obtainingelastic constants. The additionalDisplacement step setting governs the absolute size of each finitedisplacement used in the distortions.

Setting up a reaction kinetics calculationThe reaction kinetics task enables you to predict the reaction rate coefficient of a chemical reaction. Thealgorithm is based on transition state theory and involves evaluation of the partition functions of

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reactant(s), product(s), and transition state. Calculation of a partition function involves obtaining thevibration spectra, this in turn is calculated from the Hessian matrix.The reaction rate calculation process has threemain steps:1. Transition state search2. Calculation of the Hessians for all the reaction species3. Calculation of the partition functions and reaction rates for forward and reverse reactions

Transition state searchTransition state search in DMol3 can be done using LST or QST formalism. To optimize the transitionstate further (using the eigenvector following method) it is necessary to request the calculation offrequencies following a successful transition state search - check the Frequency checkbox on theProperties tab of the DMol3 Calculation dialog.The result of the transition state search is a 3D Atomistic Collection Document containing reactant,product, and transition state structures.

Hessian calculationTo calculate the Hessians for all the reaction species you should use the Reaction kinetics task.Depending on the type of reaction (isomerization, association, dissociation, or exchange) the originalreactant and product will be split into two structures if necessary and each structure will automaticallybe assigned a motion group.

Tip: Automatic determination of reaction species is disabled if you have defined motion group(s) forreactant and/or product - refer to theMotion Groups dialog topic for more information. If you defineyour own motion groups they must cover all the atoms in the reaction.

For reactions which are split into multiple structures the Hessian calculations will be carried out for eachstructure individually.

Reaction rate calculationTransition states can also be optimized via an eigenvector following procedure if the original transitionstate search included frequency calculations. For such an optimization the eigenvector with the largestimaginary frequency is chosen. If you want to select a different eigenvector to follow or inspect thespectrum you can use the Vibrational Analysis tool.

Note: The reaction rate coefficient can be calculated only if the transition state has exactly oneimaginary frequency with its eigenvector along the reaction path.

The 3D Atomistic Collection Document generated will contain all the necessary information to performthe reaction rate calculation itself.

Setting up an electron transport calculationThe electron transport task allows calculation of electron transport properties. The task requires thetarget structure to contain at least two electrodes.

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To set up an electron transport calculation1. ChooseModules | DMol3 | Calculation from themenu bar to display the DMol3 Calculation dialog.2. Select the Setup tab.3. Select Electron Transport from the Task dropdown list.4. Specify theQuality for the calculation.5. Click theMore... button to open the DMol3 Transport dialog.6. Choose whether to Calculate transmission function or Calculate current/voltage characteristics.7. Select the Electrodes tab and review the defined electrodes.8. Select the Electrostatics tab and specify the Poisson solver settings.9. Close the DMol3 Transport dialog.10. Choose the Electronic tab of the DMol3 Calculation dialog.11. Click theMore... button to open the DMol3 Electronic Options dialog and adjust the settings as

appropriate.12. Click the Run button.

Note: The DMol3 Electron Transport task cannot be run under certain circumstances, if:n On the Setup tab of the DMol3 Calculation dialog:n Use method for DFT-D correction checkbox is checkedn Functional is set to B3LYP or m-GGA optionn Spin unrestricted checkbox is checkedn Charge is set to any non-zero value

n On the Electronic tab of the DMol3 Calculation dialog:n Core treatment is not set to DFT Semi-core Pseudopots when there is an element with Z > 20n Use solvation model checkbox is checked

n On the Properties tab of the DMol3 Calculation dialog, any of the following are selected:n Density of statesn Electron densityn Electrostaticsn Frequencyn Fukui functionn Opticsn Orbitalsn Population analysis

Requesting electronic and structural propertiesIt is possible to request electronic or structural properties through the Properties tab of the DMol3Calculation dialog. These properties are computed as part of a calculation and viewed using the DMol3Analysis dialog. Each time that you want to computemore properties, you must submit another DMol3calculation.The properties that can be accessed through the Properties tab are:

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n Electron densitiesn Electrostaticsn Vibrational frequenciesn Raman intensitiesn Fukui functionsn Molecular orbitalsn Atomic populationsn Band structuren Density of states (DOS)n Fermi surfacesn Sigma profilen OpticsAll properties are computed at the end of a calculation using the converged charge density at the finalgeometry.

Setting up electron densitiesWhen you check the Electron density checkbox, you are presented with the option of creating 3D plotsof three types of densities:n Total density - the self-consistent charge density computed via Eq. DFT-4.n Deformation density - the total density with the density of the isolated atoms subtracted. Positive

regions indicate areas where bonds have formed.n Spin density - the difference between the charge density for alpha-spin and beta-spin electrons. Spin

density computations are available only for spin-unrestricted calculations.All the densities will be rendered on a regular rectangular grid with 0.2 Å spacing. In themolecular case,the plots extend 2.0 Å beyond themolecule; in the periodic case, the plots fill the entire unit cell.Computation of electron densities is possible for molecules and for periodics.

Tip: The default resolution of the grid is 0.2 Å. You can also modify this by editing the input files andadding the keyword Grid.

Setting up electrostaticsWhen you check the Electrostatics checkbox, you are presented with the option of displaying threetypes of electrostatic properties:n Electrostatic potential - produces a 3D rendering of the electrostatic (Coulomb) potential. This is

rendered on a regular rectangular grid with 0.2 Å spacing. In themolecular case, the plots extend2.0 Å beyond themolecule; in the periodic case, the plots fill the entire unit cell. Computation ofelectrostatic potential is possible for molecules and for periodics using the Γ-point andmultiple k-points.

n Electrostatic moments - produces a list ofmultipole moments from dipole through hexadecapole.This option is available only for molecules. Thesemoments appear in the output file; open the.outmol file in Materials Studio to view the results.

n Nuclear electric field gradients - computes fields that are an important component of the nuclearmagnetic shift. The nuclear electric field gradients appear in the output file; open the .outmol file inMaterials Studio to view the results.

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Tip: The default resolution of the grid is 0.2 Å. You can also modify this by editing the input files andadding the keyword Grid.

Note: If Electrostatics are requested for a slab, DMol3 analysis can be used to calculate the workfunction.

Setting up vibrational frequenciesWhen you check the Frequency checkbox, DMol3will compute a Hessian and vibrational spectrum. Youcan visualize the vibrational spectrum and the results of the calculation by using the Vibrational Analysisdialog. The frequencies and corresponding intensities are also given in the .outmol file. Frequencies,including intensities, can be computed for any molecular or periodic system.

Note: For intensity calculations symmetry should not be used, ensure that theUse Symmetrycheckbox on the Setup tab is unchecked. If symmetry is used only frequencies will be calculated andthe results will not include any intensities.

DMol3 computes the Hessian by finite differences of analytic first derivatives. This means that each atomin the system must be displaced in each Cartesian direction (including positive and negative directions).DMol3 uses point group symmetry to reduce the total number of displacements whenever possible.A good approximation to the Hessian can sometimes be obtained by limiting the number of atoms thatare displaced. This is useful when you need a Hessian to search for a transition state, but only a fewatoms are involved in the reaction coordinate. An especially important example of this is a moleculereacting on a surface, where the atoms in the second and third layers are not involved in the reaction.By default, all atoms are included in a Hessian calculation, To create a list of atoms that you want tomove, select the atoms and use the Edit Sets dialog to create a set named HessianAtoms. Only whenthis set is present in the system will the Calculate partial Hessian checkbox become enabled. Checkingthis checkbox limits the Hessian calculation to only those atoms in the HessianAtoms set.

Setting up Raman intensitiesRaman intensities are necessary for the prediction of Raman spectra during analysis.To generate Raman intensities1. ChooseModules | DMol3 | Calculation from theMaterials Studio menu bar.2. Select the Properties tab.3. Check the Frequency option on the properties list.4. Check the Calculate Raman intensities checkbox.

Note: For Raman intensity calculations symmetry will not be used, even if theUse Symmetrycheckbox on the Setup tab is checked. This can cause convergence problems with certain some highlysymmetric systems. If this happens, enabling thermal smearing can be used to accelerate theconvergence.

Setting up Fukui functionsFukui functions provide information on chemical reactivity. When you check the Fukui functioncheckbox, you are presented with the option of creating 3D plots of three types of Fukui functions:

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n f(-) Electrophilic - computes the f- Fukui function, which reflects susceptibility to electrophilic attack.n f(+) Nucleophilic - computes the f+ Fukui function, which reflects susceptibility to nucleophilic attack.n f(0) Radical - computes the f0 Fukui function, which reflects susceptibility to attack by radicals. This is

simply the average of f+ and f-.All the functions will be rendered on a regular rectangular grid with 0.2 Å spacing. In themolecular case,the plots extend 2.0 Å beyond themolecule; in the periodic case, the plots fill the entire unit cell.Computation of Fukui functions is possible for molecules and for periodics that use the Γ-point, but notfor periodic structures with multiple k-points.

Tip: The default resolution of the grid is 0.2 Å. You can also modify this by editing the input files andadding the keyword Grid.

Note: Due to the algorithm used, Fukui calculations on highly symmetric or/and near-degeneratesystems may exhibit difficulty converging to the ground state. If this happens, checking theUsesymmetry checkbox on the Setup tab of the DMol3 Calculation dialog or enabling thermal smearingcan accelerate the convergence.

Setting up molecular orbital analysisWhen you check theOrbitals checkbox, you are presented with the option of creating 3D plots of DFTmolecular orbitals:n HOMO - produces a plot of the HOMO (highest occupied molecular orbital).n LUMO - produces a plot of the LUMO (lowest unoccupied molecular orbital).n Levels above and below the HOMO level - specifies additional orbitals above and below the HOMO

level to be computed. For example, entering a value of 5 results in a total of 5 occupied and 5 virtualorbitals being computed, in addition to the HOMO.

All the functions will be rendered on a regular rectangular grid with 0.2 Å spacing. In themolecular case,the plots extend 2.0 Å beyond themolecule; in the periodic case, the plots fill the entire unit cell.Computation of orbitals is possible for molecules and for periodics that use the Γ-point, but not forperiodic structures with multiple k-points.

Tip: The default resolution of the grid is 0.2 Å. You can also modify this by editing the input files andadding the keyword Grid.

Setting up a population analysisWhen you check the Population analysis checkbox, you are presented with the option of performingseveral types of atomic population analysis:

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n Mulliken analysis - produces charges based on the density matrix and atomic overlap matrix. This isthemost common sort of charge analysis. See theMulliken and Mayer bond orders topic for moredetails. Three different analysis options are available:n Atomic Charge - computes the total Mulliken charges on each atom, as in Eq. DMol3-62.n Orbital & Charge - computes the contribution to the atomic charge from each atomic orbital on

each atom.n Overlap Matrix - computes the overlap population in each pair of atomic orbitals on different

atoms, as in Eq. DFT-58.Whenever Mulliken bond orders are calculated, DMol3will automatically computeMayer bondorders as well. Mayer bond orders gives valences that are close to the classical values. UnlikeMullikenbond orders, Mayer quantities are less dependent on the basis set choice and are transferable, sothey can be used to describe similar molecules. See theMulliken and Mayer bond orders topic formore details.

Note: Bond orders can only be calculated for nonperiodic structures. Symmetry informationshould not be used when calculating bond orders, i.e., theUse symmetry checkbox on the Setuptab of the DMol3 Calculation dialog should be unchecked.

n Hirshfeld analysis - produces partitioned charges that are defined relative to the deformation density,which is the difference between themolecular and the unrelaxed atomic charge densities. See theHirshfeld charge analysis topic for more details. Three different analysis options are available:n Chargen Dipolen Quadrupole

n ESP charges - produces atomic-centered charges that best reproduce the DFT Coulomb potential.This method is often used to derive charges to be used in forcefield calculations. See the Fittingatomic point charges to the electrostatic potential topic for more details.

Setting up band structuresWhen you check the Band structure checkbox, you are presented with options for controlling bandstructure calculations.Calculating band structure properties produces electronic energies along high symmetry directions inthe Brillouin zone. The standard path for each lattice type is taken from Bradley and Cracknell (1972).The path can bemodified using the Brillouin Zone Path dialog, accessed via the Path... button. Thedensity of points along the path, which affects the appearance of the resulting chart, can be controlledby the selection for the k-point set dropdown list or the approximate k-point separation can bemanually specified in the Separation text box, in Å-1, on the Properties tab of the DMol3 Calculationdialog. Conduction band states can be included by specifying a non-zero value in the Empty bands textbox.

Setting up density of statesWhen you check theDensity of states checkbox, you are presented with options for controlling densityof states calculations.For periodic systems, calculating densities of states produces electronic energies on theMonkhorst-Pack mesh of k-points. The k-point set can be specified using the DMol3 Density of States Optionsdialog, accessed via theMore... button. The quality of the k-points set is controlled by the k-point setdropdown list. Conduction band states can be included by specifying a non-zero value in the Emptybands text box. A partial density of states can be requested by checking the Calculate PDOS checkbox.

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Tip: To obtain representative density of states it is recommended to use a k-point set which is eitherthe same or finer quality than the one used in the SCF calculations.

Setting up Fermi surfacesIn order to generate Fermi surfaces for the structure resulting from a calculation density of statesproperties must be selected.To generate Fermi surfaces1. ChooseModules | DMol3 | Calculation from theMaterials Studio menu bar.2. Select the Properties tab.3. Check theDensity of states option on the properties list and set the appropriate DOS options.4. Click theMore... button to open the DMol3 Density of States Options dialog.5. Click the Separation radio button and specify a value of 0.01 1/Å or less. This ensures that enough k-

points are used for generating the Fermi surface data without requiring such fine settings for the restof the calculation.

Setting up COSMO Sigma profile calculationIn order to generate Sigma profiles for the structure resulting from a calculation theUse solvation modelelectronic option must be selected.To generate Sigma profile chart1. ChooseModules | DMol3 | Calculation from theMaterials Studio menu bar.2. On the Electronic tab check theUse solvation model checkbox.3. Click theMore... button to open the DMol3 Electronic options dialog and, if required, set the

appropriate solvent details on Solvent tab.At the end of the calculation, the Sigma profile chart will be generated automatically.

Setting up an optics calculationIn order to generate optical properties for the structure resulting from a calculation the type of optics tocalculatemust be selected.

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To generate optics information1. ChooseModules | DMol3 | Calculation from theMaterials Studio menu bar.2. On the Properties tab select and check theOptics checkbox.3. Choose the type of optics from the Calculate dropdown list and themethod of calculation from the

Use dropdown list.4. Check the Calculate polarizability checkbox if required and click theMore... button to configure

specific options on the DMol3 Optics Options dialog.5. Check theOptimize geometry checkbox.

Note: Geometry optimization of an excited state uses the original structure as the initial point. Ifthe Task is set to Geometry Optimization and excited state optimization is requested, the resultsfolder will contain two sets of geometry optimization results, both with the same initial point.The name of the results file for the excited state optimization has the form <seedname>_[S,T,E]<n>_GO.xsd, where:n S is a singlet staten T is a triplet staten E is a spin unrestricted staten <n> is the number of the excited state

6. Modify the excitation number which should have its geometry optimized.The optimized structure for the specified excitation will be saved in the <seedname>_[S,T,E]<n>_GO.xsd output file.

Tip: If the job is not reaching convergence in the TD-DFT process, modifying the input file and addingtighter convergence criteria might help, as explained on the tddft_crit keyword page in the onlinehelp.

Manipulating filesDMol3 is a file-based application, all input and output is delivered in a mixture of text and binary files.This section describes some file handling issues which may arise, especially when the DMol3 server is runin a standalonemode and not via a gateway.

Input filesThe DMol3 Job Files dialog allows you to save input files for subsequent manual editing or for running instandalonemode.To save input files1. ChooseModules | DMol3 | Calculation from themenu bar to display the DMol3 Calculation dialog.2. Click the Files... button to open the DMol3 Job Files dialog.3. Click the Save Files button.

Note: The Save Files button is enabled only if a suitable 3D model document is active.

Only one input file, <rootname>.input, is displayed in the Project Explorer. This file contains theparameters specified using the DMol3 interface. You can add to it parameters that access functionalitynot supported though the interface. Any other input files are hidden, since they are not intended to beedited manually.

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To edit the input file1. Select the desired file in the Project Explorer.2. Double-click to open the file in the text editor.3. Make your changes - adding, deleting, or modifying input as desired.4. Choose File | Save from themenu bar to save your changes.

Note: DMol3 input files use whitespace as the delimiting character, tabs are not supported.

Input files can be run on a server after they have been edited.To run DMol3 using an existing set of input files1. ChooseModules | DMol3 | Calculation from themenu bar to display the DMol3 Calculation dialog.2. Click the Files... button to open the DMol3 Job Files dialog.3. Double-click on the input file.4. Click the Run Files button.

Note: The Run Files button is enabled only if a suitable .input file is active.

If your server does not support the gateway protocol, you may have to run DMol3 in standalonemodeusing the RunDMol3.sh or RunDMol3.bat files provided with the installation. In such circumstances, itis necessary to copy all the input files from the project folder to the appropriate directory on the servermachine. You can find complete instructions for transferring files in Uploading data to the computeserver.

Output filesOnly one output file, <rootname>.outmol, is displayed in the Project Explorer. However, several otherfiles are created during a DMol3 run. Though they are not visible in the Project Explorer, all of theseoutput files are automatically placed in the correct project folder when the job is run using the gateway.If DMol3 is run in standalonemode, the output files must be copied manually from the server to theappropriate project folder, as described in Downloading data from the compute server.Some output files can be quite large (for example .tpvec files can easily be in the order of hundreds ofMB). If these files are not likely to be required to restart a job, then it is recommended that you delete orarchive them.

Restarting a DMol3 calculationIt is not possible to seamlessly restart a completed DMol3 job through the interface. However, it ispossible to take advantage of a great deal of information when starting follow-on jobs.

Note: If a job with File usage set to Memory fails, restart files will not be created.

Note: In order to restart a job, the output files from the previous run must be present in the projectfolder. If the files are present, their transfer to the server happens automatically whenever you launcha job.

Restarting with the SCF coefficientsWhen a molecular DMol3 calculation completes, two files (<rootname>.tpdensk and<rootname>.tpotl) containing the total density and Kohn-Sham potential are returned and placed inthe results folder for the calculation. These files are hidden, so you will not see them in the Project

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Explorer. Using these files to start a subsequent SCF calculation will reduce the number of iterationsneeded to reach convergence.

Note: The .tpdensk, and .tpotl files are binary, and can only be used on the platform on which itwas created. So, the .tpdensk and .tpotl files can only be used to restart a run on the sameplatform.

Whenever the .tpdensk and .tpotl files are present, they will be uploaded to the server, but they willnot be read unless you instruct DMol3 to do so. To submit a DMol3 job that makes use of these files,perform the following steps:1. ChooseModules | DMol3 | Calculation from themenu bar to display the DMol3 Calculation dialog.2. Open the results folder for the completed DMol3 job in the Project Explorer.3. Open the .input file in the text editor by double-clicking on it.4. Add the line

scf_restart onanywhere in the input file.

5. Click the Files... button to open the DMol3 Job Files dialog.6. Click the Run Files button.7. If prompted to save the file, choose Yes.For periodic systems, the procedure is similar, but requires minor modifications. DMol3 does not savedensity and potential information at every SCF step, so if you expect to run a restart, an additionalkeyword needs to be added to the original DMol3 input file telling the program to save density andpotential at each step.The keyword to add is save_density_each_it.The edited input file can then be used to restart the DMol3 periodic job.

Restarting with the HessianYou can use a Hessian to restart a geometry minimization or TS search. When running through MaterialsStudio, it is not necessary to have an explicit .hessian file once a Hessian has been loaded into themodel. You can obtain a starting Hessian from several sources as described in Importing a Hessian file.To use a Hessian in a geometry optimization or transition state optimization1. Load the Hessian data. If you have generated a Hessian using Materials Studio, then the data are

automatically loaded for you upon job completion. If you need to load a .hessian file generatedoutsideMaterials Studio, use the Edit | Insert From... command on themenu bar.

2. ChooseModules | DMol3 | Calculation from themenu bar to display the DMol3 Calculation dialog.3. Set the Task to Geometry Optimization or TS Optimization.4. If you are performing a geometry optimization, click theMore... button to open the DMol3

Geometry Optimization dialog and check the Use starting Hessian checkbox.5. If you are performing a TS optimization, a starting Hessian is required, so there is no option to

specify this.6. Click the Run button.

Restarting a frequency calculation or Hessian evaluationDMol3 evaluates a Hessian by finite-difference of analytic gradients. This means that each atom in thesystem must be displaced in each Cartesian direction (including positive and negative directions). Aseach displacement is made, the gradient is written to a file called <rootname>.hesswk. If the Hessianevaluation is interrupted, this file may be used to restart the calculation.

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Note: If the frequency calculation that has been interrupted was a continuation of a GeometryOptimization task, then you must delete the .hessian file left behind in the job folder by thegeometry optimization before you restart the run.

Like the .tpdensk and .tpotl files, the .hesswk file is returned to the project folder, but hidden.Whenever the .hesswk file is present, it will be uploaded to the server, but it will not be read unless youinstruct DMol3 to do so.To submit a DMol3 job that makes use of the .hesswk file1. ChooseModules | DMol3 | Calculation from themenu bar to display the DMol3 Calculation dialog.2. Open the results folder for the completed DMol3 job in the Project Explorer.3. Open the .input file in the text editor by double-clicking on it.4. Add the line

vibration_restart onanywhere in the input file.

5. Click the Files... button to open the DMol3 Job Files dialog.6. Click the Run Files button.7. If prompted to save the file, choose Yes.

Importing a Hessian fileAHessian file is required input for a transition state optimization and can also be used in a geometryminimization. There are several ways that you can create a Hessian and import it into your model.n Run a frequency calculation with VAMP or DMol3. At the end of jobs of this type a Hessian matrix is

produced. If the job was run via theMaterials Studio interface, the result will automatically bedisplayed in Materials Studio.

n Run a geometry optimization with DMol3. This calculation uses an approximate Hessian matrix tofind theminimum energy configuration. If the job is run through theMaterials Studio interface, theresult will automatically be displayed in Materials Studio.

n Read in a Hessian matrix from an earlier calculation. You can import a Hessian from any earliercalculation if the file is in the correct format and uses the file extension ".hessian". This method isconvenient if you have generated a Hessian matrix using another Accelrys product in standalonemode. To read a Hessian into your model:a. Make sure the desired molecule or solid is the active document.b. Choose Edit | Insert from... from theMaterials Studio menu bar. The Insert Into Active Document

dialog is displayed.c. Set the value of the file types dropdown list for the File name to Hessian Files (*.hessian;*.vres).d. Browse to the location of the Hessian file and click the Insert button.Hessian files produced by Materials Studio aremarked as "hidden" files. To display any hidden files inthe Insert Into Active Document dialog, you must remove the "hidden" attribute:n Browse to the file's location using theWindows Explorer.n Right-click on the file and select Properties from the shortcut menu.n Uncheck the checkbox labeled Hidden. The file should become visible in the Insert Into Active

Document dialog.

Analyzing DMol3 resultsDMol3 results become available for analysis on completion of the DMol3 run, once all the output fileshave been successfully downloaded to the results folder.

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Select the results to be analyzed by opening the 3D structure document (.xsd) in the results folder. Thisallows all related DMol3 results to be analyzed.

Note: The structure is updated automatically on successful download of output files from acompleted DMol3 job that was run using a gateway (the structure is not automatically updated if theDMol3 job was run in standalonemode).

The atoms in the updated structure document have an extra property, ServerAtomIndex, associatedwith them. This shows the atom sequence numbers as used in the DMol3 output files and can be seenby labeling atoms in the structure with the ServerAtomIndex property. (This property will be seen onlyin structures generated from DMol3 and other similar applications).

All other analysis functions require you to perform certain actions using the DMol3 Analysis dialog.

Tip: If you have calculated a Hessian matrix (i.e., by checking the Frequency checkbox on theProperties tab of the DMol3 Calculation dialog) as part of a DMol3 run, you can create a list ofvibrational modes and view the spectrum for the structure using the Vibrational Analysis tool.

Vibrational intensities can only be obtained for nonperiodic systems. Without intensities, thedisplayed spectrum consists of points on the frequency axis only.

Note: The Hessian file resulting from a DMol3 geometry optimization run should not be used toobtain the vibrational spectrum.

Updating structureUpdating the atomic coordinates after geometry optimization, TS optimization, or TS search is therecommended first step in the analysis process.When a DMol3 job that was run through a gateway is completed, the output files are copied to theresults folder and the structure is updated automatically. The procedure described below for updatingthe structure applies to jobs that were run in standalonemode. You can also use this procedure toreturn the view of a structure you'vemodified to its last saved form.The procedure also applies if you manually modified the final structure produced by DMol3, and youwant to revert it back to the unmodified form.

Note: If the chemical composition (i.e., number of atomic species or number of each kind of atoms)has changed sinceMaterials Studio saved the .xsd file in the results folder, you cannot update thestructure.

As a result of the update, the coordinates of the atoms are set to the values returned by the DMol3 runin the (hidden) .car file.To update the structure1. ChooseModules | DMol3 | Analysis from themenu bar to display the DMol3 Analysis dialog.2. Select Structure from the list of properties.3. Make sure that the 3D structure document you wish to be updated is the currently active

document.4. Click theUpdate button.

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An error message will be displayed if the .car structure file is incomplete or if the chemical compositionof themodel has been changed (i.e., atoms were added, removed, or modified). TheUpdate button isdisabled if the .car file is not present or if the current document cannot be updated.

Displaying trajectory and chart dataDepending on the type of calculation performed, a DMol3 run may produce a trajectory document andone or more chart documents. These documents have a special association with each other becauseeach of the points on the graph corresponds to a frame in the trajectory.DMol3 produces a trajectory (.xtd) file whenever you run a geometry optimization, a TS optimization,or a TS search. In each case, a history of the optimization is returned in a file called seedname.xtd,where seedname is the name entered as the Job description on the Job Control tab.When you run a geometry or TS optimization, two chart documents are generated:n name Energies.xcd contains a plot of total energy vs. frame number for all steps of the

calculation.n name Convergence.xcd contains three plots that describe the degree of convergence of the

optimization as a function of frame number:n change in energy vs. frame numbern maximum Cartesian force vs. frame numbern maximum Cartesian step size vs. frame numberBecause these values span several orders ofmagnitude, the data are plotted on a log

10scale.

When you run a calculation with COSMO solvation a chart document is generated:n name Sigma prfile.xcd contains a plot of screening charge density vs. Sigma profile.When you run a TS search, a single chart containing a graph of energy vs. reaction coordinate for eachstep of the calculation, name TransitionState.xcd, is generated. This includes an individual graphfor each LST or QST "uphill" cycle as well as a graph for each conjugate gradient minimization. SeeTransition state searching via synchronous transit methods for additional information on themeaningof these components of a TS search.

Creating a trajectory and chartWhen you run DMol3 via theMaterials Studio interface, the creation and display of these trajectoriesand charts are automatic. If you select Automatically view output on the DMol3 Job Control Optionsdialog, the graphs will be displayed automatically upon completion of the calculation. If you selectUpdate graphs on the DMol3 Job Control Options dialog, these graphs will be displayed and updatedwith intermediate results throughout the course of the calculation.To create charts from output files generated by a standalone calculation1. Download the files from the compute server to your PC using the procedure described in Running

DMol3 in standalonemode. Be sure to retrieve the .car, .outmol, .arc, and .summ files.2. ChooseModules | DMol3 | Analysis from themenu bar to display the DMol3 Analysis dialog.3. Select Energy evolution from the list of properties.4. Make sure that the .outmol file is the currently active document.5. Click theUpdate button.If you have run the calculation through theMaterials Studio interface, you can regenerate the chartdocuments by following a similar procedure.

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1. Open either the .xsd or .outmol file and make it the currently active document.2. ChooseModules | DMol3 | Analysis from themenu bar to display the DMol3 Analysis dialog.3. Select Energy evolution on the DMol3 Analysis dialog.4. Click theUpdate button.

Animating the trajectoryYou can use the controls on the Animation toolbar to animate the trajectory, stepping through each ofthe frames of the document. If the chart is open during the animation, the point corresponding to theactive frame becomes highlighted.

Chart Viewer point selectionAlternatively, you can use Chart Viewer point selection to display the trajectory frames of the points youselect from the chart document.To display a trajectory frame for a point on a chart document

1. Click the Selection Mode button on the Chart Viewer toolbar to enter selection mode.2. Making sure you have the corresponding trajectory document open, select a data point on the

chart document.3. The corresponding trajectory frame is displayed.4. Drag themouse over other data points on the chart document to display their corresponding

trajectory frames.5. If DMol3 generated a second chart document, its related data points will also be highlighted.

Tip: To make it easier to see the chart and trajectory documents, close all the other documents andthen maximize the sizes of these two documents by selectingWindow | Tile Vertically from themenubar.

Visualizing volumetric dataMaterials Studio allows you to visualize the spatial distribution of electron density, electrostaticpotential, molecular orbitals, or Fukui functions calculated by DMol3. The relevant data fromDMol3.grd files are used to add a field to themodel. This field can be subsequently visualized in avariety of ways, for example direct field visualization, isosurfaces, or slices.

Electron densityMaterials Studio uses the information generated by DMol3 to create a field that corresponds to the totalelectron density. When you analyze a spin-unrestricted calculation, you can also create a field for thespin density (the difference between the density of alpha and beta electrons). This field allows you tovisualize the spatial distribution of themagnetic moment in a spin-unrestricted system.You can also create a field of the deformation density, the total density with the density of the isolatedatoms subtracted. Regions of positive deformation density indicate the formation of bonds, whilenegative regions indicate electron loss.

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To create a density field1. ChooseModules | DMol3 | Analysis from themenu bar to display the DMol3 Analysis dialog.2. Select Electron density from the list of properties.3. Make sure that the desired 3D structure document (.xsd) is the currently active document.4. Select the type of density you wish to display (total, deformation, or spin) from theDensity field

dropdown list. The choices are limited to those that you specified in the Electron density section onthe Properties tab when you ran the calculation.

5. Optionally, check or uncheck the View isosurface on import checkbox. This is checked by default.6. Click the Import button.

Tips:If you select View isosurface on import, you should see a 3D contour after the field has beenimported. To change the value of the contour, open the Display Style dialog and select theIsosurface tab. If you do not see an isosurface, the default value is possibly outside of the range ofthe field values. Select the Isosurface tab and choose a different value.If you do not check the View isosurface on import checkbox, you will not see a volumetric datadisplay.Use the Volume Visualization toolbar and Display Style dialog to control the display of the fielddata.

Tip: If the dipole slab correction has been applied in the calculation, the structuremay have beenmodified by Materials Studio in order to place the center of the vacuum region in the center of thecell. In this case you can improve the display by using the Display Style dialog to change the latticedisplay style on the Lattice tab to In-Cell, for example. This change would improve thecorrespondence between the display of atoms and of fields.

Electrostatic potentialMaterials Studio uses the information generated by DMol3 to create a field that corresponds to theelectrostatic, or Coulomb, potential. Positive regions correspond to electron-deficient areas and aresubject to nucleophilic attack, negative regions correspond to electron-rich areas and are subject toelectrophilic attack.To create an electrostatic potential field1. ChooseModules | DMol3 | Analysis from themenu bar to display the DMol3 Analysis dialog.2. Select Potentials from the list of properties.3. Make sure that the desired 3D structure document (.xsd) is the currently active document.4. Select the type of potential you wish to display from the Potential field dropdown list. The choice is

limited to electrostatic potential, and that only if you requested it in the Electrostatics section on theProperties tab.

5. Optionally, check or uncheck the View isosurface on import checkbox. This is unchecked by default.6. Click the Import button.If you wish to use the potential to color an isosurface, see the Color and contour mapping topic.

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Tips:If you select View isosurface on import, you should see a 3D contour after the field has beenimported. To change the value of the contour, open the Display Style dialog and select theIsosurface tab. If you do not see an isosurface, the default value is possibly outside of the range ofthe field values. Select the Isosurface tab and choose a different value.If you do not check the View isosurface on import checkbox, you will not see a volumetric datadisplay.Use the Volume Visualization toolbar and Display Style dialog to control the display of the fielddata.

Fukui functionsMaterials Studio uses the information generated by DMol3 to create a field that corresponds to theFukui functions. There are three different functions that you can view: f(-) Electrophilic reflectssusceptibility to electrophilic attack; f(+) Nucleophilic reflects susceptibility to nucleophilic attack; f(0)Radical reflects susceptibility to attack by radicals. Further information is available in the Fukui functionstopic.To create a Fukui function field1. ChooseModules | DMol3 | Analysis from themenu bar to display the DMol3 Analysis dialog.2. Select Fukui function from the list of properties.3. Make sure that the desired 3D structure document (.xsd) is the currently active document.4. Select the type of field you wish to display (f(+), f(-), or f(0)) from the Fukui field dropdown list. The

choices are limited to those that you specified in the Fukui function section on the Properties tabwhen you ran the calculation.

5. Optionally, check or uncheck the View isosurface on import checkbox. This is unchecked by default.6. Click the Import button.If you wish to use the potential to color an isosurface, see the Color and contour mapping topic.

Tips:If you select View isosurface on import, you should see a 3D contour after the field has beenimported. To change the value of the contour, open the Display Style dialog and select theIsosurface tab. If you do not see an isosurface, the default value is possibly outside of the range ofthe field values. Select the Isosurface tab and choose a different value.If you do not check the View isosurface on import checkbox, you will not see a volumetric datadisplay.Use the Volume Visualization toolbar and Display Style dialog to control the display of the fielddata.

Molecular orbitalsMaterials Studio uses the information generated by DMol3 to create a field that corresponds to any ofthemolecular orbitals in the system. Themolecular orbitals are the single-particle wavefunctionsconstructed from linear combinations of atomic orbitals as discussed in the theory section. The highestoccupied orbital (HOMO) and lowest unoccupied orbital (LUMO) are especially important in determiningthe chemical reactivity of a system.The Filter dropdown list allows you to control which orbitals have their information displayed in thetable:

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n All displays data for all orbitals.n Available displays data only for orbitals that are available to create fields.n Spin up displays data only for alpha-spin orbitals. In the unrestricted case, this is the same as All.n Spin down displays data only for beta-spin orbitals. In the unrestricted case, no data are displayed.The orbital analysis table provides a list of eigenvalues and information about each orbital. The list ofeigenvalues starts with the lowest core orbital and extends to include ten orbitals above the Fermi level(i.e., above the HOMO). If there are fewer than ten virtual orbitals in the list, it is because there are notthat many in your particular system. The accompanying information includes:n Field contains Yes when field data have been computed and is blank otherwise.n N indicates the number of the orbital, with 1 corresponding to the lowest energy orbital. In an

unrestricted calculation, the alpha- and beta-spin orbitals are numbered separately.n s indicates spin, + for alpha, - for beta. In a spin-restricted calculation, all orbitals are labeled as +.n Eigenvalue indicates the orbital eigenvalue in Hartree.n Type indicates the HOMO and LUMO. These labels appear in the appropriate row.To create a molecular orbital field1. ChooseModules | DMol3 | Analysis from themenu bar to display the DMol3 Analysis dialog.2. Select Orbitals from the list of properties.3. Make sure that the desired 3D structure document (.xsd) is the currently active document.4. Select the row in the table corresponding to the orbital you wish to display. The choices are limited

to those that you specified in the Orbitals section on the Properties tab when you ran thecalculation.

5. Optionally, check or uncheck the View isosurface on import checkbox. This is checked by default.6. Click the Import button.

Tips:If you select View isosurface on import, you should see a 3D contour after the field has beenimported. To change the value of the contour, open the Display Style dialog and select theIsosurface tab. If you do not see an isosurface, the default value is possibly outside of the range ofthe field values. Select the Isosurface tab and choose a different value.If you do not check the View isosurface on import checkbox, you will not see a volumetric datadisplay.Use the Volume Visualization toolbar and Display Style dialog to control the display of the fielddata.

Tip: The list of all eigenvalues is much longer than the list of those available to create fields. Set theFilter to Available to see only those orbitals that can be used to create fields.

Field visualizationMaterials Studio provides a number of tools for field visualization. They are accessed via the VolumeVisualization toolbar and Field, Isosurface, and Slice tabs on the Display Style dialog.The Volume Visualization toolbar provides access to the Volumetric Selection dialog, which enables youto specify the field to be visualized and set visibility attributes for fields, slices, and isosurfaces. Thistoolbar also contains controls for creating new isosurfaces and slices, including the shortcuts fororienting the slice based on either the cell axes or the coordinates of selected atoms. The Color Mapsdialog, which can also be accessed from the Volume Visualization toolbar, provides control over the

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coloring of volumetric objects (it also provides useful shortcuts for determining theminimum andmaximum values of the field).The Field tab of the Display Style dialog allows you to visualize the field directly using either theDots orVolume display styles.The Isosurface tab of the Display Style dialog allows you to alter the visualization style of a selectedisosurface, change its isovalue, or use another field for color mapping.The Slice tab of the Display Style dialog allows you to alter the visualization style of a selected slice.

Note: The volumetric visualization tabs on the Display Style dialog are displayed only if an object ofthe relevant type is present in the active document. If a field, isosurface, or slice is selected, forexample by using the Volumetric Selection dialog, the volumetric visualization tabs that are notrelevant to the selection will be removed from the Display Style dialog.

Tip: Field visualization in Materials Studio fully supports periodic display. You can use the Field tab onthe Display Style dialog to change the range of a field to display more or less than one unit cell of astructure.

Note: The default settings for field visualization result in the fields being displayed over one unit cell ofa structure. It might be helpful to use the "In-Cell" display mode for the lattice (accessed from theLattice tab on the Display Style dialog) to make sure that the field is positioned around displayedatoms.

Visualizing Fermi surfacesFermi surfaces are generated from information from DMol3 calculations which is stored in the .bandsoutput file. Fermi surfaces can be considered as the energy isosurfaces in reciprocal space.

Tip: The results under analysis must include density of states information generated during thecalculation. Select Density of states on the Properties tab of the DMol3 Calculation dialog.

To ensure that the generated Fermi surface(s) are reliable you must use as many Density of states k-points as computational resources will allowwhen setting up the calculation.

To create a Fermi surface1. ChooseModules | DMol3 | Analysis from themenu bar to open the DMol3 Analysis dialog.2. Select Fermi surface from the list of properties.3. Ensure that the 3D Atomistic document to be analyzed is the active document.4. Select the Band for which to display the Fermi surface.5. Click the Import button.To change the Fermi level used for the Fermi surface1. Create a Fermi surface according to the steps above.2. Open the Display Style dialog and select the Isosurface tab.3. In theGeneration section change the Isovalue. The Fermi surface will be updated appropriately.

Displaying population analysis resultsADMol3 calculation can compute atomic charges by Mulliken, Hirshfeld, and ESP-fitted charge analysis.In addition, spins can be computed using Mulliken or Hirshfeld analysis and both Mulliken and Mayer

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bond orders can be calculated.Mulliken analysis is one of themost common types of charge, spin, and bond order analysis. The spindensity matrix and atomic overlap matrix are used to partition charges among the atoms. This methodis, however, very sensitive to the choice of basis set. See theMulliken and Mayer bond orders topic formore details.Hirshfeld charge and spin analysis is based on the deformation density, as described in the Hirshfeldcharge analysis topic. This method is more stable with respect to the basis set than Mulliken chargeanalysis, but seems to generally underestimate the atomic charges.ESP-fitted charge analysis fits atom-centered charges to the DFT Coulomb potential, as described inFitting atomic point charges to the electrostatic potential (ESP). Charges computed in this manner havefrequently been used in subsequent forcefield calculations.Mayer bond order analysis gives valences that are close to the classical values. UnlikeMulliken bondorders, Mayer quantities are less dependent on the basis set choice and they are transferable, so theycan be used to describe similar molecules. See theMulliken and Mayer bond orders topic for moredetails.

Displaying computed charges, spins, and bond ordersTo import and display computed atomic charges, spins, and bond orders, the output structure from thecalculation (.xsd) and the DMol3 output file (.outmol) must be saved in a folder within the currentproject.

Note: If the calculation is to be a standalone job, you will need to save your .car file in .xsd formatbefore you start.

To update an output structure with charges, spins, and bond orders1. ChooseModules | DMol3 | Analysis from themenu bar to display the DMol3 Analysis dialog.2. Select Population analysis from the list of properties.3. Make sure that the 3D Atomistic document (.xsd) output from the DMol3 calculation is the

currently active document.4. Select the type of charges (Mulliken, Hirshfeld, or ESP), spins (Mulliken or Hirshfeld), or bond orders

(Mayer or Mulliken) that you wish to apply from the respective dropdown lists. The choices arelimited to those properties that you specified in the Population analysis section on the Propertiestab when you ran the calculation.

5. Click the appropriate Assign button to import the charge, spin, or bond order data into thestructure document.

6. Right-click in the 3D Atomistic document and select Label from the shortcut menu to display theLabel dialog. Set theObject type to Atom, select Charge or Spin from the Properties list, and click theApply button to display the charges or spins.

7. On the Label dialog, set theObject type to Bond, select BondOrder from the Properties list, and clickthe Apply button to display the bond orders.

Once you have imported the charges, spins, and bond orders using the Assign charges to structure,Assign spins to structure, and Assign bond orders to structure buttons, you can export a .car file thatcontains these data.

Displaying band structure chartsBand structure charts show how electronic energies depend on the k-vector along high symmetrydirections in the Brillouin zone. These charts provide a useful tool for qualitative analysis of theelectronic structure of a material; for example, it is easy to identify the narrow bands of d and f states, as

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opposed to the free electron-like bands that correspond to s and p electrons. It is also instructive to lookfor directions with relatively flat, dispersionless bands, as these directions are likely to contributestrongly to optical absorption, thus allowing the anisotropy of optical properties to be explained. Theenergy band gap is also easily deduced from the band structure plots, as it normally corresponds to theenergy difference between two states at high symmetry points.To create a band structure chart1. ChooseModules | DMol3 | Analysis from themenu bar.2. Select Band structure from the list of properties.3. Ensure that the desired 3D Atomistic document (seedname.xsd) or corresponding output file

(seedname.outmol) is the currently active document.

Note: If you are using an output file, make sure you select the output file from themain DMol3run (seedname.outmol) rather than that from the band structure calculation (seedname_BandStr.outmol).

4. Select the display style (Points or Lines) from theGraph style dropdown list.5. Optionally, check the ShowDOS checkbox and set the DOS options.6. Click the View button.7. A new chart document, seedname Band Structure.xcd, is created in the results folder.

Note: The lower energy limit for the band structure graph can be changed, if necessary, by modifyingPlot_DOS keyword with a numeric argument. The default value is set to -1.0 a.u.

Displaying density of states chartsDensity of states (DOS) and partial density of states (PDOS) charts give a quick, qualitative picture of theelectronic structure of a material and, sometimes, can be related directly to experimental spectroscopicresults.

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Full density of statesTo create a DOS chart1. ChooseModules | DMol3 | Analysis from themenu bar.2. Select Density of states from the list of properties.3. Ensure that the desired 3D Atomistic document (seedname.xsd) or corresponding output file

(seedname.outmol) is the currently active document.

Note: If you are using an output file, make sure you select the output file from themain DMol3run (seedname.outmol) rather than that from the density of states calculation (seedname_DOS.outmol).

4. Select the Full radio button to display the total DOS.5. For spin-polarized calculations, select the required DOS component from theDOS display dropdown

list.6. Optionally, click theMore... button to open the DMol3 DOS Analysis Options dialog, where

additional analysis options can be set.

Tip: The Interpolation integration method gives more accurate results than the Smearingmethod, although it is slightly slower.

Note: The Interpolation integration method is only available for calculations on periodic systems.

7. Click the View button.8. A new chart document, seedname DOS.xcd, is created in the results folder.

Note: The lower energy limit for the density of states graph can be changed, if necessary, bymodifying Plot_DOS keyword with a numeric argument. The default value is set to -1.0 a.u.

Partial density of statesMaterials Studio produces PDOS plots for certain angular momenta on selected atoms. The Sum curverepresents the local density of states (LDOS) when one atom is selected. If more than one atom isselected, the contributions in each angular momentum channel from all selected atoms are addedtogether. When no atoms are selected, the behavior is the same as if all atoms were selected.

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To create a PDOS chart1. ChooseModules | DMol3 | Analysis from themenu bar.2. Select Density of states from the list of properties.3. Ensure that the desired 3D Atomistic document (seedname.xsd) or corresponding output file

(seedname.outmol) is the currently active document.

Note: If you are using an output file, make sure you select the output file from themain DMol3run (seedname.outmol) rather than that from the density of states calculation (seedname_DOS.outmol).

4. Select the Partial radio button to display the partial DOS.5. Check the appropriate checkboxes to select the required angular momentum components for the

PDOS.6. Select the atom or atoms in themodel for which the PDOS is to be created.7. For spin-polarized calculations, select the required DOS component from theDOS display dropdown

list.8. Optionally, click theMore... button to open the DMol3 DOS Analysis Options dialog, where

additional analysis options can be set.

Tip: The Interpolation integration method gives more accurate results than the Smearingmethod, although it is slightly slower.

Note: The Interpolation integration method is only available for calculations on periodic systems.

9. Click the View button.10. A new chart document, seedname PDOS.xcd, is created in the results folder.

Tip: It is recommended that you rename this file to indicate the atoms on which it is based.

Note: The lower energy limit for the partial density of states graph can be changed, if necessary, bymodifying Plot_DOS keyword with a numeric argument. The default value is set to -1.0 a.u.

Calculating elastic constantsElastic constants are basic mechanical properties of periodic crystals. DMol3 provides calculation of pureelastic constants and compliance tensors and a variety of derived quantities such as bulk modulus,shear modulus, and their approximations for polycrystallinematerials.To calculate elastic constants1. ChooseModules | DMol3 | Analysis from theMaterials Studio menu bar.2. Select Elastic constants from the list of properties.3. Ensure that the desired 3D Atomistic document (seedname.xsd) or corresponding output file

(seedname.outmol) is the currently active document.4. Click the Calculate button.5. A new text document, seedname Elastic Constants.txt, is created in the results folder.

Displaying the averaged potential chart for work function calculationsThe DMol3 Analysis dialog can be used to generate plots of the change in electrostatic potential througha slab, which is related to the energy required to remove an electron from the bulk into the vacuum (the

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work function). The plots are created by averaging electrostatic potential in the planes perpendicular tothe slab normal.

Note: Work functions can only be calculated for slabs for which electrostatics have been calculatedduring a DMol3 run and theWork function checkbox is checked.

The electrostatic potential is reported along the fractional coordinate of the unit cell in the direction ofthe vacuum. The energy required to free an electron is greater at the layers and smaller between thelayers, in the vacuum it is negligible. The Fermi level is reported on the work function chart.To create an averaged potential chart1. ChooseModules | DMol3 | Analysis from themenu bar to open the DMol3 Analysis dialog.2. Select Potentials from the list of properties.3. Make the 3D Atomistic document containing the 3D periodic slab the active document.4. Select the Potential field from the dropdown list.5. Optionally check the View isosurface on import checkbox.6. Click the Import button.7. A new chart document, seedname Potential Profile.xcd, is created in the results folder and

becomes the active document. The selected potential field is imported into the 3D Atomisticdocument and may be displayed as an isosurface.

Analyzing optical propertiesThe DMol3 Analysis dialog can be used to generate plots of the optical absorption spectrumThese plots are generated based on the excitation energies and oscillator strengths reported in theDMol3 .outmol file.DMol3 enables you to calculate the electronic states of the final output structure from a run. The Opticsselection option on the DMol3 Analysis dialog allows you to view excitation data and to generate optical(UV-Vis) spectra in both chart and grid form.To view excitation data or create optical spectrum, you need to have the structure file (.xsd) and DMol3output file in a folder in the Project Explorer.To create optical spectrum1. ChooseModules | DMol3 | Analysis from themenu bar to open the DMol3 Analysis dialog.2. Select Optics from the list of properties.3. Make sure that the 3D structure document you wish to be updated is the currently active

document.4. Optionally, select the required Units from the dropdown list.5. Click the View spectrum button.To create optical grid1. ChooseModules | DMol3 | Analysis from themenu bar to open the DMol3 Analysis dialog.2. Select Optics from the list of properties.3. Make sure that the 3D structure document you wish to be updated is the currently active

document.4. Optionally, select the required Units from the dropdown list.5. Click the View grid button.

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Note: In order to calculate the optical excitations, you must request optics properties in the initialcalculation.

Note: Oscillator strengths are available only for singlet state calculations.

To analyze excited states optimization1. Open the .outmol file corresponding to the excited state optimization.2. Search for the first occurrence of the words Done calculating TDDFT forces.3. The next three lines contain the excitation energy and the dissociation energy for the initial state of

the geometry optimization. The value listed as Excitation energy corresponds to the photonabsorption energy of themolecule in its initial state.

4. Search for the last occurrence of the words Done calculating TDDFT forces.5. The next three lines contain the excitation energy and the dissociation energy for the final state of

the geometry optimization. The value listed as Excitation energy corresponds to the photonemission energy of themolecule in its optimized configuration, which is the fluorescence energy.

Displaying Raman spectraRaman intensities and activities are calculated in DMol3 by the finite differentiation technique. A numberof separate gradient calculations are performed in the presence of varying electric fields in order togenerate the polarizability tensor derivative which defines the Raman activity.You can only generate Raman spectra if the necessary intensities have been obtained during thecalculation.To display a Raman spectrum1. ChooseModules | DMol3 | Analysis from themenu bar to display the DMol3 Analysis dialog.2. Select Raman spectrum from the list of options at the top of the dialog.3. Make sure that the 3D Atomistic document (.xsd) output from the DMol3 calculation is the currently

active document.4. Select the Function of themode to be calculated.5. If the Function is set to Intensity set the Temperature.6. Set the Smearing value to be used.7. Select theUnits for the X axis.8. Specify whether to reverse the wavenumber and intensity axes.9. Click the View button.10. A new chart document, seedname Raman Spectrum.xcd, is created in the results folder.

Calculating reaction kineticsReaction kinetics are described in terms of reaction rate coefficients. The rate coefficients are evaluatedin the transition state theory framework using information about the energies, geometries andvibrational frequencies of reactants, products and transition state. In order to achieve better agreementwith experiment it might be advantageous to increase the reaction threshold value from the DFTcalculated one, and also to scale calculated harmonic frequencies to account for DFT deficiency and foranharmonic effects.The threshold correction can be applied either on a basis ofmore accurate ab initio calculations, orbased on the comparison of calculated and experimental rate coefficients. It appears that value in theregion of 6-7 kcal/mol describes DFT error quite adequately.

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The recommended correction factors for DFT frequencies can be found at the NIST website(http://cccbdb.nist.gov/vibscalejust.asp) for a variety of exchange-correlation functionals.To calculate reaction kinetics1. ChooseModules | DMol3 | Analysis from theMaterials Studio menu bar.2. Select Reaction kinetics from the list of properties.3. Ensure that the desired 3D Atomistic collection document (seedname.xod) is the currently active

document.4. Specify the temperature range of interest.5. Check the Apply tunneling correction checkbox if the reaction involves motion of light elements.6. Optionally specify a Threshold correction and a Vibrational frequencies scaling factor.7. Click the Calculate button.8. A new study table document, seedname.std, is created in the results folder.

Displaying solvation propertiesCOSMO surfaces are generated from information from DMol3 calculations which is stored in the .cosmooutput file. COSMO surfaces are generated from the point charges used in the DMol3 calculation andrepresent the cavity that excludes solvent and includes the solute.To create a COSMO surface1. ChooseModules | DMol3 | Analysis from themenu bar to open the DMol3 Analysis dialog.2. Select Solvation properties from the list of properties.3. Ensure that the 3D Atomistic document to be analyzed is the active document.4. Select COSMO surface from the list of properties to show.5. Click the Import button.To display COSMO charges1. ChooseModules | DMol3 | Analysis from themenu bar to open the DMol3 Analysis dialog.2. Select Solvation properties from the list of properties.3. Ensure that the 3D Atomistic document to be analyzed is the active document.4. Select COSMO point charges from the list of properties to show.5. Click the Import button.To create a sigma chart1. ChooseModules | DMol3 | Analysis from themenu bar.2. Select Solvation properties from the list of properties.3. Ensure that the desired 3D Atomistic document (seedname.xsd) or corresponding output file

(seedname.outmol) is the currently active document.4. Check the View sigma chart on import checkbox.5. Click the Import button.6. A new chart document, seedname Sigma Profile.xcd, is created in the results folder.

Note: The sigma chart is automatically generated and imported at the end of any DMol3 calculationwhich includes solvent. Creating the sigma chart from the DMol3 Analysis dialog will generate a newcopy of the same chart.

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Analyzing current and transmission propertiesThe transmission function provides an assessment of how electrons are transmitted between electrodesas a function of their energy. It is often fundamental to the understanding of other transport properties.The current/voltage chart shows how the current through an electrode depends on the appliedpotential.To perform current analysis1. ChooseModules | DMol3 | Analysis from themenu bar.2. Select Current from the list of properties.3. Ensure that the desired 3D Atomistic document (seedname.xsd) is the currently active document.4. Click the View button.To perform transmission analysis1. ChooseModules | DMol3 | Analysis from themenu bar.2. Select Transmission from the list of properties.3. Ensure that the desired 3D Atomistic document (seedname.xsd) is the currently active document.4. Click the View button.

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DMol3 jobsThe topics in this section cover controlling and running remote DMol3 jobs, running jobs in standalonemode, deviations from the generic remote job procedure, and potential reasons why DMol3might fail.

Using DMol3 job controlMaterials Studio can run DMol3 jobs as background processes on a server. The following tools areprovided to setup and control the jobs:n Use the Job Control tab on the DMol3 Calculation dialog to select the gateway location and job

parameters.n Use the Server Console to add new servers and to monitor multiple jobs.n Use the Job Explorer to monitor multiple jobs.For further information on using job control see themain job control and live updates help topics. Liveupdates can be requested on the DMol3 Job Control Options dialog.

Remote DMol3 jobsDMol3 in Materials Studio uses a client-server architecture so you use your PC to control calculations ofthe total energy and electronic properties of a system, or geometry optimization running on a remotecomputer. This separation of the client user interface from the server system running calculations allowsyou to use a high performance supercomputer from yourWindows desktop PC. It also allows you to usespare CPU cycles on other desktop PCs.DMol3 jobs are controlled by input files that are generated by Materials Studio when you start a job.DMol3writes the results of the calculations in various output files which are loaded upon job completioninto your Materials Studio project.DMol3 remote jobs run according to the standard sequence of processes described in A sample remotejob run with the differences explained in the Sample DMol3 run help topic.

A sample DMol3 runWhether you perform a single-point energy calculation, minimize a structure, run a molecular dynamicssimulation, or perform a transition-state search, the sequence of steps that is executed to run a remoteDMol3 job is always the same. When you click the Run button on the DMol3 Calculation dialog, thesteps described in A sample remote job run happen with the following differences:For all calculations using the COSMO solvation model a COSMO Sigma Profile plot, named <seedname>Sigma Profile.xcd, is returned.For Energy calculations, ifn Update structure is checked: there is no effect, as no structural changes are associated with this task.n Update graphs is checked: there is no effect.n Update textual results is checked: Materials Studio downloads a text file called Status.txt that

contains a summary of the calculation performed (task, DFT functional, basis set, system charge andspin, etc.), the SCF iteration number, the total energy, and the total energy convergence (i.e., thechange from the previous iteration).

For Geometry Optimization calculations, if

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n Update structure is checked: Materials Studio downloads a snapshot of the structure and modifies acopy of the original structure accordingly.

n Update graphs is checked: Materials Studio creates a chart document called [seedname]Energies.xcd, showing the total energy versus optimization step, and another chart documentcalled [seedname] Convergence.xcd, showing, on the logarithmic scale, the total energy change,themaximum displacement, and themaximum force versus optimization step.

n Update textual results is checked: Materials Studio downloads a text file called Status.txt thatcontains a summary of the calculation performed (task, DFT functional, basis set, system charge andspin, etc.), the SCF iteration number, the number of completed optimization steps, the total energy,the total energy convergence (i.e., the change from the previous iteration), themaximumdisplacement, and themaximum force for the last completed optimization step.

For Dynamics calculations, ifn Update structure is checked: Materials Studio downloads a snapshot of the structure and modifies a

copy of the original structure accordingly.n Update graphs is checked: Materials Studio creates a chart document called [seedname]

Constant.xcd, showing the constant ofmotion versus simulation time, and another chartdocument called [seedname] Temperature.xcd, showing the temperature versus simulationtime.

n Update textual results is checked: Materials Studio downloads a text file called Status.txt thatcontains a summary of the calculation performed (task, DFT functional, basis set, system charge andspin, etc.), the number of completed dynamics steps, the temperature, and the constant ofmotionfor the last completed optimization step.

For TS Search calculations, ifn Update structure is checked: Materials Studio downloads a snapshot of the structure and modifies a

copy of the original structure accordingly.n Update graphs is selected: Materials Studio creates a chart document called [seedname]

TransitionState.xcd, showing the total energy versus reaction coordinate. For each phase ofthe transition-state search, a separate graph is displayed within the chart document.

n Update textual results is selected: Materials Studio downloads a text file called Status.txt thatcontains a summary of the calculation performed (task, DFT functional, basis set, system charge andspin, etc.), the SCF iteration number, the phase of the transition-state search currently beingprocessed (whether for a maximum or relativeminimum), the reaction path coordinate, the totalenergy, the total energy convergence (i.e., the change from the previous iteration), and the RMSdisplacement and RMS force for the last completed optimization step.

For TS Optimization and TS Confirmation calculations, the behavior is the same as for a GeometryOptimization run.Once the job has finished, Materials Studio will transfer the output files back to your PC, where you canview and edit them, analyze the results, or use them for further calculations. Additional output files maybe generated or modified depending on the type of calculation you performed.

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n For Energy runs, Materials Studio downloads all the DMol3 output files.n For Geometry Optimization runs, Materials Studio downloads all the DMol3 output files, updates the

structure it has copied into the results folder to show the final geometry, and creates a trajectory file,[seedname].xtd, that contains the history of the optimization process. The trajectory file can beanimated using the tools on the Animation toolbar.

n For Dynamics runs, Materials Studio downloads all the DMol3 output files, updates the structure ithas copied into the results folder to show the configuration at the beginning of the dynamics run,and creates a trajectory file, [seedname].xtd, that describes themolecular dynamics calculation.The trajectory file can be animated using the tools on the Animation toolbar.

n For TS Search, TS Optimization, and TS Confirmation runs, the behavior is the same as for a GeometryOptimization run.

The description given above is somewhat simplified, but provides a reasonable overview of a DMol3 run.

If a remote DMol3 job failsMaterials Studio checks most of the data and settings required to perform a DMol3 job prior to launch.If it cannot start the job, error messages are generated detailing the reasons.However, sometimes jobs may fail for reasons which cannot be checked prior to launch. In such cases,an error message giving more detailed information appears in the [seedname].outmol file producedby the job and, in some situations, in the job log window as well. Other files stored in the job directoryon the server may also contain further clues. To view the server-side files, you can use the Remote Viewfacility of the Job Explorer.Below is a list of themost common reasons for DMol3 jobs to fail. It may help you to identify and fix anyproblems you have with your remote DMol3 jobs. For generic reasons for remote job failures pleaseconsult the If a remote job fails help topic.

Tip: Select View | Project Log from themenu bar to see if any error or warning messages have beenreported.

Cannot start a DMol3 jobRun button is grayed outn The active document is not a 3D Atomistic document.

If something other than a 3D Atomistic document is the current document, a chart or text document,for example, then the Run button will be grayed out. To run the calculation, select an appropriatedocument.

n The active document is 2D periodic.DMol3 can only operate on molecules and 3D periodic structures. To model a 2D structure, build aslab with a region of vacuum from the surface.

n The active document does not contain a trajectory and you are trying to perform a transition-statesearch.To perform a transition-state search, you must first create a trajectory using the Reaction Previewtool. See Transition state searching via synchronous transit methods for additional information.

Common reasons for a DMol3 job to fail to startServer-side problems

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n Parallel DMol3 job fails with runtime input/output error message under Linux.Depending upon the options selected, DMol3may use significant amounts of disk space to storescratch files. Scratch files are created by each node during the execution of a parallel DMol3 job.DMol3 uses the value of the environment variable GATEWAY_TMP as the location to be used to savethese files; this variable is set by share/bin/ms_vars.sbd and can be changed using the gateway'sweb interface. You should ensure that the location that will be used on each node points to a filesystem with at least 1 GB of free space. Note that the ./tmp setting for GATEWAY_TMP correspondsto using the common file space on the head node, in the actual job directory, to store the temporaryfiles. This setting can have a detrimental effect on the performance of Linux clusters.An additional problem may occur if the NFS mount of the head node file system is set up incorrectlyon the nodes. This mount should be done in a synchronous mode using hard mounts, as detailed inInstalling Materials Studio on Linux systems.

n DMol3 job fails when B3LYP functional used.B3LYP calculations are very demanding in terms ofmemory use. The exact amount ofmemoryrequired for a B3LYP calculation is not easy to estimate, but DMol3will try to optimize the algorithmto fit within the requested limit. If the job fails, either try to allocatemorememory (if available) ormodify the job parameters (such as basis set size, atomic cutoff, or system size) to reduce theamount ofmemory required.

Tip: It is important to identify the reason for the failure of a DMol3 job before taking any action. Inmost cases, the error message will give a good indication of the reason for the failure. If the errormessage indicates that the job failed, but does not provide specific reasons, check the[seedname].outmol file produced by the job or check the project log.

Note: If a job with File usage set to Memory fails, restart files will not be created.

Running DMol3 in standalone modeThemost convenient way of running DMol3 is through theMaterials Studio interface, which performs allthe preparatory tasks required to run a DMol3 job. However, in some circumstances, it may benecessary to run DMol3 in standalonemodewith a set of input files prepared elsewhere. For example,you may wish to use results files from an earlier DMol3 calculation or you might want to run a calculationon a server that has not been configured as a gateway (i.e., a computer that does not communicate withyour Materials Studio client).

Generate the input filesIn order to run, DMol3 requires an .input file containing specifications for the calculation and a .carfile containing the Cartesian coordinates of the atoms. Some calculations also require an .mdf or .arcfile. You can create these files using a text editor, such as WordPad on Windows or vi on Linux. However,because the number of input files required is quite large and the information they contain quitecomplex, you should useMaterials Studio to generate them for you. You can create the required filesusing the DMol3 Job Files dialog, see the Running jobs in standalonemode topic for further information.

Transfer the input files to the serverIf you generated the input files manually using a text editor on the server machine, then no file transferis required. However, if you generated the files on your PC using Materials Studio, you must transferthem to the server before you can start the calculation.If you are unable to access the hard drive on the server, you should use the File Transfer tool to transferfiles from the client to the server.

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Execute the jobTo assist you in running DMol3 in standalonemode, a batch/shell file called RunDMol3 is supplied. It canbe found in the directory in which the DMol3 executables are located, usually etc/DMol3/bin in themain Materials Studio directory. RunDMol3 scripts are used to start DMol3 jobs in standalonemode.RunDMol3.sh is provided for Linux servers, while RunDMol3.bat is provided for Windows servers.Usage:

RunDMol3.sh [-h] [-nodelete] [-np number of cores] [-q queue name] seedname(Linux)or

RunDMol3.bat [-h] [-nodelete] [-np number of cores] [-q queue name] seedname(Windows)

Argument Description

-h Displays the help text.

-nodelete Specifies whether job and scratch files created during DMol3 execution aredeleted. When this option is used, all temporary and scratch files areretained on the server. If the option is not used, the script deletes these filesupon the termination of the job.

-np Specifies the number of cores on which to run DMol3. When this option isnot specified a single core is used.

number of cores The number of cores to use.

-q Submits the job to the specified queue.

queue name The name of the queue on which to run the job.

seedname The seed used to identify the set of DMol3 input and output files. The inputfiles should be present in the directory in which the DMol3 script is started.

If you wish to calculate properties, you should execute the script for themain run first:

RunDMol3.sh -nodelete seedname

When that run is complete, you should make copies of the .car, .tpdensk and .tpotl files that willbe used in all subsequent properties runs:

cp seedname.car seedname_BandStr.carcp seedname.car seedname_DOS.caretc

Specifically, one needs the following files for a DOS calculation:

seedname_DOS.tpotlseedname_DOS.carseedname_DOS.kpoints (for periodic structures only)seedname_DOS.tpdensk (for periodic structures only)

and the following files for a Band structure calculation:

seedname_BandStr.tpotlseedname_BandStr.car

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seedname_BandStr.kpoints (for periodic structures only)seedname_BandStr.tpdensk (for periodic structures only)

When the appropriate copies have been made, execute RunDMol3 for each properties run:

RunDMol3.sh -nodelete seedname_DOSRunDMol3.sh -nodelete seedname_BandStr

These jobs can be run independently because they do not share input or output files.When running jobs on computers equipped with a queuing system it may be necessary to define certainenvironment variables which DMol3 is using:n DMOL_TMP - directory where DMol3will store large temporary files during calculation. By default it is

/var/tmp on Linux and C:\TEMP on Windows.n DMOL3_DATA - directory containing DMol3 runtime files, for example BASFILE, AREP, DSPP etc. The

default location is share/Resources/Quantum/DMol3.

Download the output files from the serverWhen the DMol3 calculation is complete, you must transfer the output files back to your PC for analysisin Materials Studio. See Running jobs in standalonemode for further information.To transfer the output files back to your PCTransfer the following output files to the client PC either using copy and paste or the File Transfer tool:

seedname.carseedname.mdfseedname.outmolseedname.tpdenskseedname.hessianseedname.hesswkseedname.arcseedname*.summseedname*.grdseedname*.bandsseedname*_pdos.weights

If DOS or band structure calculations were performed, all above files with seedname_DOS andseedname_BandStr should also be copied.Not all of these files will necessarily be present in every case.

Tip: If you have transferred files into a Materials Studio project folder, but you cannot see them in the

Project Explorer, try using the Refresh button to update the Project Explorer.

Open the output files in Materials StudioProvided that you have transferred the correct files from the server to your PC and stored them in afolder in a Materials Studio project, you should be able to make use of the DMol3 analysis optionsdescribed in the topic Analyzing DMol3 results.To view the final geometry

Open the .xsd file, you should use the Structure section on the DMol3 Analysis dialog, click theUpdate button. See the Updating structure topic for more information.

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To create a chart of energy and/or gradients vs. geometry optimizationOpen the .xsd file, you should use the Energy evolution section on the DMol3 Analysis dialog, clickthe View button. See the Displaying trajectory and chart data topic for more information.

To link the charts to a trajectoryYou can use the resulting trajectory and chart documents as described in the Displaying trajectoryand chart data topic.

To perform vibrational analysis1. Open the .xsd file from the calculation by double-clicking on the file in the Project Explorer.2. Load a .hessian file using the Insert Into Active Document dialog.3. Navigate to and select the .hessian file you wish to load into the project.4. Click the Insert button.5. When a .hessian file has been associated with a structure, you can make use of the Vibrational

Analysis dialog, which is accessed from the Tools menu.To perform charge, spin, and bond order analysis

Open the .xsd file, you should use the Population analysis section on the DMol3 Analysis dialog, todisplay atomic charges, spins, and bond orders. See the Displaying population analysis results topicfor further details.

DMol3 file formatsThe DMol3 server program requires a number of different input files and produces a number of outputfiles. The number and type of input files required and output files produced depend on the details of theDMol3 job to be performed.The table below summarizes information on the format and purpose of themajor file types, andprovides links to further information.

File type Input or Output Brief description

.input Input General input file

.car * Input / Output Cartesian coordinates

.mdf * Input Supplementary structure information

.outmol Output Textual results of the calculation

.hessian * Input / Output Hessian matrix

.tpvec * Input / Output LCAO MO coefficients

.tpdensk * Input / Output Charge density

.hesswk * Input / Output Components of a finite-difference Hessian

.arc * Input / Output Trajectory data

.grd * Output Volumetric data

.occup * Input / Output Orbital occupations

.bands * Input / Output Eigenvalues

.pdos_weights * Input / Output Weights required to calculate PDOS

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File type Input or Output Brief description

.cosmo * Output Solvent charges and COSMO details* These files are hidden by default, so they will not appear in theMaterials Studio Project Explorer; thesefiles are only visible in Windows Explorer ifWindows on your machine is configured to show hidden files.

DMol3 file formats - ARCDMol3 stores an optimization history of a calculation in the .arc file. When you run a geometryoptimization, TS optimization, or TS search, each geometry and energy is written to the .arc file. This isreturned to theMaterials Studio client and may be used to analyze the trajectory of the optimization asdescribed in Displaying trajectory and chart data.See the ARC file format topic for details of the .arc file.

DMol3 file formats - BANDSThe .bands file contains electronic eigenvalues for a DMol3 job. The data in this file are used for bandstructure plotting and optics, DOS, and PDOS calculations.The eigenvalues are given in atomic units. The k-points are specified using fractional coordinates, whichare followed by the corresponding k-point weight.

Note: For nonperiodic systems, the number of k-points is specified as 0 in the .bands file.

DMol3 file formats - CAR andMDFDMol3 reads data from the .car file. This file is generated by Materials Studio when youn launch a calculationn select Save Files from the Job Files dialog orn export a file using File | ExportThe data read include Cartesian coordinates, atom labels, and element types. Other data may bepresent in the .car file, but are ignored. At the end of a calculation, the coordinates in the .car file areupdated by DMol3.When a .car file is created by Materials Studio an .mdf file is also written. DMol3 jobs do not require an.mdf file, but if one is present DMol3 reads the following from it:n Bonding information, used to construct internal coordinates for the optimizer. When no .mdf file

exists, DMol3 generates bonds based on proximity of atoms.n The presence of any frozen atoms. If there is a set named "MDF_FIXED_ATOMS_SUBSET" then the

Cartesian coordinates of these atoms will be held fixed. If this subset is not present, all atoms will bemoved. Such a set is generated by Materials Studio whenever needed.

n The presence of any partial Hessian atoms. If there is a subset named "HessianAtoms" in the .mdffile, then only these atoms will be perturbed during the finite-difference evaluation of the Hessian. Ifthis subset is not present, all atoms will bemoved. This information is ignored if you are not runninga Hessian or frequency calculation or explicitly choose to use all atoms in the DMol3 frequencycalculation. Such a set is generated by Materials Studio whenever needed.

DMol3 file formats - COSMOWhen Use solvation model calculation is specified on the Electronics tab of the DMol3 Calculation dialogthe results folder will contain a .cosmo file. This file contains information related to the solvent effect ona studied system.

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The first part of the file contains details of the solvent-related input. The data is taken either fromspecifications in the .input file or from internal DMol3 defaults.The second part of the file lists atomic centers and corresponding COSMO surface/charge parameterson a per-atom basis.The third part of the file lists output energies and properties calculated with the COSMO IBS formalism.COSMO-related energy components are listed in Hartree, eV, and kcal/mol.The last and largest part of the file contains a table with COSMO segment details. For each segment theposition, charge, corresponding area, and potential are listed.The information in the $segment information part can be used for further analysis, for examplecalculating COSMO Sigma profiles.

DMol3 file formats - GRDThe .grd file stores 3D volumetric data. These files may be imported and used to create fieldsisosurfaces and 2D slices of volumetric data. See GRD file format for more detailed information on thisfile.

DMol3 file formats - HESSIANADMol3 geometry optimization begins with an initial guess for the Hessian and updates it with eachoptimization step. After each step, the latest Hessian data are stored in the .hessian file.The final Hessian in a DMol3 vibrational frequency or Hessian evaluation is also saved in the .hessianfile.You can use an existing .hessian file for the initial guess in a geometry optimization or a transitionstate optimization as described in Restarting a DMol3 calculation.See the HESSIAN file format topic for an explanation of the format of the .hessian file.

DMol3 file formats - HESSWKWhen DMol3 performs a vibrational frequency or Hessian evaluation, it evaluates the Hessian by finitedifferences of gradients. This requires an evaluation of the forces for each possible Cartesiandisplacement of atoms in themolecule. The gradients for each displacement are stored in the .hesswkfile. Once all the displacements have been performed, the data are consolidated into a .hessian file.If a Hessian calculation terminates before all the displacements have been performed, you can supplythe .hesswk as input. DMol3 can read the data from a .hesswk and continue the job from the point oftermination. This procedure is described in Restarting a DMol3 calculation.The format of the .hesswk file is explained in detail below:The file begins with one line for each atom in the file describing the integration mesh.Including this information ensures that a restarted calculation uses the samemesh. These lines aregenerated by the program; users should not alter them.Following this come the forces for each atom for each displaced geometry. Each section begins withthree integers that indicate:n The number of the atom being moved (as numbered in the car file)n The direction of the displacement, 1=x, 2=y, 3=zn Whether the direction is in the positive or negative direction, 1 or 2, respectively.Following these integers is the step size in Bohr and the binding energy in Hartree. The next line containsthe forces on each atom in Hartree per Bohr. The order of the atoms is the same as in the .car file. Afterthe Cartesian forces appears the dipole moment in atomic units at the displaced geometry.The first list of forces is for the undisplaced geometry, and uses "0 0 0" as the integers to indicate that.

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DMol3 file formats - INPUTThe DMol3.input file supplies the parameters for a job including, for example, the type of calculation,charge, spin state, and convergence tolerances. The file consists of lines, keywords and options.A .input file is generated by Materials Studio when you launch a calculation or when you select SaveFiles from the DMol3 Job Files dialog. Job options selected through the interface appear as keywords inthe resulting .input file.Under special circumstances you may wish to add manually certain keywords to an .input file that arenot supported in the interface. The procedure is described in Manipulating files.The following rules govern keywords in the .input file:n Line width is 80 charactersn Delimiting character is a space, tabs are not supportedn Keywords may appear in any ordern The keywords and values are case-insensitiven Only one keyword and its options may appear on a linen Keywords that do not appear in the .input file are set to their default valuesn Comment lines (those beginning with "#") and blank lines are ignoredA typical .input file has the form:

# Commentkeyword_1 option_1keyword_2 option_2# Commentkeyword_3 option_3...Keywords and options are fully described in DMol3 keywords in the online help.

DMol3 file formats - OCCUPWhen Fixed is specified for the value of the Occupation keyword the occupations are read from the.occup file.The basic format of the occup file is:

N oc od Representation

in format (I5, 2f10.6,2x,a).n N (integer) indicates the number of orbitals having this occupationn oc (real) is the spin-up (alpha) orbital occupation numbern od (real) is the spin-down (beta) orbital occupationn Representation is the symmetry symbol of the orbital occupationTerminate the occupation for each irreducible representation with a line containing N=0.

DMol3 file formats - OUTMOLThe .outmol file contains the numerical output of a DMol3 job in text format. The header describes thesettings used and system specifications (unit cell vectors, atomic coordinates), followed by thecalculation results.

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DMol3 file formats - PDOS_WEIGHTSThe .pdos_weights file contains the weights that are required to generate partial densities of state(PDOS), based on the results of a DMol3 job.

DMol3 file formats - TPVECThe .tpvec file holds themolecular orbital coefficients for a wavefunction. These are available formolecules and solids using the Γ-point. For solids using multiple k-points, the charge density is storeddirectly in the .tpdensk file.The .tpvec file is updated after each SCF iteration. At the end of a calculation, you can use the .tpvecfile to supply an initial SCF guess to a subsequent calculation, thereby speeding convergence.The .tpvec file is in binary format and is not intended to be read outside of DMol3. The small codesample below illustrates how the data are stored:

read (iunit) ms, (Vec(i),i=1,ms)if(nspin.gt.0) read (iunit) (Vecbeta(i),i=1,ms)read (iunit) (eig(i), elno(i) ,i=1,lx)

where Vec is theMO coefficient for alpha spin (or for closed shells); Vecbeta is the coefficient for betaspin; eig is the eigenvalue in Hartree; and elno is the orbital occupationTheMO coefficients are stored in Vec as a series of symmetry blocks. Say there areN irreduciblerepresentations, and representation i contains n

iorbitals, 1 ≤ i ≤N. Then:

lx = Σ niif nspin=0

lx = 2 × Σ niif nspin>0

ms = Σ ni2

nspin = 0 for restricted calculations and nspin > 0 for unrestricted calculations.

DMol3 file formats - TPDENSKThe .tpdensk file holds the charge density at each integration point for computations using multiple k-points. The .tpdensk file is updated after each SCF iteration. At the end of a calculation, you can usethe .tpdensk file to supply an initial SCF guess to a follow-on calculation, thereby speedingconvergence.The .tpdensk file is in binary format and is not intended to be read outside of DMol3.

Reaction Kinetics Study TableThe results of the reaction rate calculation are collected in a study table which contains three tabs:n Summary - contains a summary of the results, reporting themain parameters of the calculation, fit

coefficients, and root-mean-square error (RMSE) which is calculated for ln(k(T)). If the fit parameters(also shown on theGraphs tab) produce too high n, or Ea becomes negative, the corresponding linesin the study table are highlighted in red.

n Graphs - contains the temperature dependence of the reaction rates coefficients (k(T)) for forwardand backward reactions together with equilibrium constants. It also contains results of the fit usingArrhenius form (see Kinetics constants theory) with temperature T

0= 298 K together with standard

Arrhenius form (n = 0, the temperature independent pre-exponential coefficient).n Partition Function - contains the calculated partition functions for reactant(s), product(s), and

transition state.

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Theory in DMol3

The following topics provide specifics about the theory behind DMol3.

Density functional theory (DFT) in DMol3

This section provides information specific to the implementation of DFT in the DMol3 program.A general overview of DFT is provided elsewhere. The overview provides information on the concepts ofcharge density, DFT functionals, the SCF procedure, and band structures, which are generally applicableto any computational implementation of DFT. The application of dispersion corrections to DFT is alsodescribed. In contrast, this section provides background on aspects of DFT unique to DMol3.

Functionals in DMol3

Local functionalsThe exchange-correlation energy is given by Eq. DFT-7. The specific local functionals provided in DMol3are the VWN functional (Vosko et al., 1980) and PWC (Perdew and Wang, 1992). The default is PWC.

Nonlocal functionalsThe so-called nonlocal or gradient-corrected functionals depend on dρ/dr as well as on ρ. This providesa considerable increase in the accuracy of predicted energies and structures, but with an additional cost.The NLSD functionals available in DMol3 include:

Name Description Reference

PW91 Perdew-Wang generalized-gradient approximation Perdew and Wang (1992)

BP Becke exchange plus Perdew correlation Becke (1988), Perdew and Wang (1992)

PBE Perdew-Burke-Ernzerhof correlation Perdew et al. (1996)

RPBE Revised PBE functional by Hammer et al. Hammer et al. (1999)

PBEsol PBE functional optimized for solids Perdew et al. (2008)

HCTH Hamprecht, Cohen, Tozer and Handy functional Boese and Handy (2001)

BLYP Becke exchange plus Lee-Yang-Parr correlation Becke (1988), Lee et al. (1988)

BOP Becke One Parameter functional Tsuneda et al. (1999)

VWN-BP

BP functional with the local correlation replaced bythe VWN functional.

Vosko et al. (1980), Becke (1988), Perdewand Wang (1992)

Hybrid functionalsThe B3LYP hybrid functional is provided in DMol3 (Becke, 1993, Stephens et al., 1994).Hybrid functionals attempt to improve the exchange-correlation energy functional by incorporating aportion of exact exchange from Hartree-Fock theory along with exchange and correlation contributionsfrom other, mainly local, functionals with carefully chosen weights. The weights are obtained by fittingto experimental data.Apart from the exact Hartree-Fock exchange term, Ex

HF, B3LYP employs the local VWN (EcVWN) and LDA

(EcLDA) correlation functionals as well as local LDA exchange (Ex

LDA). In addition, Becke's gradientcorrection (ΔEx

B88) to the exact exchange and LYP correlation functional (EcLYP) are used.

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Eq. B3LYP-1

E aE a E b E cE c E= +(1 − ) + ∆ + +(1 − )XCB LYP

xHF

xLDA

xB

cLYP

cVWN3 88

Becke (1993) suggested a = 0.2, b = 0.72, and c = 0.81 based on fitting to heats of formation of smallmolecules.

Meta-GGA functionalsIn addition to the generalized gradient (GGA) functionals which depend on the local density and itsgradient, DMol3 can handle functionals that depend on the kinetic energy density:

τ ψ( ) = ∑ ( )i ioccup

i

1

2

2∇r r

The following meta-GGA functionals are available:

Name Description Reference

M06-L Minnesota 2006meta-GGA functional Zhao and Truhlar (2006)

M11-L Minnesota 2011meta-GGA functional Peverati and Truhlar (2012)

Numerical basis setsThematrix elements needed to solve the SCF equations and compute the total energy are given by theexpressions in Eq. DFT-15 and Eq. DFT-16. DMol3 uses numerical orbitals for the basis functions, eachfunction corresponding to an atomic orbital (AO). This section describes in more detail how such orbitalsare generated and used.

Atomic basis sets are generated numericallyThe basis functions χ

μare given numerically as values on an atomic-centered spherical-polar mesh,

rather than as analytical functions (i.e., Gaussian orbitals). The angular portion of each function is theappropriate spherical harmonic Ylm(θ,φ). The radial portion F(r) is obtained by solving the atomic DFTequations numerically. A reasonable level of accuracy is usually obtained by using about 300 radialpoints from the nucleus to an outer distance of 10 Bohr (~5.3 Å).Radial functions are stored as a set of cubic spline coefficients for each of the 300 sections, so that F(r) isactually piecewise analytic. This is an important consideration for generating analytic energy gradients.In addition to the basis sets, the - ∇2/ 2 terms required for evaluation of the kinetic energy are alsostored as spline coefficients.Atomic basis sets are confined within a cutoff value, r

c, appropriate for a particular quality level of DMol3

calculations. This is an important feature of the numerical basis set that can lead to much fastercalculations, particularly for solid state systems. DMol3 uses a so-called soft confinement potential,which ensures the strict localization of the basis set within an r

cvalue, without discontinuous derivatives

at rc. Geometry optimization is efficient, even with small cutoff values.

Advantages of numerically derived basis setsThe use of the exact DFT spherical atomic orbitals has several advantages. For one, themolecule can bedissociated exactly to its constituent atoms (within the DFT context). Because of the quality of theseorbitals, basis set superposition effects (Delley, 1990) areminimized and it is possible to obtain anexcellent description, even for weak bonds.

Additional basis functions, including polarizationGreater variational freedom is obtained by providing larger basis sets. Generation of an entire secondset of functions results in doubling the basis set size; this is referred to as a double-numerical (DN) set.

Theory in DMol3  | Page 63

This notation is used by analogy with Gaussian double-zeta (DZ) sets, but theN is used to emphasize thenumerical nature of these orbitals. Additional basis functions, including polarization, are obtained byseveral procedures:n DFT atomic ion calculationsn DFT excited-state atom calculationsn Hydrogenic orbitalsFor first-row atoms, functions from +2 ions provide a reasonable double basis set. A hydrogenic 3Dorbital obtained for a nucleus of Z = 5 provides a good polarization function for each of these atoms. Ahydrogenic 2p function for Z = 1.3 is used for hydrogen. The use of various nuclear charges to generatepolarization functions is analogous to the variation of zeta in Gaussian basis sets. For metals, 4ppolarization functions are generated by solving the atomic equations for a 4s → 4p excited state. Basisset quality has been analyzed in detail by Delley (1990).The triple-numerical (TNP) set has been recently generated and validated by Delley (2006).The table below summarizes the basis sets used in the program.

BasisName Description Examples

MIN Minimal basis. One AO for each occupied atomicorbital.Yields low accuracy but fast computation.

H: 1sC: 1s 2s 2pSi: 1s 2s 2p 3s 3p

DN Double Numerical. MIN + a second set of valenceAOs.Improved accuracy over MIN.

H: 1s 1s'C: 1s 2s 2p 2s' 2p'Si: 1s 2s 2p 3s 3p 3s' 3p'

DND Double Numerical plus d-functions. Like DNwitha polarization d-function on all non-hydrogenatoms.The default basis set, providing reasonableaccuracy for modest computational cost.

H: 1s 1s'C: 1s 2s 2p 2s' 2p' 3dSi: 1s 2s 2p 3s 3p 3s' 3p' 3d

DNP Double Numerical plus polarization. Like DNDincluding a polarization p-function on allhydrogen atoms.Best accuracy, highest cost. Important forhydrogen bonding.

H: 1s 1s' 2pC: 1s 2s 2p 2s' 2p' 3dSi: 1s 2s 2p 3s 3p 3s' 3p' 3d

TNP Triple Numerical plus polarization. Like DNPincluding additional polarization functions on allatoms.Available only for H to Cl except He and Ne.Best accuracy, highest cost.

H: 1s 1s' 2p 1s" 2p' 3dO: 1s 2s 2p 2s' 2p' 3d 2s" 2p" 3p 4dS: 1s 2s 2p 2s' 2p' 3s 3p 3s' 3p' 3d 3s" 3p"3d' 4d

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BasisName Description Examples

DNP+ Double Numerical plus polarization, withaddition of diffuse functions.Good accuracy for cases requiring diffusefunctions, very high cost coming mostly fromvery large atomic cutoffs required for this set.Important for anions, excited state calculationsand for cases where long-range effects are non-negligible.The bold components are the additional diffusefunctions.

H: 1s 1s' 2p 1s" 2p'C: 1s 2s 2p 2s' 2p' 3d 1s' 2p" 3d'Si: 1s 2s 2p 3s 3p 3s' 3p' 3d 1s' 2p' 3d'

Numerical integrationEvaluation of the integrals in Eqs. DFT-15 and DFT-16must be accomplished by a 3D numericalintegration procedure, due to the nature of the basis functions. Thematrix elements need to beapproximated by the finite sums:Eq. DMol3-1

Eq. DMol3-2

The sums run over several numerical integration points ri. The term Heff

( ri) represents the value of theintegrand of Eq. DFT-15 at point r

iand w(r

i) represents a weight associated with each mesh point.

Increasing the number ofmesh points improves the numerical precision of the integral but also resultsin additional computational cost.

Atomic and molecular integration gridsCareful selection of a set of integration points is important for the quality of the calculation (Delley, 1990;Ellis and Painter, 1968; Boerrigter et al., 1988). In general, the grid used to generate the atomic basis setis not suitable for molecular calculations. The grid used for atomic basis sets can take advantage ofspherical symmetry, which greatly simplifies matters. For molecules, it is necessary to be able tocorrectly handle the rapid oscillations of themolecular orbitals near the nuclei, and to avoid integrationof the nuclei themselves because of the nuclear cusps (Delley, 1990).

Integration points, atomic size, precision, and computational costThe integration points are generated in a spherical pattern around each atomic center. Radial points aretypically taken from the nucleus to an outer distance of 5.5 Å (~10.4 Bohr). The number of radial pointswithin this distance is designed to scale with increasing atomic number. For example, Fe requires morepoints than C. The typical number of radial points N

Rfor a nucleus of charge Z is:

Eq. DMol3-3

Theory in DMol3  | Page 65

This number may, of course, bemanually adjusted to accommodate the required precision or allowedcost of a calculation. The spacing between points is logarithmic. Points are spaced more closely near thenucleus where oscillations in the wavefunction aremore rapid.

Atomic shellsAngular integration points N

θare generated at each of theN

Rradial points, creating a series of shells

around each nucleus. Angular points are selected by schemes designed to yield points ri and weights w(ri), which could yield exact angular integration for a spherical harmonic with a given value of l. Suchquadrature schemes (Stroud, 1971; Lebedev, 1975 and 1977; Konyaev, 1979) are available for functionsup to l = 41. Alternatively, a product-Gauss rule in cos θ and ϕ may be used for arbitrary values of l(Stroud, 1971). The product-Gauss methods use (l + 1) points on each shell, while the quadraturemethods usemore points. The scheme used in DMol3 provides the following numbers of points for eachvalue of l:

l 5 7 11 17 23 29 35 41

Nθ 14 26 50 110 194 302 434 590

Assuring consistent precision during integrationIn practice, few angular points are needed near the core or far from an atomic center, since the chargedensity is fairly homogeneous. By contrast, in the valence region around an atom the angular densityvaries quite a bit. Therefore, one would like to use as many points as practical to assure good precision;at the same time, one does not want to usemore points than are necessary, as this increases the cost ofthe calculation. In DMol3 the number of angular points is "ramped-up" from a modest value near thenucleus to a maximum value in the valence region. Input may be used to fine tune the precise numberof points, but a typical calculation will use about 1000 points per atom.

Partition functions improve convergence and avoid nuclear cuspsPartition functions are used to increase the convergence of the numerical integration and to avoidintegrating over nuclear cusps (Delley, 1990; Hirshfeld, 1977; Becke, 1988). A partition function ρ

αis

defined as:Eq. DMol3-4

where α is an atom index and gα(r - R

α) is a function that typically is large for small r - R

αand small for

large r - Rα(i.e., larger near the nucleus). Integrals are rewritten using partition functions as:

Eq. DMol3-5

which is further reduced to a sum over 3D integration points:Eq. DMol3-6

In practice, the partition functions are combined with the integration weights w(ri) to simplify thecomputation. The default choice for a partition function is:

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Eq. DMol3-7

where r = |ri - Rα|, r

0= 0.5, and ρ

ais the atomic charge density for atom α. Other options for partition

functions are available in DMol3 but are not recommended.Evaluation of the exchange-correlation energy, E

xc, may be accomplished by numerical integration of the

expression in Eq. DFT-7. Matrix elements of the exchange-correlation potential are evaluated byinserting the expression for μ

xcfrom Eq. DFT-11 into Eq. DFT-17 in place ofH

eff.

This requires numerical evaluation of the charge density ρ(r) at many points in space (i.e., εxc and μxc aretabulated numerically). This restriction actually applies to most density function methods, even ifanalytical basis functions are used (Andzelm et al., 1989; Versluis and Ziegler, 1988). The use of numericalbasis functions facilitates this process, since all required quantities are already available on a grid ofadequate numerical precision. An alternative approach (Baerends et al., 1973) is to fit the charge densityto an analytic multipolar expansion via a least-squares fitting procedure. This simplifies the evaluation ofεxc and μxc, but still requires the use of a numerical grid for the least-squares fitting.

PseudopotentialsPseudopotentials reduce computational effort by replacing some basis functions with a simplifiedanalytic or numerical form. Thematrix elements over these functions need to be computed only onceand are excluded from the self-consistent field procedure.Consider a molecule or solid as a collection of valence electrons and ion cores. The ion cores containnuclei and tightly bound core electrons. The valence electron wavefunctions are orthogonal to core-electron wavefunctions. All-electron DFT methods treat core and valence electrons on an equal footing.In the pseudopotential approach ion cores are considered to be frozen. This means that properties ofmolecules or solids are calculated on the assumption that the ion cores are not involved in chemicalbonding and do not change as a result of structural modifications.The pseudopotential approximation replaces core electrons and the strong Coulomb potential by aweaker pseudopotential that acts on a set of pseudo wavefunctions. Matrix elements of this potentialcan be computed efficiently. Pseudo wavefunctions ideally should have no nodes inside the core regionsand thus they may be represented by a small number of functions.Traditionally, pseudopotentials are constructed so as to reproduce faithfully the scattering properties ofthe full ionic potential. The phase shift produced by the ionic core is different for each angularmomentum component (s, p, d, etc.) of the valence wavefunction. Thus, the scattering from thepseudopotential must be angular momentum dependent. Themost general form for a pseudopotentialis:VNL

= Σ |lm> Vl <lm|where |lm> are the spherical harmonics and Vl is the pseudopotential for angular momentum l. Apseudopotential that uses the same potential in each angular momentum channel is called a localpseudopotential. Local pseudopotentials are computationally much more efficient than a nonlocal ones,however, only a few elements can be described accurately using local pseudopotentials.DMol3 offers three different ways to treat the core electrons:

Theory in DMol3  | Page 67

1. DSPP: The Density functional Semi-core PseudoPotentials were generated by fitting all-electronrelativistic DFT results. Thus the DSPPs have been specifically designed to reproduce accurate DMol3calculations. These potentials have a nonlocal contribution for each channel up to l =2, as well as anonlocal contribution to account for higher channels. The potentials are norm conserving.

2. ECP: The Effective Core Potentials (Dolg et al. 1987, Bergner et al. 1993) are best used in Hartree-Fockcalculations. DSPP is now the preferred method for DFT calculations.

3. Scalar relativity: These potentials do not replace core electrons; instead they supplement the corepotentials with approximate relativistic effects. Such effects are important for heavier elements, andare certainly required starting with the second row of transition metals (element 39, Yttrium). Usingthese potentials yields themost accurate results, though at the highest cost. The DSPP also includerelativistic effects.

You cannot restrict the use of ECPs or DSPPs to specific elements. Whenever you use either option,DMol3 examines a data file that contains the potentials. If DSPP or ECP data are found for an element,then the core electrons for that element are replaced; if the data are not found for an element, then allits electrons are retained. Currently, DSPPs and ECPs are provided beginning with element number 21,Sc. For example, in a system containing H, O, Al, Cu, and Au, if you opt to use ECPs or DSPPs, only thecore electrons for Cu and Au will be replaced; H, O, and Al will be treated as in the all-electron case.

Norm-conserving pseudopotentialsThemain requirement of the pseudopotential approach is that it reproduces the valence charge densityassociated with chemical bonds. It has been shown (Hamann et al., 1979) that for pseudo and all-electron wavefunctions to be identical beyond the core radius, R

c, it is necessary for the integrals of

squared amplitudes of the two functions be the same. This is equivalent to requiring norm-conservationfrom pseudo wavefunctions, i.e. that each of them should carry exactly one electron. This conditionensures that the scattering properties of the pseudopotential are reproduced correctly.

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Figure 1. Schematic representation of the all-electron and pseudo wavefunctions and potentials

The typical method for generating pseudopotentials is as follows. All-electron calculations are carried outfor an isolated atom in a chosen electronic configuration (not necessarily in the ground state). Thisprovides valence electron eigenvalues and valence electron wavefunctions for the atom (shown as ψ inFigure 1). A parameterized form for the ionic pseudopotential (or the pseudo wavefunction) is chosen.The parameters are then adjusted, so that a pseudoatom calculation with the same exchange-correlation potential as the all-electron atom gives pseudo wavefunctions, ψ

ps(Figure 1), that match the

valence wavefunctions outside some cutoff radius, Rc, and pseudoeigenvalues that are equal to the

valence eigenvalues. This procedure involves direct inversion of the radial Kohn-Sham equation in thecase when the pseudo wavefunction, and not the pseudopotential itself, is parameterized. If eachwavefunction, pseudo and all-electron, is normalized to one, then the norm-conservation constraint isautomatically satisfied as a result ofmatching the wavefunctions outside R

c.

Evaluating the Coulombic potential numericallyThe Coulombic potential is evaluated by solving the Poisson equation for the charge density:Eq. DMol3-8

rather than by explicitly evaluating the Coulombic term as:Eq. DMol3-9

Theory in DMol3  | Page 69

In the this approach, the Poisson equation is solved in a completely numerical (non-basis set) approach(Delley, 1990). This provides greater numerical precision, since the evaluation of V

eis essentially exact

once the form of ρ(r) has been specified. Such a method requires specification of an analytic form of ρ(r),as discussed above. However, rather than use a least-squares fitting procedure, a projection scheme isused. The charge density is first partitioned into atomic densities and then decomposed into multipolarcomponents. Appropriate partition functions can ensure that such an expansion is rapidly convergent.

The model charge densityThe density obtained in this way is called themodel density. The term ρ

alm |r - R

α| gives themodel

density for themultipolar component lm on atom α for a shell at |r - Rα| distance from the nucleus:

Eq. DMol3-10

Note that the partition function pαused for decomposition of the density is in general not the same as

that used to improve the numerical integration in Eq. DMol3-6. The total model density is obtained fromthe summation over all ρ

alm:

Eq. DMol3-11

Effect of angular truncation on precision of model charge densityThe total model charge density is, in general, not equal to the orbital density ρ because of angulartruncations. However, the flexibility of this model charge density is superior to that obtained with fittingprocedures. The degree of angular truncation can be specified as an input parameter. Typically, a valueof l one greater than that in the atomic basis provides sufficient precision; for example, the use of l = 3truncation when p functions are present in the basis or l = 2 truncation if only p functions are used.

The Coulombic potentialThe Coulombic potential for each component is calculated using the Green's function of the Laplacian(Delley, 1990):Eq. DMol3-12

The total potentialThe total potential is given by:Eq. DMol3-13

Computational self-consistent field procedureInterpolating the numerical atomic bases onto the molecular gridBefore the self-consistent field (SCF) procedure can be used, a step is required that is analogous to theevaluation of integrals over atomic orbitals, such as in Hartree-Fock methods. This is the interpolation of

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the numerical atomic basis set onto themolecular grid. Neglecting symmetry and any frozen-coreapproximations, this step requires a computational effort on the order ofN × P for N atomic orbitals andP integration points. The basis set is controlled by the user, the number of points typically being on theorder of 1000 points per atom. The overlap matrix (Eq. DFT-16) and the constant portion of the effectiveHamiltonian (Eq. DFT-15) (kinetic and nuclear attraction terms) are constructed at this time, and eachrequires N × (N + 1) × P operations. The interpolated values can be stored externally and read as they arerequired. Alternatively, these data can be generated as needed, obviating the need for storage. This istermed a direct SCF procedure, by analogy with the direct Hartree-Fock method (Almlöf et al., 1982).

Constructing the initial molecular electron densityIn practice, it is more convenient to skip choosing an initial C

iμand constructing an initial set of ϕi, and

to begin instead with an initial ρ constructed from the superposition of atomic densities (quantities thatare readily constructed from the numerical atomic basis set). In the SCF procedure, reconstruction ofthe new density requires a computational effort on the order ofN ×N

ox P, whereN

ois the number of

occupied orbitals.

Additional computational costsOnce ρ(r) is known, evaluation of the exchange-correlation potential μ

xcrequires only P operations.

Construction of the Coulombic potential requires only P ×M effort, whereM is the number ofmultipolarfunctions.M is typically on the order of 9 functions atom-1 (l = 2) or 16 functions atom-1 (l = 3). Neither ofthese steps is especially time consuming.Construction of the Hamiltonian matrix elements (Eq. DFT-14) is among themost time-consuming steps,requiring N × (N + 1) × P operations each iteration. Solution of the secular equation is also timeconsuming, requiring N3 operations. This can be reduced by solving only for the eigenvectorscorresponding to occupied orbitals to N2 ×N

o.

Reducing the computational costFor large systems, the computational cost does not necessarily grow as rapidly as implied by the abovecomments. Since the atomic basis functions have a finite extent (~10 Bohr), only a limited number ofpoints contribute to each matrix element and P eventually converges to a constant. In addition,construction of the density and the secular matrix can be accomplished using sparsematrix multiplierroutines, further reducing the computational cost.

Damping and convergenceConstruction of a new density follows solution of the secular equation. Damping is usually required toensure smooth convergence. In the current method, simple damping is possible:Eq. DMol3-14

where d is the damping factor, ρold

is the density that was used to construct the secular matrix, ρnew

isthe density constructed from the newMO coefficients without damping, and ρ is the density that isactually used in the next iteration. An interpolation/extrapolation scheme is available. This techniqueconstructs an effective vector from ρ

oldto ρ

newfor the current iteration and for the previous iteration.

The effective vectors are generally skew vectors. The point of closest approach between ρold

and ρnew

isused to extrapolate the actual density for the next iteration.

Efficiently calculating the electrostatic potentialThe equations of density functional theory include an electrostatic potential arising from the negativelycharged electron density. For more efficient calculations, the potential is found by solving the Poisson

Theory in DMol3  | Page 71

equation rather than by the equivalent approach of four-center direct integrals. Using the Poissonequation requires an auxiliary density representation ρ~, which is a function rather than the sum ofsquares of a function. ρ~ differs from ρ (Eq. DFT-4):Eq. DMol3-15

Effect of auxiliary density approximation on accuracy of calculated total energyTo minimize the impact of this difference a total-energy formula is used that is second-order in δρ (Delleyet al., 1983; Delley, 1990; Delley, 1991). The default starting density in DMol3 is the sum of the sphericalatom densities. The total energy calculated in the first SCF cycle is thus the so-called Harrisapproximation (Harris, 1985). The atomic dissociation energy in the first cycle is usually overestimated,since the electrostatic error term for the total energy:Eq. DMol3-16

is negative definite. The less important second-order term for local density functionals is positivedefinite, which leads to a slight overestimation of the total energy during the SCF iterations.The complete total-energy formula, correct to the second order in δρ, is now:Eq. DMol3-17

where

are the densities for spin alpha and beta, respectively; niσ

are the occupations of orbitals with theorbital and spin labels i, σ; εi

σis the corresponding eigenvalue, which has been calculated using the

static V~e and exchange-correlation potential μ~xcσ arising from the spin densities ρ~σand E

xcis the

exchange-correlation functional (local or nonlocal).

SCF convergence acceleration by DIISAmethod based on the direct inversion of the iterative subspace (or DIIS) technique developed by Pulay(1982) has been implemented in DMol3 as a mechanism to speed up SCF convergence. Themethod restson the suitable definition of an error vector that is zero when convergence is achieved and onperforming a linear combination of a set of error vectors sampled along iterations that produces a newerror vector with minimal norm. The DIIS method is much more powerful if one allows for a slightlylarger dimension of iterative subspace. The default dimension currently adopted in DMol3 is 6.The error vector for the DIIS procedure is defined as the difference between the input and output chargedensities:Eq. DMol3-18

The final model density is a linear combination of the densities at each SCF iteration i:

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Eq. DMol3-19

with the constraint that:

The Cicoefficients are calculated by minimizing the norm:

Eq. DMol3-20

Where:

For spin-unrestricted calculations, the error vectors obtained from the total density (sum of densities forelectrons of spin alpha and spin beta) and the spin density (difference of densities for electrons of spinalpha and spin beta) are combined. In practice, the spin density error vector is appended to the totaldensity error vector.Inversion of the DIIS linear equation system is achieved by means of a singular value decomposition.This is necessary for dealing with singularities caused by linear dependencies between error vectors.

Energy gradientsPredicting chemical structureThe ability to evaluate the derivative of the total energy with respect to geometric changes is critical forthe study of chemical systems. Without the first derivatives, a laborious point-by-point procedure isrequired, which is taxing to both computer and human resources. The availability of analytic energyderivatives for Hartree-Fock (Pulay, 1969), CI (Brooks et al., 1980), and MBPT (Pople et al., 1979) theories(to name just a few) has made these remarkably successful methods for predicting chemical structures.The energy gradient formulas for the Hartree-Fock-Slater method were first derived by Satako (1981) andlater implemented practically using Slater basis sets (Versluis and Ziegler, 1988). Others have usedGaussian basis sets to compute derivatives of the DFT energy (Andzelm et al., 1989).

First derivative of total energy with respect to change in nuclear positionThe derivative of the total energy in Eq. DFT-12with respect to a nuclear perturbation in direction a (x, y,or z) of atom αmay be written as:Eq. DMol3-21

where the derivative density is defined as:Eq. DMol3-22

Theory in DMol3  | Page 73

with:Eq. DMol3-23

Derivative of the basis functionThe derivative of the basis function χmwith respect to the perturbation a can be computed analyticallybecause of the representation of the numerical basis sets. The angular portion of χm is a sphericalharmonic function, which is analytic and easily differentiated. The radial portion is represented byseveral cubic splines, each of which is also differentiable.

Derivation of other termsThe derivatives of the eigenvalues can be obtained from Eq. DFT-10. Multiplying by ϕi and integratinggives an expression for εi:Eq. DMol3-24

Differentiating and rearranging yields:Eq. DMol3-25

The terms in Eqs. DMol3-25 and DMol3-29 involving Zαrepresent the Hellmann-Feynman force

(Hellmann, 1937; Feynman, 1939), which gives the derivative in the absence of any orbital relaxation.Substituting Eq. DMol3-25 into Eq. DMol3-21 yields:Eq. DMol3-26

Where Eatis the Hellmann-Feynman term. Now (Andzelm et al., 1989):

Eq. DMol3-27

and recalling the definition in Eq. DFT-11:Eq. DMol3-28

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The final equation for the derivative of the energyTherefore, the terms in Eq. DMol3-26 involving εxc cancel. In addition, if Eq. DMol3-9 is used to constructthe charge density, then the last two terms in Eq. DMol3-26 also cancel, leaving:Eq. DMol3-29

which is formally the same as the equation derived by other researchers (Andzelm et al., 1989; Versluisand Ziegler, 1988). In practice, however, it is necessary to compute both ρVa/2 and ρaV/2, because themodel density from Eq. DMol3-11 is not exactly equal to the numerical charge density computed fromEq. DFT-4.

Computational costsThe time required to evaluate all 3N first derivatives for an N-atom system is typically the same as thetime required for 3-4 SCF iterations. If convergence is achieved in, say, 10-12 iterations, then 25-30%additional time is required to evaluate the derivatives. Others have obtained similar results (Versluis andZiegler, 1988).

Potential problemsBecause of numerical precision, two potential problems have been observed in evaluating gradients.First, the energy minimum does not correspond exactly to the point with zero derivative (Versluis andZiegler, 1988). The gradients are typically about 10-4 at the energy minimum. A second important pointis that the sum of the gradients is not always zero, as it must be for translational invariance. The sumcan be as high as 10-3 if the calculation is very poor. Increasing the quality of the integration mesh andthe number ofmultipolar functions in themodel density can reduce this to about 3.0 × 10-5. Thismagnitude of error seems to be permissible for geometry optimizations: the error introduced in thegeometry is typically on the order of 0.001 Å. Only for very flat potential energy surfaces should this be aproblem.

Minimization algorithms; molecular symmetryCurrently, the geometry is optimized using both Cartesian and internal coordinates. When thegeometry is optimized under conditions of symmetry, only forces that maintain molecular symmetryare evaluated, resulting in considerable time savings. Even in the absence of symmetry, certain forcescan be omitted from the calculation, resulting in faster calculations. For example, for a substrateadsorbed on a metal cluster, it is possible to compute gradients for the substrate only and perform nooptimization on themetal.

Electronic excitations with TD-DFTPredicting UV-Vis spectraPredicting visible and near-visible UV spectra involves calculations of excitations between discreteelectronic levels in a system. These excitation energies indicate the location of absorption peaks in thespectrum, whereas the peak intensities are evaluated by calculating transition dipole moments betweenthe states involved in the given excitation.Themost common means of calculating the excitation energies in the DFT formalism is the Time-Dependent DFT method (TD-DFT). This method has been developed by Runge et al. as an extension ofthe standard, time-independent DFT and implemented in DMol3 by Delley (Delley, 2010).The time-dependent analog of the Hohenberg-Kohn theorem shows that, for a given initialwavefunction, there is a uniquemapping between the time-dependent external potential of a system

Theory in DMol3  | Page 75

and its time-dependent density. This analogy allows themost significant limitation of conventional DFTto be overcome, which is its inability to describe electronic excitations. Excited states in time-independent DFT are not properly described and this shortcoming restricts the use of "conventional"DFT to properties such as optical absorption and emission, polarizabilities, and higher order nonlineareffects.Similar to time-independent DFT the new formalism reduces themany-electron problem to a self-consistent single-particle equation (Vasiliev et al, 2002) :Eq. DMol3-21

which generates time-dependent density:Eq. DMol3-22

Themost convenient way to express these equations is to use the linear responsemethod. The linearresponse function describes how the electron density changes with changes in external potential. Thisfunction describes the response of the charge density to a potential that couples to the charge densityof the system. Because of this, the response function has poles at the excitation energies of the system,meaning that the induced density also has these poles. This method can be used when the external fieldis small (it does not change the ground state) and is therefore treated as perturbation. By the nature ofbeing linear in perturbation, the first order response properties will depend only on the ground statedensity and are therefore easily obtained. The response of the Kohn-Sham density matrix can beobtained by introducing a time-dependent perturbationEq. DMol3-23

which is used as a basis for further calculation of the excited state energies as poles of the responsefunction evaluated with respect to the unperturbed charge densities (linear approximation). The linearresponse of the density matrix expressed in frequency space (through Fourier transformation) δP

σ(ω) is

defined as:Eq. DMol3-24

and is dependent on the difference of occupation numbers λσ, difference of eigenvalues ω -ω

σand

(frequency dependent) SCF response δνσscf.

Computational costsThe responsematrix can be, in general, very large in the order of N

orb*N

orb, where N

orbis the number of

orbitals used in calculation. Diagonalization of such a largematrix is a difficult task but all its eigenvaluesare rarely needed. Themost physically significant are the lowest solutions or lowest energy excitationsand these can be calculated iteratively using, for example, the Davidson iterative process (Davidson,1975).

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Accuracy of excitation energies and orbital overlapThere exists a clear correlation between excitation energy errors and the degree of spatial overlapbetween the occupied and virtual orbitals involved in an excitation. The errors increase as the amount ofoverlap reduces. A simple diagnostic test for judging the reliability of a given excitation is; if the overlap isless than 0.4 the excitation is likely to be in very significant error (Peach et al., 2008). This quantity is notunique and its diagnostic value is qualitative rather than quantitative. However, it captures the essentialphysics of the problem and is useful in practical calculations. The DMol3 output file contains the value ofoverlap for every excitation to assist with the evaluation of potential TD-DFT errors.

TD-DFT in combination with hybrid functionals in DMol3

The DMol3 implementation of time-dependent density functional theory only considers the exchange-correlation functionals which can be defined with the keyword tddft_xc. In particular, the exchange-correlation functional in TD-DFT does not take into account any non-local effects of hybrid functionals. Itis not recommended to use a hybrid functional, such B3LYP, if you intend to run an optical propertycalculation after themain ground state calculation.

Molecular dynamicsMolecular dynamics (MD) involves the stepwise integration of Newton's equations from a given startingpoint. It is themost natural method of performing equilibrium statistical-mechanical calculations viasimulation.Molecular dynamics in total energy DFT schemes is implemented in essentially the sameway as inconventional forcefield-based methods. Themain difference is that the atomic forces are derived bysolving DFT equations rather than from empirical potentials of interatomic interactions. Electrons arekept on the Born-Oppenheimer surface by means of explicit electronic structure optimization after eachMD step. A side effect of this is that evaluation of force and energy from first principles is always themost computationally expensive part of ab initio MD. As a result, the efficiency of theMD step itself hasno impact on the speed of the calculation.MD in DMol3 is based on the velocity Verlet algorithm for integration of the equation ofmotion. Theimplemented algorithm performs the Yoshida-Suzuki multiple-step numerical integration of varyingquality, depending on the choice of interpolation parameter (Y. Liu, 2000, M. Suzuki, 1991, H. Yoshida,1990).

EnsemblesIntegrating Newton's equations ofmotion allows you to explore the constant energy surface of asystem. However, most natural phenomena occur under conditions where the system is exposed toexternal pressure and/or exchanges heat with the environment. Under these conditions, the totalenergy of the system is no longer conserved and extended forms ofmolecular dynamics are required.Several methods are available for controlling temperature. Depending on which state variables - theenergy, E, enthalpy, H (i.e., E + PV), number of particles, N, pressure, P, stress, S, temperature, T, andvolume, V - are kept fixed, different statistical ensembles can be generated. A variety of structural,energetic, and dynamic properties can then be calculated from the averages or the fluctuations of thesequantities over the ensemble generated.Both isothermal (where heat is exchanged with a temperature bath to maintain a constantthermodynamic temperature) and adiabatic (where no heat exchange occurs) ensembles are available:n Constant energy, constant volume (NVE)n Constant temperature, constant volume (NVT)

Theory in DMol3  | Page 77

NVE ensembleThe constant energy, constant volume ensemble (NVE), also known as themicrocanonical ensemble, isobtained by solving the standard Newton equation without any temperature and pressure control.Energy is conserved when this (adiabatic) ensemble is generated. However, because of rounding andtruncation errors during the integration process, there is always a slight fluctuation, or drift, in energy.True constant energy conditions (i.e., without temperature control) are not recommended for theequilibration phase of the simulation because, without the energy flow facilitated by temperaturecontrol, the desired temperature cannot be achieved.However, during the data collection phase, if you are interested in exploring the constant energy surfaceof the conformational space or if, for some other reason, you do not want the perturbation introducedby temperature bath coupling, this is a useful ensemble.

NVT dynamicsThe Nosé thermostat (Nosé, 1984) generates deterministic dynamics, with the temperature controlledby a fictitious additional coordinate, s, added to the Lagrangian of the system. The thermostat employsa feedback loop between the instantaneous kinetic energy and the required temperature. The rate offeedback is determined by themass parameter, Q. This parameter should be chosen so that the naturaloscillation frequency of the Nosé coordinate is close to the characteristic frequency of the actual system.Themass parameter is related to the thermostat relaxation time by:Eq. DMol3-30Q = g(k

BT/τ2)

where g is the number of degrees of freedom (usually 3N - 3, where N is the number of atoms), kBis

Boltzmann's constant, T is the thermostat temperature, and τ is the relaxation time.An improvement on the standard Nosé thermostat (or Nosé-Hoover thermostat) is the Nosé-Hooverchain method, described in detail by Tuckerman et al. (2001). In this method, the kinetic energyfluctuations of the thermostat variable are controlled by coupling it to another thermostat variable. Thekinetic energy fluctuations of the second thermostat are, in turn, controlled by coupling to a thirdthermostat, and so on, to form a chain ofM thermostats. This new coupling (the Nosé-Hoover 'chain'thermostatting mechanism) leads to a more general canonical dynamics method.Several other thermostat options are also implemented in DMol3:n Massive Nosé-Hoover chain

This method is a generalization of the Nosé-Hoover (NH)method where each degree of freedom iscoupled to its own independent NH thermostat. The bath particle itself is the subject of an equationofmotion that is simply a function of the kinetic energy of the system and the desired temperature.

n Gaussian thermostatOne way to define a temperature is to apply Gauss' principle of non-holonomic constraints. In thenon-holonomic case (when the final state of the system is path dependent) the constraints are givenby the function g(r, v, t) = 0. The constraint is non-holonomic because it includes velocities. Theconstant temperature constraint is nonlinear and has the form (Windikis and Delley, 2003):Eq. DMol3-31

where Nfare the degrees of freedom, k

Bis the Boltzmann constant, and T

setis the desired

temperature. Applying Gauss' principle yields:

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Eq. DMol3-32

To derive the Gaussian equation ofmotion with these constraints, miaiis substituted with F

i= ξm

ivi.

The resulting equation is then solved for the time derivative of the friction coefficient, ξ, which yields:Eq. DMol3-33

The conserved energy in this formalism then becomes:Eq. DMol3-34

n Generalized Gaussian moments thermostatThe Generalized Gaussian moments (GGM) thermostat is based on controlling the fluctuations of anarbitrary number ofmoments of themultidimensional Gaussian momentum distribution function(Tuckerman et al., 2000). In this approach, one thermostat is coupled to all degrees of freedom, justas for a Nosé-Hoover chain. The GGM thermostat is explicitly reversible, which means that Newton'sequations ofmotion possess the symmetry of time reversibility. This method produces dynamicswith well-defined conserved quantities.This thermostat is controlled by a characteristic time scale, τ, which governs the size and speed ofthermostat (and temperature) fluctuations. For a stable thermostat run, τ must be significantly largerthan themolecular dynamics time step, with a recommended ratio of 10 to 100.

n Massive generalized Gaussian moments thermostatThis method is a generalization of the GGM method where each degree of freedom is coupled to itsown independent GGM thermostat. This technique forces the canonical distribution of the kineticenergy over the degrees of freedom and, hence, produces rapid equilibration.This thermostat is also governed by a time scale, τ, which must be significantly (for example, 10-100times) larger than themolecular dynamics time step.

The thermostat implementation in DMol3 is described in detail by Windikis and Delley (2003).

ConstraintsDMol3 can be used to perform MD simulations with structural constraints. The examination of slowermodes in a system (for example, torsional conformation interconversion) necessitates relatively longsimulation times because the upper limit of theMD time step is determined by the presence of fastmodes (for example bond stretching and bond-angle vibrations). Hence, a large number of short timesteps is required. Substantial improvement in the efficiency ofMD simulations can be achieved byfreezing the fast structural modes through constraint of the appropriate degrees of freedom.DMol3 supports two types of constraints during molecular dynamics simulations through MaterialsStudio interface:

Theory in DMol3  | Page 79

n Internal coordinates can be fixed (distances, angles, and torsions)n Individual atom positions can be fixed

Point group symmetryDMol3 supports most of the chemically important symmetry point groups. If you select an unsupportedpoint group system, DMol3 automatically switches to the highest order subgroup.The supported groups are:

Cs CiC2 C2v C2h D2 D2h D2D

C3v D3 D3h D3D

C4v D4 D4h D4d

C5v D5 D5h D5d

C6v D6 D6h D6d

Td O Oh I IhThe C

n, C

nh, and S

2ngroups are not supported. Neither are the rotational groups C∞

vand D∞

h,

however, such systems can be computed in C6vand D

6h, respectively, without significant loss in

efficiency.

COSMO-solvation effectsDMol3 includes certain COSMO controls, which allow for the treatment of solvation effects.The COnductor-like Screening MOdel (COSMO; Klamt and Schüürmann, 1993; Delley, 2006) is acontinuum solvation model (CSM; Tomasi and Persico, 1994) in which the solutemolecule forms a cavitywithin the dielectric continuum of permittivity, ε, that represents the solvent:

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The charge distribution of the solute polarizes the dielectric medium. The response of the dielectricmedium is described by the generation of screening (or polarization) charges on the cavity surface. Incontrast to other implementations of CSMs, COSMO does not require solution of the rathercomplicated boundary conditions for a dielectric in order to obtain screening charges, but insteadcalculates the screening charges using a much simpler boundary condition for a conductor. Thesecharges are then scaled by a factor, f(ε) = (ε - 1) / (ε + 1/2), to obtain a good approximation for thescreening charges in a dielectric medium.The deviations of this COSMO approximation from the exact solution are small. For strong dielectrics likewater, they are less than 1%, while for nonpolar solvents with ε ~ 2, they may reach 10% of the totalscreening effects. However, for weak dielectrics, screening effects are small, and the absolute errortherefore amounts to less than 1 kcal/mol.Altogether, COSMO is a considerable simplification of the CSM approach without significant loss ofaccuracy. Because of this simplification, COSMO allows for a more efficient implementation of the CSMinto quantum chemical programs and for accurate calculation of gradients, which allows geometryoptimization of the solute within the dielectric continuum.The screening charges are determined from the boundary condition of vanishing potential on thesurface of a conductor. If q is defined as a vector of the screening charges on the surface of the cavity,and Q = ρ + Z for the total solute charges such as electron density, ρ, and nuclear charges, Z, then thevector of potentials, V

tot, on the surface is V

tot= BQ + Aq = V

sol+ V

pol, where BQ is the potential arising

from the solute charges, Q, and Aq is the potential arising from surface charges, q. B and A are Coulombmatrices. For a conductor, the relation V

tot= 0must hold, which defines the screening charges as:

Theory in DMol3  | Page 81

Eq. DMol3-35

For further details of the COSMO theory, see Klamt and Schüürmann (1993). COSMO provides theelectrostatic contribution to the free energy of solvation. In addition, there are non-electrostaticcontributions to the total free energy of solvation that describe the dispersion interactions and cavityformation effects.

DMol3/COSMOThe COSMO electrostatic energy is analogous in form to the DMol3 electrostatic energy, with theCoulombic operator replaced by the dielectric operator D = BA-1B. From Eq. DMol3-17:Eq. DMol3-36

where ρ~ represents the auxiliary density, which is introduced to solve the Poisson equation for theelectrostatic potential of the solute. This total energy is minimized, resulting in the Kohn-Shamequations for themolecular orbitals. The Kohn-Sham Hamiltonian now includes an electrostatic COSMOpotential:Eq. DMol3-37

This potential is present in every SCF cycle. This direct incorporation of the solvent effects within the SCFprocedure is a major computational advantage of the COSMO scheme. Since the DMol3/COSMOorbitals are obtained using the variational scheme, accurate analytic gradients with respect to thecoordinates of the solute atoms can be derived. The complete theory is presented in Klamt andSchüürmann (1993) and Andzelm et al. (1995). The gradients include the forces between the solutecharges, Q, and the screening charges, q.To summarize, a DMol3/COSMO calculation begins with the construction of the cavity surface. Thescreening charges are then evaluated using Eq. DMol3-35 and the initial solute charges, Q. This allows forcalculation of the electrostatic COSMO potential. The process is repeated until DMol3 SCF convergenceis achieved. The final total energy includes the DMol3/COSMO electrostatic energy (Eq. DMol3-36).If geometry optimization is requested, DMol3/COSMO gradients are evaluated and the new geometry iscalculated. The next optimization cycle begins with reconstruction of the cavity surface and the processcontinues until the DMol3 optimization convergence criteria aremet.The DMol3/COSMO method has been tested extensively (Klamt and Schüürmann, 1993; Andzelm et al.,1995). The results depend mainly on the choice of the van derWaals radii used to evaluate the cavitysurface. The other parameters defining the cavity surface (see below) are less important. Of course,solvation energies depend on the choice of DMol3 parameters, such as the type of DFT functional, thebasis set, and integration grid. Results obtained so far (Andzelm et al., 1995) suggest that theDMol3/COSMO model can predict solvation energies for neutral solutes with an accuracy of about2 kcal/mol.Recently, the DMol3/COSMO method has been generalized to the periodic boundary cases (Delley,2006). In this case, all the screening charge is localized at the cavity surface. This is achieved with the useof Lagrange constraints with a new integration scheme based on a larger number of integration meshpoints (Delley, 1996).

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Determination of the cavity surface (or solvent-accessible surface)The surface is obtained as a superimposition of spheres centered at the atoms, discarding all parts lyingon the interior part of the surface (Klamt and Schüürmann, 1993). The spheres are represented by adiscrete set of points, the so-called basic points. Eliminating the parts of the spheres that lie within theinterior part of themolecule thus amounts to eliminating the basic grid points that lie in the interior ofthemolecule.The radii of the spheres are determined as the sum of the van derWaals radii of the atoms of themolecule and of the probe radius. The surviving basic grid points are then scaled to lie on the surfacegenerated by the spheres of van der Waals radii alone. The basic points are then collected intosegments, which are also represented as discrete points on the surface. The screening charges arelocated at the segment points.

Determination of non-electrostatic contributions to the free energy of solvationThe free energy of solvation is calculated as:Eq. DMol3-38

where Eo is the total DMol3 energy of themolecule in vacuo, E is the total DMol3/COSMO energy of themolecule in solvent, and ΔG

non-electrostaticis the non-electrostatic contribution due to dispersion and

cavity formation effects. The non-electrostatic contributions to the free energy of solvation areestimated from a linear interpolation of the free energies of hydration for linear-chain alkanes as afunction of surface area:Eq. DMol3-39

In the present implementation, the VWNpotential, DNP basis set, and fine integration grid of DMol3were used to calculate energies ofmethane and octane (C

2h). The experimental values of the free energy

of solvation are 1.9 and 2.9 kcal/mol for methane and octane, respectively (Ben-Naim and Marcus,1984). The calculated surface areas, using the default COSMO parameters, were 38.4 and 104.1 Å2 formethane and octane, respectively. The following values ofA and Bwere used:n A = 1.67274 (kcal/mol)n B = 0.02052 (kcal/mol Å2)The best A and B values to use depend on the choice of DMol3 and COSMO input parameters. Tests(Andzelm et al., 1995) indicate that selection of other parameters, such as the nonlocal BP potential andthe van derWaals radii of atoms, can influence ΔG

nonelectrostaticby as much as 0.5 kcal/mol.

COSMO-SAC modelThemost popular methods of COSMO-based prediction of activity coefficients and thermodynamicproperties are COSMO-RS (conductor-like model for real solvents, Klamt et al., 1998) and COSMO-SAC(COSMO segment activity coefficient). COSMO-SAC model has been proposed by Lin and Sandler (2002)and further enhanced by Lin et al. (2004). Subsequent improvements resulted in COSMO-SAC 2007(Wang et al., 2007), COSMO-SAC 2010 (Hsieh et al., 2010), and COSMO-SAC 2013 (Xiong et al., 2014)models.In all of thesemethods molecules are treated as a collection of surface segments. A solutemolecule ismoved from a vacuum to a perfect conductor, where the interaction energies between segments aredetermined from a COSMO calculation, that is, a solvation calculation for themolecule in the conductor.Then the solute is transferred from the perfect conductor to the real solvent, and for this process the

Theory in DMol3  | Page 83

chemical potential of each segment is self-consistently determined from statistical mechanics. Thechemical potential of each molecule is then obtained by summing the contributions of the individualsegments. In this way, thermodynamic properties of liquids are predicted in an a priorimanner (Xiong etal., 2014). Thesemodels enable calculation of activity coefficients, vapor pressures, heats ofvaporization, and phase equilibria for both pure fluid and liquid mixtures.Calculations based on COSMO-SAC models require .cosmo files produced by DMol3, and those filesmust be generated with specific COSMO settings that include high density of surface segments and thatcorrespond to a conductor dielectric constant.

COSMO sigma profileThe sigma profile shows the amount of surface area for a given COSMO charge density.This profile is represented as the probability distribution of a molecular surface segment having a specificcharge density.This is obtained by averaging surface charge densities from the .cosmo file and finding an effectivesurface charge density on a standard surface fragment:Eq. DMol3-25

where ni(σ) is the number of segments with a discretized surface charge density σ, A

iis the total cavity

surface area, and Ai(σ) is the total surface area of all of the segments with a particular density σ.

The default number of segments is 110 for all non-hydrogen atoms and 50 for hydrogen atoms.

Electric field gradientsThe electric field gradient at a nucleus provides information about the electronic environment of thatatom. The property can be probed experimentally by measuring NMR line widths for molecular speciesthat contain NMR-active isotopes with a nuclear quadrupolemoment where the quadrupolar relaxationmechanism determines the observed line width. The fact that electric field gradients are a function of thechemical environment is also exploited in NQR (zero-field NMR, or commonly, nuclear quadrupoleresonance) scanning to detect explosives (C&E News, 1996).The electric field gradient at a nucleus may be obtained by differentiating the electric field around themolecule. It is, however, more practical to evaluate this as the second derivative of the electrostaticpotential, V:Eq. DMol3-40

where R0is the position at which the derivative is evaluated, Q is the electric field gradient, V is the

electrostatic potential, R is a general position vector, and a and b are x, y, or z.The electric field vector, F, at a given position is related to the first derivative:

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Eq. DMol3-41

The trace of Q defined as above yields (Poisson equation):Eq. DMol3-42

where ρ is the charge density.Q can be transformed into a traceless tensor Q' (or matrix) via:Eq. DMol3-43

In DMol3, the tensor Q is computed through expanding the electrostatic potential into a Taylor serieswith respect to each of the nuclei (if symmetry is imposed, only the symmetry-unique nuclei are visited).ThematrixQ then appears as the coefficient of the second-order term in the Taylor expansion:Eq. DMol3-44

The energy of an electrostatic quadrupolemoment embedded in an electrostatic potential isdetermined by the electric field gradient at the position of the quadrupole. This interaction contributesto the NMR line width (as further outlined below).A complete quantitative description of this interaction is actually more complex than what is presentedabove and is captured by the so-called Sternheimer factor (Sternheimer, 1966).The electric field gradient at a quadrupolar nucleus (spin I > 1/2) within a molecule determines the NMRlongitudinal relaxation rate, 1/T

1, or the line width, W

1/2, (this assumes that the quadrupolar relaxation

mechanism dominates):Eq. DMol3-45

Note: Miyake et al. (1996) use a different formula, in which ε enters into the equation as (1 + ε2)/3.

In Eq. DMol3-45, I is the nuclear spin quantum number (for example, I = 1 for 14N, I = 5/2 for 17O, I = 3/2for 33S, I = 7/2 for 45Sc); χ is the nuclear quadrupolar coupling constant, which is given by e2Q q

zz/h,

where qzzis the largest principal component of the EFG tensor, q; ε is the asymmetry parameter, given

by |qxx- q

yy|/q

zz.

The x, y, and z axes are chosen such that |ε| < 1. Since ε enters into the relaxation time as ε2, the sign ofε is not important and may be dropped (Bagno and Scorrano, 1996).tcis the rotational correlation time and can be estimated from the Debye-Stokes-Einstein formula as t

c=

Vmη/(kT), where V

mis the hydrodynamic volume (= 4 (π/3) R3, where R is the hydrodynamic radius) and

η is the solution viscosity.

Theory in DMol3  | Page 85

The hydrodynamic volume can be estimated from (Noggle and Schirmer, 1971):Eq. DMol3-46

whereM is themolecular weight, ρ is the solute density, and Nais Avogadro's number.

The EFG in atomic units can be converted to SI units with the conversion factor:Eq. DMol3-47

Nuclear quadrupolemoments, Q, are listed as areas, where εQ is themaximum expectation value of thezz traceless tensor element:1 b = 100 fm2 = 10-28m2

For example:n 14NQ = 2.01 fm2

n 17O Q = -2.558 fm2

n 33S Q = -6.78 fm2

n 45Sc Q = -22 fm2 (Q < 0: oblate, Q > 0: prolate)Quadrupole interaction energy tensor:Eq. DMol3-48

Thermodynamic calculationsThe results of a vibrational analysis or Hessian evaluation can be used to compute enthalpy (H), entropy(S), free energy (G), and heat capacity at constant pressure (C

p) as functions of temperature. The DMol3

total energy yields the total electronic energy at 0 K. The various translational, rotational, andvibrational components are used to compute H, S, G, and C

pat finite temperatures as discussed below.

When you perform a vibrational analysis with DMol3, these results appear in the .outmol file. You cancreate a chart of the result using the thermodynamic analysis tools. You can control the temperatures atwhich the properties are evaluated using the keyword thermo_range in the input deck.The formulas below are based on work by Hirano, 1993. In each case, two expressions are provided forrotational contributions: one for linear and one for nonlinear systems.

EnthalpyThe enthalpy correction, H, in the ideal gas approximation is given by:H(T) = E

vib(T) + E

rot(T) + E

trans(T) + RT

where the subscripts stand for vibrational, rotational, and translational contributions, respectively, andR is the ideal gas constant. The contributions are given by:

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Eq. DMol3-51

E RT

E linear RT

E nonlinear RT

E hυ

=

( ) =

( ) =

= ∑ + ∑

tra

rot

rot

vib

R

ki i

R

ki

hυ hυ kT

hυ kT

3

2

3

2

1

2

exp(− / )

[1 −exp(− / )]

i i

i

Where:k is Boltzmann's constanth is Planck's constantνi are the individual vibrational frequencies

EntropyThe contributions to the entropy, S, are given by:Eq. DMol3-52

where w is themolecular weight, Ixis themoment of inertia about axis x, σ is the symmetry number, and

the other quantities are as described above.

Heat capacityFor nonperiodic systems, DMol3 calculates the heat capacity at constant pressure, C

p, based on the

ideal gas for the translational and rotational terms. Its contributions are given by the formulas below.The subscript p has been dropped from these equations.Eq. DMol3-53

Theory in DMol3  | Page 87

For solids, the only applicable term is the vibrational contribution Cvib, which corresponds to the heat

capacity at constant volume, Cv. In the output, DMol3 specifies explicitly whether C

por , C

vhas been

calculated.

Using the resultsThe DMol3 .outmol file or the thermodynamic analysis chart provides the corrections for H, S, and Gfor finite temperature. The SCF energy computed by DMol3 is the total electronic energy at 0 K. You canestimate ΔH or ΔG for a chemical reaction using the quantities from the table.To compute the ΔE of a reaction, you add up the DMol3 total energies for the reactants and the energiesfor the products. The energy of reaction is simply E

product- E

reactant. To compute ΔH(T), simply add the

computed enthalpy to the electronic energy of each component. Remember that total energies arereported in Hartree/atom and the thermodynamic results are in kcal/mol (1 Hartree/atom =627.5 kcal/mol). The table below provides a hypothetical example.

Thermodynamics for A + B = C

A B C C - (A + B)

Energy -62.20 Hartree -15.50 Hartree -77.99 Hartree -181.98 kcal/mol

Enthalpy 298.15 K kcal/mol 98.2 50.1 150.55 -179.73

Fitting atomic point charges to the electrostatic potential (ESP)Atomic multipole properties are often used to obtain the electrostatic parameters of classical forcefields.One of themost common approaches is to determine the atomic multipole properties by fitting them soas to reproduce themolecular electrostatic potential (ESP) (Singh and Kollman, 1984). Numerousapplications of ESP-fitted charges in simulations of biochemical systems prove the usefulness of thistechnique (Bakalarski et al., 1996; Bayly et al., 1993; Merz, 1992). The ESP-derived charges can reproducethe intermolecular interaction properties ofmolecules well with a simple two-body additive potential.The ESP is generated in the space of a molecule and can be calculated from the positions of the atomicnuclei, α, and the electron density, ρ:Eq. DMol3-54

where wiis the integration weight at point i, V(r

i) is the Coulomb potential at point i, and q

αis the fitted

charge on atom α.The total molecular charge is conserved, using a Lagrangemultiplier.The grid points i in Eq. DMol3-54 are selected based on the following criteria:Eq. DMol3-55

where Rαint and R

αext are the internal and external radii of the atomic α shells, and depend on the atom

type.To make the results less sensitive to the selection of the grid, the concept of a layer border wasintroduced. The weights, w

i, change smoothly across the border layer, as is evident from the following

formula:

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Eq. DMol3-56

where wiαint and w

iαext are the partial weights calculated with respect to all ESP centers in the system:

Eq. DMol3-57

Eq. DMol3-58

where ΔR is the "diffusion" width of the layer border.Thus, the w

ichange smoothly from 0 to 1 in the region R

αint - ΔR, R

αint + ΔR and from 1 to 0 across the

external radii Rαext - ΔR, R

αext + ΔR.

The final set of linear equations is solved via the Gauss elimination technique to determine the pointcharges.The accuracy of the fit can be evaluated by calculating the rms deviation as follows:Eq. DMol3-59

It is quite common to obtain a rrms error of 20% for uncharged molecules, which can amount to a fewkcal/mol of rms error obtained by using the fitted potential.

Mulliken and Mayer bond ordersThe concept of bond order and valence indices is well established in chemistry. It allows forinterpretation and deeper understanding of the results of DMol3 calculations using ideas familiar tochemists.First, a density matrix must be defined, or as it is sometimes called, a charge-density bond-order matrix.If ϕ is a molecular orbital and C

iμare the SCF expansion coefficients, then:

Eq. DMol3-60

and matrix Pμνand a set of atomic orbitals completely specify the charge density (Eq. DMol3-22).

The trace ofmatrix P and the overlap S is equal to the total number of electrons in themolecule:Eq. DMol3-61

Theory in DMol3  | Page 89

Summing (PS)μνcontributions over all μ∈ A, ν∈ B , where A and B are centers, P

ABcan be obtained,

which can be interpreted as the number of electrons associated with the bond A-B. This is the so-calledMulliken population analysis (Mulliken, 1955). The net charge associated with the atom is then given by:Eq. DMol3-62

where ZAis the charge on the atomic nucleus A.

Mayer (1986) defined the following quantities.n Bond order between atoms A and B:

Eq. DMol3-63

where Pα, Pβ are the density matrices for spin α and β.n Actual total valence of atom A in themolecule:

Eq. DMol3-64

n Actual free valence of atom A in themolecule:Eq. DMol3-65

where PS = Pα - Pβ.TheMayer bond orders and valence indices have several useful properties:1. The values of bond orders are close to the corresponding classical values. This means that the

double bond in H2CO would have a C-O Mayer bond order close to 2.0.

2. The total valence indicates howmany single bonds are associated with the atom. For example, in themethanemolecule, the C atom would have a total valence close to 4.0.

3. The free valence index is zero for closed-shell systems. For open-shell radicals, it is a measure of thereactivity. The free valence index indicates whether free electrons are available for bonding on aparticular atom.

4. UnlikeMulliken bond orders, Mayer quantities are less dependent on the basis set choice and theyare transferable, so they can be used to describe similar molecules.

5. For similar molecules, the trends in Mayer quantities can be correlated well with electronic andgeometrical changes due to substituents.

Hirshfeld charge analysisHirshfeld partitioned charges (Hirshfeld, 1977) are defined relative to the deformation density. Thedeformation density is the difference between themolecular and the unrelaxed atomic charge densities:

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Eq. DMol3-66

where ρ(r) is themolecular charge density and ρα(r - R

α) is the density of the free atom α located at

coordinates Rα. Using the deformation density, the effective atomic charges, dipoles, and quadrupole

are defined as (Delley, 1986):Eq. DMol3-67

Eq. DMol3-68

Eq. DMol3-69

The weight function Wα(r) is defined as the fraction of the atomic density from atom α at coordinate r:

Eq. DMol3-70

Fukui functionsThe chemical potential, chemical hardness and softness, and reactivity indices have been used by anumber of workers to assess a priori the reactivity of chemical species from their intrinsic electronicproperties. Various methods have included atomic charge computation, free valency, spin populations,and the Laplacian of the charge density, among others. Perhaps one of themost successful and bestknown methods is the frontier orbital theory of Fukui. Developed further by Parr and Yang (1989), themethod relates the reactivity of a molecule with respect to electrophilic and nucleophilic attack to thecharge density. These so-called Fukui functions (FFs) are a qualitative way ofmeasuring and displayingthe reactivity of regions of a molecule.Specifically, the FF measures the sensitivity of the charge density, ρ(r), with respect to the loss or gain ofelectrons via the expressions:Eq. DMol3-71

The expression f+(r) measures changes in the density when themolecule gains electrons and, hence,corresponds to reactivity with respect to nucleophilic attack. Conversely, f-(r) corresponds to reactivitywith respect to electrophilic attack (loss of electrons). The FF for radical attack, f0(r), is simply the averageof these two.

Theory in DMol3  | Page 91

Using the finite difference approximation shown above, the charge densities are converged to self-consistency for the neutral molecule, the cation, and the anion. The FFs are computed using the finitedifference approximation and the self-consistent charge densities for the neutral molecule, the cation,and the anion. They may bemay be viewed using the volumetric analysis tools. Generally, users willobtain themust useful information by mapping the FF onto an isodensity surface rather than by viewingisosurfaces of the FFs themselves.More quantitative predictions can be obtained from the condensed FF for an atom k:Eq. DMol3-72f-k= q

k- q

kcation

f+k= q

kanion - q

kIn this case, the q

kare atomic-centered charges that are computed in some reasonablemanner, such as

from aMulliken population analysis or from a numerical integration procedure such as a Hirshfeldanalysis. This procedure effectively assigns the 3D FF to specific atoms, just like a charge analysis tries toassign charge density to atoms.In conventional FF computations, a value of 1.0 is used for ΔN, i.e., one full electron is removed or addedfor the calculation of the charge density of the ions. DMol3 can use fractional charges for this purpose.This yields faster SCF convergence and results closer to the limit of ΔN=0. A value of 0.1 is recommended.

Raman spectraRaman spectroscopy is used to study the vibrational, rotational, and other low-frequency modes in asystem. It is based on the Raman effect of inelastic scattering ofmonochromatic light. This interactionwith vibrations results in the energy of incident photons being shifted up or down. The energy shift isdefined by the vibrational frequency and the proportion of the inelastically scattered light is defined bythe spatial derivatives of themacroscopic polarization, technical details are described by Porezag andPederson (Porezag et al.).Spatial derivatives of the polarization are calculated in DMol3 based on finite difference calculation of thepolarizability tensor derivatives with respect to the normal mode coordinates.There are two ways of calculating these derivatives: displacing normal modes and evaluating vibrationalfrequencies or displacing the electric field and calculating gradient. Due to the high cost of vibrationalfrequency calculations (also evaluated using finite displacements) the DMol3 implementation calculatesthe polarizability derivatives by 19 gradient evaluations at specified values of external electric field.Additionally, after calculating Raman activities, DMol3 can display corresponding Raman cross sections(intensity) for the Stokes component of the ithmode for a given experiment incident light frequency andtemperature using the following expression:Eq. DMol3-23

Where νsis the frequency of scattered light, c is the speed of light, h is Planck constant, n

iis the Bose-

Einstein statistical factor, and IRam is the Raman activity of the given mode.Since ν

scan be obtained from the frequency of incident light ν

0, i.e. ν

s= (ν

0- ν

i), Raman intensities can

be calculated in experimental conditions T and ν0.

Note: It is important to remember that Raman intensities are effectively third order derivatives, so toobtain reasonable results very accurate calculations are required.

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Basis set superposition errorBasis set superposition error (BSSE) is the effect of lowering of the total energy when the electrons ofeach atom spread into the space defined by the basis functions provided by the other atoms due to anincomplete basis set. This effect is well pronounced when using Gaussian basis sets but for numericalbasis sets, as used in DMol3, it can be neglected in most cases (Inada et al, 2008). However, high qualitycalculations involving weakly interacting moieties should include the BSSE correction when determiningpotential energy surfaces and interaction energy.DMol3 calculates the BSSE correction by means of counterpoisemethod.The counterpoisemethod, in a system AB consisting of subsystems A and B, is defined as a difference inenergies of both subsystems in the full system basis set, E[A;AB], E[B;AB], and the subsystems alone, E[A] and E[B], (van Duijneveldt et al, 1994:)

To allowDMol3 to calculate the BSSE correction, two sets of atoms need to be created, defininginteracting subsystems. These selections must bemutually exclusive and span the whole system. Inorder to help with the selection, DMol3 allows you to define the first set and it will automaticallyconsider the rest of the 3D Document the second set. In addition, you should ensure that the chargeson your BSSE sets are correct on the DMol3 Energy dialog.

Note: The BSSE correction calculation is enabled for nonperiodic systems only and for Energy task.

Converging SCFIn general, the Kohn-Sham equations of density functional theory are solved iteratively using the SCFprocedure outlined in the DFT theory topic. A reasonable guess of wavefunction coefficients is used as astarting point, the resulting density and potential are calculated, and then the Schrödinger equation issolved before obtaining a new density from the updated wavefunction coefficients. Repeating thisprocedure should, in principle, lead to convergence. In practice however, it is numerically unstable touse the density result from one iteration to calculate the potential of the next iteration directly. Toresolve this difficulty, the initial and the updated charge and spin densities aremixed, such that theactual self-consistent density is approached slowly but in a numerical stable procedure. Moreover, thedensity guess for one iteration is likely to overshoot considerably in the initial stages of the SCF cycle.Themixing algorithm tends to dampen the overshoot.The important parameters for successfully achieving convergence consist of the charge and spin mixingfactors and the number of histories from which new guesses are calculated. In addition, it is possible todampen long-range density fluctuations using a charge density preconditioner. The default settingsprovided for these parameters are chosen to give good convergence in 90% of all systems and usuallyshould not need to be changed. However, if a calculation takes more than 30-40 SCF cycles to convergeit can be useful to check whether small adjustments to themixing factors can improve the situation orwhether the checklist provided below can help convergence.

Note: Decreasing themixing factors often improves numerical stability and therefore convergenceperformance.

Note: A poor choice of parameters can lead to a significant increase in the computational cost of anycalculation.

Theory in DMol3  | Page 93

Challenging systemsFor problematic systems there are some changes to settings that can improve the convergencebehavior:n Surface slab models, particularly when they involve polar and/or metallic surfaces with adsorbates.

Issues can arise from interactions between periodic images of the same surface. This can be resolvedby adding a dipole slab correction on the SCF tab of the DMol3 Electronic Options dialog.

n Systems with spatially separate but degenerate states (such as surface states in a thick-slab ormulticenter organometallic molecules).Use the checklist, with a focus on the charge density preconditioner.

n Spin frustrated systems or molecules/atoms with highly degenerate half-occupied states (forexample. half-filled d-shells, transition metal clusters).Check whether it is sensible to break some of the existing symmetries and investigate the effects ofsmearing (SCF tab of the DMol3 Electronic Options dialog).

n Inappropriate charge statesReview the Charge setting on the Setup tab of the DMol3 Calculation dialog.

n AnionsTo address problems with anions increase the orbital cutoff, grid, and basis accuracies (Orbital Cutofftab of the DMol3 Electronic Options dialog, Setup tab of the DMol3 Calculation dialog).

n Solid systems may cause problems in cases of incomplete Brillouin sampling.Check whether an increase in the quality of the k-point grid helps (k-points tab of the DMol3Electronic Options dialog).

n A calculation that stops converging at a certain threshold might require more accuratematrixelement to achieve better numerics.Increase the Integration accuracy to Fine (Electronic tab of the DMol3 Calculation dialog).

In difficult cases the convergence behavior of the SCF cycle should always be examined. If it is steadilydecreasing but just a little slow, an increase of the number of iterations will definitely help while a smallchange of themixing parameters in either direction could lead to quicker convergence.

ChecklistFor systems with problematic convergence use the following steps to make improvements:n Check your model for physical consistency. In particular, make sure that all of the following have

physically correct and intended settings: spin, charge, symmetry, metal, smearing, dipole slabcorrection (Setup tab of the DMol3 Calculation dialog, SCF tab of the DMol3 Electronic Optionsdialog).

n Decrease the density mixing Charge and Spin settings to about 0.1 and increase theMax. SCF cyclesto 100 or more. Optionally, increase theDIIS size (SCF tab of the DMol3 Electronic Options dialog).

n For large systems (more than 50 atoms) turn on the charge density preconditioner (SCF tab of theDMol3 Electronic Options dialog).

n Unless it is already Fine, increase the Integration accuracy of the grid and the k-point set if applicable(Electronic tab of the DMol3 Calculation dialog).

n Further decrease the density mixing Charge and Spin settings to about 0.05 or even 0.01. However,this should be employed only as an emergency measure and should not be necessary for physicallysensible problems (SCF tab of the DMol3 Electronic Options dialog).

n For geometry optimizations or dynamics which fail to converge only on the second (or subsequent)geometry steps, add the Reset_SCF keyword to the .input file.

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n Should all of these fail, you might wish to change themixing scheme from the default Pulay mixer andexplore other options. However, this should really be taken as the ultimate last resort as the Pulaymixer generally outperforms the other schemes implemented in DMol3 (keyword SCF_DIIS).

Theory in DMol3  | Page 95

Dialogs in DMol3

The following topics and their subtopics describe the DMol3 dialogs:n DMol3 Calculation dialogn DMol3 Analysis dialogUse the Save settings... option to save the current dialog settings.

DMol3 Calculation dialogThe DMol3 Calculation dialog allows you to set up and display the parameters for a calculation.The DMol3 Calculation dialog contains the following tabs:n Setup: Allows you to choose the type and quality of calculation that DMol3will perform, along with

other basic input options, such as the basis set, DFT functional, spin state, and total charge.n Electronic: Allows you to set the parameters that control the details of the energy evaluation,

including the integration accuracy and the SCF convergence.n Properties: Allows you to select the properties that will be computed by DMol3. These include

volumetric visualizations (such as charge density and molecular orbitals) and electronic properties.n Job Control: Allows you to specify job settings for the DMol3 calculation.

Tip: See the Performance tips topic for ways to optimize DMol3 calculations.

Run: Runs a job using the settings specified. The results are placed in a subfolder of the currentMaterials Studio project directory.Run  | Copy Script: Converts the current settings to a script and copies the script to the clipboard. Referto the Generating scripts topic for more information on using sections of scripts generated from adialog.Files...: Provides access to the DMol3 Job Files dialog which allows you to save input files for a DMol3calculation without running the job, or to run a job using an existing set of input files.This functionality is provided for users who need to run the DMol3 server program in standalonemode,or who wish to edit the DMol3 input files in order to gain access to features not supported by the DMol3interface.Help: Displays the Help topic for the current tab.

Access methods

Menu Modules | DMol3 | Calculation

Toolbar | Calculation

Setup tabThe Setup tab allows you to choose the type and quality of calculation that DMol3will perform, alongwith other basic input options, such as the basis set, DFT functional, spin state, and total charge.Task: Select the type of calculation that you wish to perform from the dropdown list. Available optionsare:

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n Energy - performs a single-point energy calculationn Geometry Optimization - searches for a minimum energy structuren Dynamics - performs a molecular dynamics calculationn TS Search - searches for a transition state using linear synchronous transit (LST) and quadratic

synchronous transit (QST)methodsn TS Optimization - searches for a transition state using eigenvector-following methodsn TS Confirmation - produces a refined reaction path based on an LST or QST searchn Elastic Constants - performs an elastic constants calculationn Reaction Kinetics - calculates rate coefficients for a reaction whose transition state is knownn Electron Transport - calculates electron transport properties, such as transmission and currentMore...: Provides access to further options for the selected task.Quality: Set the overall quality for the DMol3 calculation. This quality affects the basis set, k-point, andSCF convergence criteria, plus the convergence criteria for relevant tasks. Available options are:n Coarsen Mediumn FineThese three levels offer progressively more accuracy at the expense of longer calculation times.

Tip: Use the Coarse quality setting for a quick assessment of the calculation, then progress to a higherquality level to obtain more accurate results.

TheQuality setting affects all relevant task parameters that control the precision of the simulation. Ifany parameter is set by the user to a value different from that specified by the overall quality level, theQuality is displayed as Customized.Functional: Select the type of DFT exchange-correlation potential to be used in the calculation. Choosethe class of functional from the first dropdown list, then select the specific functional from the seconddropdown list.n LDA: local functionalsn PWC: Perdew and Wang, 1992n VWN: Vosko et al., 1980

n GGA: gradient-corrected functionalsn PW91: Perdew and Wang, 1992n BP: Becke, 1988; Perdew and Wang, 1992n PBE: Perdew et al., 1996n BLYP: Becke, 1988; Lee et al., 1988n BOP: Tsuneda et al., 1999n VWN-BP: Vosko et al., 1980; Becke, 1988; Perdew and Wang, 1992n RPBE: Hammer et al., 1999n HCTH: Boese and Handy, 2001n PBEsol: Perdew et al., 2008

n B3LYP: hybrid functional: Becke, 1993; Stephens et al., 1994n m-GGA: meta-GGA functionalsn M06-L: Zhao and Truhlar, 2006n M11-L: Peverati and Truhlar, 2012

Dialogs in DMol3  | Page 97

Note: The B3LYP and meta-GGA functionals are not available for periodic systems.

Use method for DFT-D correction:When checked, the selected method will be used for dispersioncorrections. Available options are:n TS for GGA (PBE and BLYP) and B3LYPn Grimme for GGA (PBE and BLYP) and B3LYPn OBS for GGA (PW91) and LDA

Note: The option selected will automatically update theUse custom DFT-D parameters setting on theDFT-D tab of the DMol3 Electronic Options dialog.

Spin unrestricted:When checked, indicates that the calculation will be performed using differentorbitals for different spins. This is known as a 'spin-unrestricted' or 'spin-polarized' calculation. Ifunchecked, the calculation uses the same orbitals for alpha and beta spins. This is known as a 'spin-restricted' or 'non-spin-polarized' calculation. Default = unchecked.Use formal spin as initial:When checked, indicates that the initial value for the number of unpairedelectrons for each atom will be taken from the formal spin introduced for each atom. This starting valuewill be subsequently optimized during the calculation. Default = checked.

Note: This option is enabled only if the Spin unrestricted checkbox is checked.

Metal:When checked this indicates that the system is metallic and requires thermal smearing and adense sampling of the Brillouin zone. When unchecked the k-point separations used by default arecoarser and the smearing is not used. Default = unchecked.

Note: This option applies only to periodic systems.

Use symmetry:When checked, indicates that symmetry information should be used in the calculation.Molecular dynamics simulations or calculations involving transition-state searching or confirmationcannot use symmetry information. Default = checked.

Note: Due to the DMol3 server-enforced symmetry snap, the total energy and other propertiesobtained in the DMol3 calculation may differ very slightly between Use symmetry set to on and off.This numerical effect may be noticeable in highly symmetric molecular systems.

Note: TheUse symmetry checkbox is not available when Functional is set to B3LYP or when Task is setto Dynamics, TS Search, TS Confirmation, Reaction Kinetics or Electron Transport. In these cases,symmetry will not be used.

Multiplicity: Select themultiplicity from the dropdown list to perform a calculation on a specific spinstate. Available options are:

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n Auton Singletn Doubletn Tripletn Quartetn Quintetn Sextetn Septetn OctetWhen Auto is selected, DMol3will attempt to determine the ground spin state by performing a spin-unrestricted calculation.

Note: This option is enabled only if the Spin unrestricted checkbox is checked and theUse formal spinas initial checkbox is unchecked.

Note: There is one limitation to specifying the spin state: it is not possible to force DMol3 to performan unrestricted singlet calculation. If you check the Spin unrestricted checkbox and set theMultiplicityto Singlet, the results will be the same as if you used the Auto setting.

Note: In the case of a periodic system, themultiplicity refers to the spin state of the electrons in asingle unit cell.

Charge: Specify the total charge on themolecule or unit cell.

Note: DMol3 can operate using fractional charges, but non-integer charges can only be specified bymanually editing the DMol3 input file.

Access methods

Menu Modules | DMol3 | Calculation | Setup

Toolbar | Calculation | Setup

DMol3 Energy dialogThe DMol3 Energy dialog allows you to define the atoms used in the basis set superposition error (BSSE)calculation and request this calculation.Calculate BSSE correction: Enables DMol3 to run a multi-stage counterpoise correction calculation.This involves calculations of separate subsystems alone and in presence of the other subsystem's basisfunctions.Add selected atoms to BSSE_1 set: Selected atoms are treated as one of two subsystems involved inthe BSSE calculation.

Note: This button is enabled only if the BSSE sets are not yet defined and a subset of atoms is selectedin the document.

Dialogs in DMol3  | Page 99

Note: The BSSE correction calculation is enabled for nonperiodic systems and for the Energy taskonly.

Select atoms in BSSE_1 set: Highlights atoms belonging to the first subsystem.BSSE_1 set charge: Sets the charge for BSSE set 1.Select atoms in BSSE_2 set: Highlights atoms belonging to the second subsystem.BSSE_2 set charge: Sets the charge for BSSE set 2.

Note: The charges on both BSSE sets need to sum exactly to the total charge specified on the Setuptab of the DMol3 Calculation dialog. This is automatically enforced when the set charges are specified.If the total Charge is changed, the BSSE set charges will not be updated and you will not be able tostart a calculation until they are adjusted such that their sum equals the total charge.

Help: Displays the Help topic in a browser.

Access methods

Menu Modules | DMol3 | Calculation | Setup | More...

Toolbar | Calculation | Setup | More...

DMol3 Geometry Optimization dialogThe DMol3 Geometry Optimization dialog allows you to set up and display the parameters that controlthe simulation in a DMol3 Geometry Optimization task.Quality: Set the geometry optimization convergence thresholds for energy change, maximum force, andmaximum displacement between optimization cycles. The optimization will stop when the energyconvergence is satisfied, along with either the displacement or gradient criteria. If the calculated initialgradients are below the threshold, the optimization will successfully stop without making a single stepand without comparing displacements and energies.Three sets of convergence thresholds are available:n Coarsen Mediumn FineThe values of the convergence thresholds in each set are given in the table below:

Value Coarse Medium Fine

Energy (Hartree) 1 × 10-4 2 × 10-5 1 × 10-5

Max. force (Hartree Å-1) 0.02 0.004 0.002

Max. displacement (Å) 0.05 0.005 0.005

Alternatively, thresholds can be specified independently for Energy,Max. force, andMax.displacement. If you enter your own values for any of these settings, theQuality is displayed asCustomized on both the DMol3 Geometry Optimization dialog and the Setup tab of the DMol3Calculation dialog.Energy: Specify the convergence threshold for themaximum energy change, in Hartree, during thegeometry optimization.

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Max. force: Specify the convergence threshold for themaximum force, in Hartree Å-1, during thegeometry optimization.Max. displacement: Specify the convergence threshold for themaximum displacement, in Å, during thegeometry optimization.Max. iterations: Specify themaximum number of geometry optimization cycles. If this number of cyclesis reached, then the calculation will stop, even if the convergence criteria are not satisfied.

Note: These convergence tolerances and theMax. iterations settings are only applied to the atomiccoordinate optimization in the unit cell.

Max. step size: Specify themaximum allowed change of any Cartesian coordinate. Geometricdisplacements are truncated such that they are less than this value. This prevents the optimizer fromtaking unreasonable steps.

Note: The default optimizer in DMol3 uses delocalized internal coordinates, themaximum Cartesianstep size is not directly applicable to this method. You should reduce the value ofMax. step size if youobserve that the actual displacements during minimization are too large and cause large energychanges.

Use starting Hessian:When checked, indicates that the Hessian associated with the current model willbe used as the initial Hessian in the new calculation. If unchecked, theminimization will start without aHessian.You can obtain a starting Hessian from several sources, as described in Importing a Hessian file.

Note: It is not possible to use a starting Hessian for geometry optimization in DMol3when symmetryis activated.

Optimize cell:When checked, indicates that the cell parameters will be optimized during the geometryoptimization, in addition to the atomic coordinates. Default = unchecked.

Note: This option is enabled only if the currently active document contains a periodic structure. If thisis disabled or unchecked then Optimization cycles and Displacement step are not available.

Note: Unit cell optimization requires many small changes in the cell vectors and a local optimizationfor each of the displacements.

Optimization cycles: Determines the number of cell optimization steps.Displacement step: Themagnitude of the cell vector displacements.Help: Displays the Help topic in a browser.

Access methods

Menu Modules | DMol3 | Calculation | Setup | More...

Toolbar | Calculation | Setup | More...

DMol3 Dynamics dialogThe DMol3 Dynamics dialog allows you to set up and display the parameters that control the simulationin a DMol3 Dynamics task.

Dialogs in DMol3  | Page 101

The DMol3 Dynamics dialog contains the following tabs:n Dynamics: Allows you to specify themain parameters for a molecular dynamics calculation, including

choice of ensemble, temperature, and the length of the run.n Thermostat: Allows you to specify the parameters that control the dynamics algorithm, including the

temperature control method and associated settings.Help: Displays the Help topic for the current tab.

Access methods

Menu Modules | DMol3 | Calculation | Setup | More...

Toolbar | Calculation | Setup | More...

Dynamics tabTheDynamics tab allows you to specify themain parameters for a molecular dynamics calculation,including choice of ensemble, temperature, and the length of the run.Ensemble: Select a thermodynamic ensemble to be used for the dynamics calculation. Available optionsare:n NVE (default) - dynamics at fixed volume and constant energyn NVT - dynamics at fixed volumewith a thermostat to maintain a constant temperatureTemperature: Specify the target temperature, in K, for the simulation. For the NVE ensemble, the initialrandom velocities of the atoms are scaled to this temperature. Default = 300.0 K.Time step: Specify the time, in fs, for each dynamics step. This value also determines the Totalsimulation time. Default = 1.0 fs.Total simulation time: Specify the total time, in ps, that the dynamics simulation will run for. This valuealso determines theNumber of steps. Default = 1.0 ps.Number of steps: Specify the number of dynamics steps to be carried out. This value also determinesthe Total simulation time. Default = 1000.

Access methods

Menu Modules | DMol3 | Calculation | Setup | More... | Dynamics

Toolbar | Calculation | Setup | More... | Dynamics

Thermostat tabThe Thermostat tab allows you to specify the parameters that control the NVT dynamics algorithm,including the temperature control method and associated settings.

Note: This tab is enabled only if the NVT ensemble is selected on the Dynamics tab.

Thermostat: Select the algorithm to be used to control the temperature of an NVT simulation. Availableoptions are:

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n Gaussiann Simple NH - simple Nosé-Hoovern NH Chain - Nosé-Hoover chainn Massive NH -massive Nosé-Hoovern GGM - generalized Gaussian momentsn Massive GGM (default) - massive generalized Gaussian momentsNosé Q ratio: Specify the value to be used to scale the fictitious mass, Q, of a Nosé-Hoover thermostat.A larger Q ratio implies decreased damping of temperature fluctuations. Default = 2.0.

Note: This control is disabled if the Gaussian, GGM, or Massive GGM Thermostat is selected.

Chain length: Specify the length of the thermostat chain to be used with the Nosé-Hoover chain,massive Nosé-Hoover, and generalized Gaussian moments methods. Default = 2.

Note: This control is disabled if the Gaussian or Simple NH Thermostat is selected.

Relaxation time: Specify the thermostat relaxation time for the generalized Gaussian moments methodas a multiple of the time step. Default = 10.0.

Note: This control is disabled if the Gaussian, Simple NH, NH Chain, or Massive NH Thermostat isselected.

Yoshida parameter: Specify the time step parameter for integration accuracy of the Nosé andgeneralized Gaussian moments methods. Available options are:n 1n 3 (default)n 5n 7n 25

Note: This control is disabled if the Gaussian Thermostat is selected.

Access methods

Menu Modules | DMol3 | Calculation | Setup | More... | Thermostat

Toolbar | Calculation | Setup | More... | Thermostat

DMol3 Transition State Search dialogThe DMol3 Transition State Search dialog allows you to set up and display the parameters that controlthe simulation in a DMol3 TS Search task.

Note: A transition state search requires a frame-based document (for example, an .arc file or .xtdfile) as input. So, even though you can set options on this dialog, you will not be able to start a jobuntil you supply an appropriate file.

Note: When a transition state search is performed on a periodic system the unit cell is fixed.

Dialogs in DMol3  | Page 103

Note: AQST calculation estimates the actual transition state from the currently selected frame in the.xtd document. If this is identical to the product or reactant, it will select the penultimate frame as atransition state estimate.

The reactants are taken from the first frame of the trajectory, and the products from the last frame ofthe trajectory. If you select a QST calculation, the next-to-the-last frame is used for the QSTmid-point.The .arc files generated by any of these transition state searches may be used as input to a QST.In such situations DMol3 uses the first and last frames for the reactant and product, respectively, andputs the best guess for the transition state in the next-to-the-last frame.Search protocol: Select the type of synchronous transit that will be performed. Available options are:n LSTMaximum - performs a single LST maximization, bracketing themaximum between the reactants

and product.n Halgren-Lipscomb - performs an LST maximization, followed by a single line search minimization.n LST/Optimization - performs an LST maximization, followed by a full conjugate gradient minimization.n Complete LST/QST (default) - performs an LST, followed by repeated conjugate gradient

minimizations and QSTmaximizations until a transition state has been located.n QST / Optimization - starting from a QST, performs repeated maximizations and conjugate gradient

minimizations until a transition state has been located.Quality: Sets the geometry optimization convergence thresholds for the rms forces on the atoms.Convergence thresholds forQuality settings:

Quality RMS Force (Hartree/Å)

Coarse 0.02

Medium 0.01

Fine 0.002

Customized User specified

Altering the value of any threshold is allowed and results in theQuality being set to Customized.RMS convergence: Specifies the value at which convergence is considered to take place, in terms of theRMS of the gradients.Max. number QST steps: Sets themaximum number of allowed QSTmaximization cycles.Optimize reactants and products: Specifies that the input structure for the reactant and product in a TSsearch calculation should be optimized to a local minimum. Selecting this allows the TS search to startfrom a "raw" trajectory, where the reactant and product structures have not already been optimized.

Note: This choicemay lead to reactant and product structures deviating substantially from the inputstructures, so it is recommended that you carefully check the final path.

Help: Displays the Help topic in a browser.

Access methods

Menu Modules | DMol3 | Calculation | Setup | More...

Toolbar | Calculation | Setup | More...

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DMol3 TS Optimization dialogThe DMol3 TS Optimization dialog allows you to set up and display the parameters that control thesimulation in a DMol3 TS Optimization task.

Note: Since a transition state optimization requires a starting Hessian, even though you can setoptions on this dialog, you will not be able to start an optimization until you associate a Hessianmatrix with the current structure.

Quality: Sets the geometry optimization convergence thresholds for Energy change,Max. force, andMax. displacement between optimization cycles. The optimization will stop when the energyconvergence is satisfied, along with either the displacement or gradient criteria.Convergence thresholds forQuality settings:

Quality Energy (Hartree) Force (Hartree/Å) Displacement (Å)

Coarse 1 × 10-4 0.02 0.05

Medium 2 × 10-5 0.004 0.005

Fine 1 × 10-5 0.002 0.005

Customized User defined User defined User defined

Altering the value of any threshold is allowed and results in theQuality being set to Customized.Energy: Specify the convergence threshold for themaximum energy change, in Ha, during the geometryoptimization.Max. force: Specify the convergence threshold for themaximum force, in Ha/Å, during the geometryoptimization.Max. displacement: Specify the convergence threshold for themaximum displacement, in Å, during thegeometry optimization.Max. iterations: Sets themaximum number of geometry optimization cycles. If the number of cycles isreached, then the calculation will stop even if the convergence criteria are not satisfied.Max. step size: Sets themaximum allowed change in any Cartesian coordinate. Geometricdisplacements are truncated such that they are less than this value. This prevents the optimizer fromtaking unreasonable steps.The transition state optimizer will follow a particular normal mode of the Hessian to the transition state.Help: Displays the Help topic in a browser.

Access methods

Menu Modules | DMol3 | Calculation | Setup | More...

Toolbar | Calculation | Setup | More...

DMol3 TS Confirmation dialogThe DMol3 TS Confirmation dialog allows you to set up and display the parameters that control thesimulation in a DMol3 TS Confirmation task.

Dialogs in DMol3  | Page 105

Quality: Sets the geometry optimization convergence thresholds for Energy change,Max. force, andMax. displacement between optimization cycles. The optimization will stop when the energyconvergence is satisfied along with either the displacement or gradient criteria.Convergence thresholds forQuality settings:

Quality Energy (Hartree) Force (Hartree/Å) Displacement (Å)

Extra-coarse 10-2 0.1 0.1

Coarse 10-4 0.02 0.05

Medium 2 × 10-5 0.004 0.005

Fine 10-5 0.002 0.005

Customized User defined User defined User defined

Altering the value of any threshold is allowed and results in theQuality being set to Customized.Energy: Specify the convergence threshold for themaximum energy change, in Hartree, during thetransition state confirmation.Max. force: Specify the convergence threshold for themaximum force, in Hartree Å-1, during thetransition state confirmation.Max. displacement: Specify the convergence threshold for themaximum displacement, in Å, during thetransition state confirmation.Path quality: Specifies the gradation of the path, by setting themaximum number of images togenerate.Max. images: The number of intermediate NEB images used during the transition state confirmation.

Quality Max. images

Coarse 6

Medium 10

Fine 20

Customized User defined

Help: Displays the Help topic in a browser.

Access methods

Menu Modules | DMol3 | Calculation | Setup | More...

Toolbar | Calculation | Setup | More...

DMol3 Elastic Constants dialogThe DMol3 Elastic Constants dialog allows you to set up and display the parameters that control thesimulation in a DMol3 Elastic Constants task.Displacement step: Specifies the finite displacement step used to set up the cell distortions necessary tocalculate the elastic constants. Default = 0.05 Å.Quality: Set the geometry optimization convergence thresholds for energy change, maximum force, andmaximum displacement between optimization cycles. The optimization will stop when the energy

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convergence is satisfied, along with either the displacement or gradient criteria. If the calculated initialgradients are below the threshold, the optimization will successfully stop without making a single stepand without comparing displacements and energies.Three sets of convergence thresholds are available:n Coarsen Mediumn FineThe values of the convergence thresholds in each set are given in the table below:

Value Coarse Medium Fine

Energy (Hartree) 1 × 10-4 2 × 10-5 1 × 10-5

Max. force (Hartree Å-1) 0.02 0.004 0.002

Max. displacement (Å) 0.05 0.005 0.005

Alternatively, thresholds can be specified independently for Energy,Max. force, andMax.displacement. If you enter your own values for any of these settings, theQuality is displayed asCustomized on both the DMol3 Geometry Optimization dialog and the Setup tab of the DMol3Calculation dialog.Energy: Specify the convergence threshold for themaximum energy change, in Hartree, during thegeometry optimization.Max. force: Specify the convergence threshold for themaximum force, in Hartree Å-1, during thegeometry optimization.Max. displacement: Specify the convergence threshold for themaximum displacement, in Å, during thegeometry optimization.Max. iterations: Specify themaximum number of geometry optimization cycles. If this number of cyclesis reached, then the calculation will stop, even if the convergence criteria are not satisfied.Max. step size: Specify themaximum allowed change of any Cartesian coordinate. Geometricdisplacements are truncated such that they are less than this value. This prevents the optimizer fromtaking unreasonable steps.

Note: The default optimizer in DMol3 uses delocalized internal coordinates, themaximum Cartesianstep size is not directly applicable to this method. You should reduce the value ofMax. step size if youobserve that the actual displacements during minimization are too large and cause large energychanges.

Help: Displays the Help topic in a browser.

Access methods

Menu Modules | DMol3 | Calculation | Setup | More...

Toolbar | Calculation | Setup | More...

DMol3 Reaction Kinetics dialogThe DMol3 Reaction Kinetics dialog allows you to set up and display the parameters that control thesimulation in a DMol3 Reaction Kinetics task.

Dialogs in DMol3  | Page 107

Optimize transition state: Perform a transition state optimization before calculation of the Hessian andtotal energy for the transition state.

Note: Transition state optimization can only be performed if the Hessian of the transition state isavailable.

Reuse Hessian for reactants and products:When checked, if any reactant or product structure alreadyhas a Hessian imported no additional geometry optimization or Hessian calculation will be performed forthat structure.Use coarse-grained parallelization:When checked, coarse-grained parallelization is used for thenumerical displacement frequency calculation. Geometrical displacement calculations necessary forgenerating the system Hessian matrix are evenly split over all available computational nodes. Eachdisplacement is then run in a serial mode and the final Hessian elements are gathered at the end of thecalculation. This is the preferred method for larger systems with many vibrational modes and a non-trivial number of computational nodes.When unchecked, numerical displacements are calculated sequentially, each in a parallel DMol3 process.This might be advantageous for smaller systems with fewer normal modes or for machines with a limitednumber of computational nodes.By default the Hessian is evaluated using a 2-point difference of analytic forces. You can change this bymodifying the Vibration_Steps keyword in the input file. See the DMol3 Job Files topic for informationon how to modify the input file.Quality: Set the geometry and transition state optimization convergence thresholds for energy change,maximum force, and maximum displacement between optimization cycles. The optimization will stopwhen the energy convergence is satisfied, along with either the displacement or gradient criteria. If thecalculated initial gradients are below the threshold, the optimization will successfully stop withoutmaking a single step and without comparing displacements and energies.Three sets of convergence thresholds are available:n Coarsen Mediumn FineThe values of the convergence thresholds in each set are given in the table below:

Value Coarse Medium Fine

Energy (Hartree) 1 × 10-4 2 × 10-5 1 × 10-5

Max. force (Hartree Å-1) 0.02 0.004 0.002

Max. displacement (Å) 0.05 0.005 0.005

Alternatively, thresholds can be specified independently for Energy,Max. force, andMax.displacement. If you enter your own values for any of these settings, theQuality is displayed asCustomized on both the DMol3 Reaction Kinetics dialog and the Setup tab of the DMol3 Calculationdialog.Energy: Specify the convergence threshold for themaximum energy change, in Hartree, during thegeometry optimization.Max. force: Specify the convergence threshold for themaximum force, in Hartree Å-1, during thegeometry optimization.

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Max. displacement: Specify the convergence threshold for themaximum displacement, in Å, during thegeometry optimization.Max. iterations: Specify themaximum number of geometry optimization cycles. If this number of cyclesis reached, then the calculation will stop, even if the convergence criteria are not satisfied.Max. step size: Specify themaximum allowed change of any Cartesian coordinate. Geometricdisplacements are truncated such that they are less than this value. This prevents the optimizer fromtaking unreasonable steps.

Note: The default optimizer in DMol3 uses delocalized internal coordinates, themaximum Cartesianstep size is not directly applicable to this method. You should reduce the value ofMax. step size if youobserve that the actual displacements during minimization are too large and cause large energychanges.

Help: Displays the Help topic in a browser.

Access methods

Menu Modules | DMol3 | Calculation | Setup | More...

Toolbar | Calculation | Setup | More...

DMol3 Transport dialogTheDMol3 Transport dialog allows you to setup and display parameters relating to the DMol3 Transporttask.It contains the following tabs:n Setup: Allows you to choose the type of calculation that will be performed. It also allows you to select

a number of transport specific properties to be computed as part of the DMol3 calculation.n Electrodes: Allows you to set parameters related to the electrodes.n Electrostatics: Allows you to specify settings for the Poisson solver.Help: Displays the Help topic for the current tab.

Note: The DMol3 Electron Transport task cannot be run under certain circumstances, if:

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n On the Setup tab of the DMol3 Calculation dialog:n Use method for DFT-D correction checkbox is checkedn Functional is set to B3LYP or m-GGA optionn Spin unrestricted checkbox is checkedn Charge is set to any non-zero value

n On the Electronic tab of the DMol3 Calculation dialog:n Core treatment is not set to DFT Semi-core Pseudopots when there is an element with Z > 20n Use solvation model checkbox is checked

n On the Properties tab of the DMol3 Calculation dialog, any of the following are selected:n Density of statesn Electron densityn Electrostaticsn Frequencyn Fukui functionn Opticsn Orbitalsn Population analysis

Access methods

Menu Modules | DMol3 | Calculation | Setup | More...

Toolbar | Calculation | Setup | More...

Setup tabThe Setup tab allows you to choose the type of calculation that will be performed. It also allows you toselect a number of transport specific properties to be computed as part of the DMol3 calculation.Calculate transmission function:When checked, this indicates that the transmission function will becomputed as part of the calculation.More...: Provides access to the DMol3 Transmission dialog, which allows you access to further optionsfor the transmission property.Calculate current/voltage characteristics:When checked, this indicates that current/voltage data willbe computed as part of the calculation.More...: Provides access to the DMol3 Current/Voltage dialog, which allows you to access to furtheroptions for the current/voltage property.

Density MixingMixing amplitude: Specify the value, to use in mixing the charge density matrix between the currentand previous iterations.For example, a value of 0.02will construct a charge density using 2% from the current iteration and 98%from the previous iterations.

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ElectrodeNumber of k-points: The number of k-points along the electrode that will be used calculate theelectrodes' Hamiltonians.

Access methods

Menu Modules | DMol3 | Calculation | Setup | More... | Setup

Toolbar | Calculation | Setup | More... | Setup

DMol3 Transmission dialogTheDMol3 Transmission dialog allows you to set options controlling the calculation of the transmissionfunction.From: Specifies the beginning of the energy range for the transmission function.To: Specifies the end of the energy range for the transmission function.Steps: The number of energy points for which the transmission function will be evaluated.Transmission pairs: Lists the available electrode pairs for the current document. A checked electrodepair will have the transmission function between the two electrodes calculated.Help: Displays the Help topic in a browser.

Access methods

Menu Modules | DMol3 | Calculation | Setup | More... | Setup | More...

Toolbar | Calculation | Setup | More... | Setup | More...

DMol3 Current/Voltage dialogTheDMol3 Current/Voltage dialog allows to you define the parameters for the current/voltagecalculation.Current through: Select the electrode through which the current will be calculated.Vary potential for: Select the electrode for which the potential will be varied.From: Specifies the beginning of the potential range.To: Specifies the end of the potential range.Steps: Specifies the number of potential points for which the current will be computed.

Note: If the number of Steps is one, the current will be calculated at a single voltage corresponding tothe From value.

Help: Displays the Help topic in a browser.

Access methods

Menu Modules | DMol3 | Calculation | Setup | More... | Setup | More...

Toolbar | Calculation | Setup | More... | Setup | More...

Electrodes tabThe Electrodes tab allows you to set parameters related to the electrodes.

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Electrode Name: The name to be used for the electrode. When the name is changed on this dialog anyother settings that depends on the name of the electrode will be updated.

Note: If the name of the electrode is changed, using the Properties Explorer or an Undo/Redo action,any settings that depend on the namewill be lost. The affected settings are: transmission pairselections, electrode potential values, and current and voltage electrode selections.

Potential (V): Determines the potential of the electrode.Direction (XYZ): Shows the direction of the electrode.

Access methods

Menu Modules | DMol3 | Calculation | Setup | More... | Electrodes

Toolbar | Calculation | Setup | More... | Electrodes

Electrostatics tabThe Electrostatics tab allows you to specify settings for the Poisson solver.Buffer length: Specifies the buffer length added to the sides of a minimum box containing the devicestructure, in Å.Max. grid spacing: Sets themaximum grid spacing used for the Poisson grid.Use default boundary conditions: If checked default boundary conditions will be applied. The default isto use the Dirichlet condition on any box face containing one or more electrodes and Neumannconditions on any other surface.More...: Provides access to the DMol3 Poisson Boundary Conditions dialog, which allows you to specifynon-default boundary conditions for the Poisson solver.

Note: This is enabled only if theUse default boundary conditions checkbox is unchecked.

Access methods

Menu Modules | DMol3 | Calculation | Setup | More... | Electrostatics

Toolbar | Calculation | Setup | More... | Electrostatics

DMol3 Poisson Boundary Conditions dialogTheDMol3 Poisson Boundary Conditions dialog allows you to specify non-default boundary conditionsfor the Poisson solver.Xmin

, Xmax

, Ymin

, Ymax

, Zmin

, Zmax

: Defines the boundary conditions for the six faces of the box used bythe Poisson solver. For numerical reasons it is not possible to use Neumann conditions on allboundaries. Options for these are:n Neumann (default for box faces with no electrodes)n Dirichlet (default for box faces with electrodes)Electrode boundary:n Global (default) - Applies the selected boundary condition to the entire face of each boxn Circle - Applies the Dirichlet boundary condition to a circular cross section around each electrode.n Square - Applies the Dirichlet boundary condition to a square cross section around each electrode.

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Electrode buffer: The length of the buffer applied to each electrode boundary region. Default = 3 Å.Set default boundary conditions: Sets the values on the dialog to the default boundary conditions.

Note: When changing to a new document or modifying an existing document the Poisson boundaryconditions are not automatically updated for the system in focus. To use the default settings click theSet default boundary conditions button or check theUse default boundary conditions checkbox onthe Electrostatics tab of the DMol3 Transport dialog.

Help: Displays the Help topic in a browser.

Access methods

Menu Modules | DMol3 | Calculation | Setup | More... | Electrostatics | More...

Toolbar | Calculation | Setup | More... | Electrostatics | More...

Electronic tabThe Electronic tab allows you to set the parameters associated with the electronic Hamiltonian.Integration accuracy: Specifies the precision used in the numerical integration of the Hamiltonian.Available options are:n Coarsen Mediumn FineTheMedium option uses about 1000 grid points for each atom in the calculation.SCF tolerance: Specifies the threshold used to determine whether an SCF has converged. Options andassociated convergence thresholds are:n Coarse = 10-4

n Medium = 10-5

n Fine = 10-6

A Customized option is also available. The parameters which control this option can be accessed usingtheMore... button.k-point set: Defines the number of integration points that will be used to integrate the wavefunction inreciprocal space. Available options are:n Gamma - a single pointn Coarsen Mediumn FineMore detailed control is available on the DMol3 Electronic Options dialog.

Note: k-point control is active only for periodic systems.

Core treatment: Four types of treatments of core electrons are available in DMol3:

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n All Electron (default) - provides no special treatment of cores. All electrons are included in thecalculation.

n Effective Core Potentials (ECP) - replaces core electrons by a single effective potential, reducing thecomputational cost. ECPs introduce some degree of relativistic correction into the core.

n All Electron Relativistic - includes all electrons explicitly and introduces some relativistic effects into thecore. This is themost accurate and also themost computationally expensive of the options.

n DFT Semi-core Pseudopots (DSPP) - replaces core electrons by a single effective potential, reducingthe computational cost. DSPPs introduce some degree of relativistic correction into the core. Theseare DFT-based potentials.

For additional details on the use of ECPs in DMol3 see Core treatment under Setting up electronicoptions.

Note: Effective Core Potentials and DFT Semi-core Pseudopots are not available for themeta-GGA exchange correlation functionals.

Basis set: Specifies the atomic orbital basis set that will be used in the calculation. Available options are:n MINn DNn DNDn DNPn TNPn DNP+For more information on basis sets, see Numerical basis sets.Basis file: Specifies the version of the basis set file to use:n 3.5n 4.4

Notes:n Selection of a Basis file is not available when Basis set is set to TNP as this has its own custom basis

file.n Selection of a Basis file is not available when Basis set is set to DNP+ as this set is available only with

version 4.4.n Selection of the DNP+ set requires very large orbital cutoff. Short cutoffs may lead to errors arising

from squeezed diffuse tails approximations.n Basis set quality has been analyzed in detail by Delley (1990).n Version 4.4 of the basis set is the newly optimized set delivering slightly improved heats of

formation. The set is described in Delley, 2006.n Version 3.5 is the original basis set file, the default.

Orbital cutoff quality: Specifies the finite range cutoff of the atomic basis set.The orbital cutoff quality determines the size of the finite range cutoff, and is dependent on the Orbitalcutoff scheme. Available options are:n Coarsen Mediumn Fine

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A Customized option is also available. The parameters which control this option can be accessed usingtheMore... button.The atomic orbitals are taken to be zero at this distance from their atomic center. Decreasing the cutoffreduces the computational time required for a calculation but introduces large approximations. Thecutoff valuemust lie between 3.25 and 20 Å.

Note: Using too small or too large a cutoff may result in failure to converge during SCF or geometryoptimization calculations. The smallest recommended values for cutoff are those in the table ofcoarse quality values. The largest value should not exceed 20 Å.

Harris approximation:When checked specifies the Harris non-self-consistent approximation be used inthe calculation. This greatly reduces the computational time required but also reduces the accuracy ofthe calculation. The Harris approximation is available only for spin-restricted calculations using LDAfunctionals without solvent effect.Use solvation model:When checked specifies that the COSMO solvation model will be used, furtherdetails can be set on the Solvent tab of the DMol3 Electronic Options dialog. When a solvation model isused theHarris Approximation is unavailable. Default = unchecked.For all calculations using the COSMO solvation model a COSMO Sigma Profile plot, named <seedname>Sigma Profile.xcd, is returned.More...: Opens the DMol3 Electronic Options dialog which provides more detailed control overparameters associated with the electronic Hamiltonian.

Access methods

Menu Modules | DMol3 | Calculation | Electronic

Toolbar | Calculation | Electronic

DMol3 Electronic Options dialogThe DMol3 Electronic Options dialog allows you more detailed control over parameters associated withthe electronic Hamiltonian.The DMol3 Electronic Options dialog contains the following tabs:n SCF: Allows you to set the parameters that control the electronic minimization.n k-points: Allows you more detailed control over the k-point set to be used in the calculation.n Orbital Cutoff: Allows you to set more detailed parameters that control the atomic orbital cutoffs.n Solvent: Allows you to set up a simulated solvent environment for the calculation.n DFT-D: Provides access to the parameters for van der Waals dispersion correction calculations.

Note: Solvent environment calculations are available only for non-Harris runs.

Help: Displays the Help topic for the current tab.

Access methods

Menu Modules | DMol3 | Calculation | Electronic | More...

Toolbar | Calculation | Electronic | More...

Dialogs in DMol3  | Page 115

SCF tabThe SCF tab allows you to set the parameters that control the electronic minimization.SCF tolerance: Specify the threshold for SCF density convergence. The SCF procedure is consideredconverged to a minimum when the largest (in magnitude) component of the DIIS density error matrix isless than this value.This will override the SCF tolerance setting specified on the Electronic tab, changing the setting toCustomized.Max. SCF cycles: Specify themaximum number of SCF iterations allowed for an energy calculation. If theSCF does not converge after the specified number of iterations, the calculation will be terminated.Multipolar expansion: Specify themaximum angular momentum function used in themultipolarrepresentation of the charge density. Available options are:n Monopolen Dipolen Quadrupolen Octupolen HexadecapoleCharge: Specify the value, f, used in mixing the charge density between the current and previousiterations. Allowed values are 0.0 < f ≤ 1.0. For example, a value of 0.2 would construct a charge densityusing 20% of the current density and 80% from the previous iterations.Spin: Specify the value used in mixing the spin density between the current and previous iterations.Allowed values = 0.0 to 1.0.Use DIIS:When checked, indicates that the DIIS (direct inversion in an iterative subspace) will be used tospeed up SCF convergence.DIIS size: Specify themaximum size of the subspace for the DIIS procedure. If the SCF does not convergewith the default number of histories, increasing this value can sometimes lead to significantly improvedSCF convergence. It is not recommended to use fewer than 4 histories. Allowed values = 1 to 10.Use preconditioner:When checked, indicates that the charge density preconditioner is turned on, thisdampens charge density oscillations between successive SCF cycles. This can speed up convergence,particularly for large systems or for surface or interface calculations.q0: Specify the reference wave vector for damping the charge density oscillations, in inverse Bohr.Allowed values = 0.5 to 20.

Note: The q0 control is only enabled when theUse preconditioner checkbox is checked.

Use smearing:When checked, indicates that thermal smearing will be applied to the orbital occupationto speed up convergence.Smearing: Specify the value, in Hartree, of the smearing parameter.

Note: The Smearing control is only enabled when theUse smearing checkbox is checked.

Note: A potential way to improve convergence for coarse k-point sets without introducing thermalsmearing is to switch off the tetrahedra integration algorithm with the defeat_tetrahedra keyword.

Apply dipole slab correction:When checked, adds an external potential to the vacuum region of theslab. This potential cancels the non-zero dipole moment of the cell due to polar adsorbates in slabs (or

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adsorbates on only one side of the slab). This correction is particularly helpful for workfunctioncalculations.

Note: The dipole slab correction is applied only for vacuum slabs, which must be at least 8 Å thick. Fora calculation with insufficient vacuum, the dipole correction will be ignored.

Note: The dipole slab correction requires P1 symmetry. If your slab has symmetry other than P1, youwill be prompted to convert the symmetry to P1 before you can continue.

Note: The dipole slab correction in DMol3 requires that the center of the vacuum coincides with thecenter of the unit cell. Materials Studio will shift the geometry accordingly prior to the calculation toenforce the correct vacuum center.

Access methods

Menu Modules | DMol3 | Calculation | Electronic | More... | SCF

Toolbar | Calculation | Electronic | More... | SCF

k-points tabThe k-points tab allows you more detailed control over the k-point set to be used in the calculation.TheMonkhorst-Pack k-point grid to be used in the calculation can be specified in several ways. For cubiccells and for the C direction of hexagonal cells the even and odd grids for theMonkhorst-Pack schemegive the same number of k-points. However, the even grid provides better sampling and will always beused automatically under these conditions. This ensures that a good grid with k-point separation at (orless than) the specified target can be achieved more economically. As a consequence, such lattices mayhavemuch finer separations than requested as odd grids have been excluded - even though they wouldhave been closer to the specified separation - and the better even grids have been taken in preference.Gamma point only:When selected, indicates that a single k-point at (0,0,0) will be used for the densityof states calculation.Quality:When selected, indicates that the k-point grid will be generated using a k-point separationappropriate to the specified quality level. Select the desired quality level from the dropdown list.Available options are:n Coarsen Mediumn FineThe k-point separations associated with the threeQuality settings depend on whether theMetalcheckbox on the Setup tab is checked and are as follows:

Qualityk-point separation (Å-1)

Metal checked Metal unchecked

Coarse 0.07 0.1

Medium 0.05 0.08

Fine 0.04 0.07

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Separation:When selected, indicates that the k-point grid will be generated according to the specified k-point separation. Specify the k-point separation, in Å-1, in the associated text box.

Note: When the Separation option is selected, theMonkhorst-Pack parameters are derived to givethe specified separation between neighboring grid points.

Custom grid parameters:When selected, indicates that the k-point grid will be generated using theMonkhorst-Pack grid parameters and the origin shift in fractional reciprocal space coordinates specifiedin theGrid parameters and Origin shift text boxes, respectively.Grid parameters: Specify theMonkhorst-Pack grid parameters in each of the lattice directions.Actual spacing: Displays the k-point separation, in Å-1, resulting from the currently specifiedMonkhorst-Pack grid parameters in each of the lattice directions.Origin shift: Specify the offset of theMonkhorst-Pack grid in fractional reciprocal space coordinates.

Note: TheGrid parameters and Origin shift controls are enabled only if the Custom grid parametersoption is selected.

Display points...: Displays the number and fractional coordinates of the reciprocal spacemesh pointsthat would be generated using the currently specified parameters.

Note: The actual set of k-points that will be used in the calculations may be altered if the symmetry ofthe system changes.

Access methods

Menu Modules | DMol3 | Calculation | Electronic | More... | k-points

Toolbar | Calculation | Electronic | More... | k-points

Orbital Cutoff tabTheOrbital Cutoff tab allows you to set more detailed parameters that control the atomic orbitalcutoffs.Orbital cutoff scheme: Specify how the orbital cutoff values are to be determined. Available options are:n Global - determines the value of the cutoff based on either the selected Quality setting or a specified

Custom cutoff valuen Use current - uses the values of theOrbitalCutoffRadius property assigned to the atoms

Note: If you select the Use current option, you must assign an OrbitalCutoffRadius value to all theatoms in the structure. The calculation will fail if any atoms have undefined OrbitalCutoffRadiusvalues.

If the Global orbital cutoff scheme is to be used in the calculation, it can be specified in one of two ways:Quality:When selected, indicates that a global orbital cutoff appropriate to the specified quality levelwill be used. Select the desired quality level from the dropdown list. Available options are:n Coarsen Mediumn Fine

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The exact value of the global orbital cutoff used will depend upon the elements present in the structurebeing studied.

Note: TheQuality global setting is not appropriate for studying reactions between compoundscontaining different atoms. The actual numerical value of the atomic cutoff radius depends on atomspresent in the system and can therefore vary between products and reactants making the resultsunpredictable. In such cases it is advised to use a constant, custom value for the global cutoff.

Custom:When selected, indicates that the value specified in theGlobal orbital cutoff text box will beused. This will override theOrbital cutoff quality setting specified on the Electronic tab, changing thesetting to Customized.

Note: TheQuality and Custom controls are enabled only if the Global option is selected from theOrbital cutoff scheme dropdown list.

Global orbital cutoff: Specify a value, in Å, for the global orbital cutoff.

Note: TheGlobal orbital cutoff control is enabled only if the Custom option is selected for the globalorbital cutoff scheme.

Assign: Assigns theOrbitalCutoffRadius property to the selected atoms in the current structure (or allthe atoms if none are selected), using the specified Global orbital cutoff parameter. Such assigned valuescan then be used in conjunction with the Use current orbital cutoff scheme.

Note: The Assign button is enabled only if the Global option is selected from theOrbital cutoffscheme dropdown list.

The global real space cutoff is selected for every system as themaximum value from all the cutoffsspecific to each element in that system.Cutoff_global = max(Cutoff_elementI)I ⊂  Elements of a systemThe following DMol3 keywords may be written into the output file:n Cutoff_Globaln Cutoff_Elementn Cutoff_Atom

Access methods

Menu Modules | DMol3 | Calculation | Electronic | More... | Orbital Cutoff

Toolbar | Calculation | Electronic | More... | Orbital Cutoff

Solvent tabThe Solvent tab allows you to set up a simulated solvent environment for the calculation.Use COSMO:When checked, indicates that the conductor-like screening model (COSMO)will be used tosimulate a solvent environment for the calculation.For all calculations using the COSMO solvation model a COSMO Sigma Profile plot, named <seedname>Sigma Profile.xcd, is returned.

Dialogs in DMol3  | Page 119

Solvent: Select a solvent from the dropdown list to be used as the solvent environment for thecalculation. Available options are:n Acetonen Acetonitrilen Benzenen Carbon tetrachloriden Chloroformn Diethyl ethern Dimethyl sulfoxiden Ethanoln Methanoln Methylene chloriden n-hexanen n-hexadecanen Nitrobenzenen Pyridinen WaterWhen a solvent is selected, theDielectric constant field is automatically updated with the appropriatevalue.

Note: If theDielectric constant parameter is set to a value different to that dictated by the selectedsolvent, the Solvent is displayed as Customized.

Dielectric constant: Specify a value for the solvent dielectric constant. This parameter is automaticallyupdated to the appropriate value when a solvent is selected from the Solvent dropdown list, however,you can enter your own custom value if you wish.

Note: The Solvent and Dielectric constant controls are enabled only if theUse COSMO checkbox ischecked.

Access methods

Menu Modules | DMol3 | Calculation | Electronic | More... | Solvent

Toolbar | Calculation | Electronic | More... | Solvent

DFT-D tabTheDFT-D tab allows you to set up customized parameters for van der Waals dispersion corrections.This can involve the definition of DFT-D corrections for exchange functionals that are not usuallysupported, the definition of support for additional elements, or changing existing parameters.Use custom DFT-D parameters: Specify whether to use custom DFT-D parameters. When this checkboxis checked, select the van derWaals scheme to use from the dropdown list, options are:n TSn Grimmen OBS

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Note: The option selected will automatically update theUse method for DFT-D correction setting onthe Setup tab of the DMol3 Calculation dialog.

Atomic parametersThis table allows you to edit the dispersion correction parameters for each of the atomic species. Thetype and number of parameters depend on the DFT-D scheme selected, please refer to the originalliterature for themeaning and usage of each parameter.The units are eV for energies and Å for lengths. The available columns are:Element: Denotes the element to be edited.C6 (eV Å6): Available for TS and Grimme schemes.R0 (Å): Available for TS and Grimme schemes.alpha (Å3): Available for TS and OBS schemes.I (eV): Available for the OBS scheme.Rvdw (Å): Available for the OBS scheme.

Note: Only the elements in the currently active document are listed in the Atomic parameters table .

Note: Each scheme includes a radius (R0 for TS and Grimme, Rvdw for OBS) that must be non-zero foreach of the active elements.

Scheme parametersScheme parameters are dimensionless numbers that define the functional form of each scheme.Please refer to the original literature to for themeaning and usage of each parameter.Depending on the van derWaals scheme selected for the custom DFT-D parameters setting, the Schemeparameters that can be specified are: n TS: sR, dn Grimme: s6, dn OBS: lambda, n

Note: The default values for these parameters depend on the exchange correlation functionalselected on the Setup tab of the DMol3 Calculation dialog.

Note: Both scheme parameters must be non-zero for the calculations to start and for input files to bewritten.

Reset All: Restores the default settings for each element in the grid.

Access methods

Menu Modules | DMol3 | Calculation | Electronic | More... | DFT-D

Toolbar | Calculation | Electronic | More... | DFT-D

Properties tabThe Properties tab allows you to select the properties that will be computed as part of a DMol3calculation.

Dialogs in DMol3  | Page 121

Choose the properties you wish to compute by checking the appropriate checkboxes in the list.Selection of certain properties activates additional Electron density options.

Access methods

Menu Modules | DMol3 | Calculation | Properties

Toolbar | Calculation | Properties

Band structure selectionChecking the Band structure checkbox on the Properties tab displays options for controlling the bandstructure calculation.Empty bands: Specify the number of empty bands (in addition to occupied bands) to be included in theband structure calculation.k-point set: Specify the quality of the k-point set for the band structure calculation. Each qualitycorresponds to a particular approximate separation between consecutive k-points on the reciprocalspace path.

Quality k-point separation (Å-1)

Coarse 0.04

Medium 0.025

Fine 0.015

Separation: Specify the approximate separation between k-points in Å-1. The default depends on theselected k-point set.Path...: Provides access to the Brillouin Zone Path dialog, which allows you to set the reciprocal spacepath for the band structure calculation.

Access methods

Menu Modules | DMol3 | Calculation | Properties | Band structure

Toolbar | Calculation | Properties | Band structure

Density of states selectionChecking theDensity of states checkbox on the Properties tab displays options for controlling thedensity of states calculation.Empty bands: Specify the number of empty bands (in addition to occupied bands) to be included in thedensity of states calculation.k-point set: Specify the quality of the k-point set for the density of states calculation. Each qualitycorresponds to a particular separation between neighboring k-points in theMonkhorst-Pack grid.Calculate PDOS:When checked, indicates that the information required to generate partial and localdensities of states will also be calculated.More...: Gives access to the DMol3 Density of States Options dialog, which provides options forcontrolling the k-point set specification.

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Note: The k-point set dropdown list and theMore... button are disabled for calculations onnonperiodic systems.

Tip: Calculations requesting Density of states properties will also provide information for thegeneration of Fermi surfaces.

Note: The default calculated range of the DOS plot for a periodic system is between -1.0 and 1.0 Ha.This range can bemodified by editing the Plot_DOS keyword in the input file. DOS plots fornonperiodic structures include all calculated orbitals. For molecules and periodic systems with only aGamma point, the entire density of states is shown including the core levels.

Access methods

Menu Modules | DMol3 | Calculation | Properties | Density of states

Toolbar | Calculation | Properties | Density of states

DMol3 Density of States Options dialogThe DMol3 Density of States Options dialog allows you to specify the k-point set used for density ofstates calculations.TheMonkhorst-Pack k-point grid to be used in the calculation can be specified in one of four ways:Gamma point only:When selected, indicates that a single k-point at (0,0,0) will be used for the densityof states calculation.Quality:When selected, indicates that the k-point grid will be generated using a k-point separationappropriate to the specified quality level. Select the desired quality level from the dropdown list.Available options are:n Coarsen Mediumn FineThe k-point separations associated with the threeQuality settings are as follows:

Quality k-point separation (Å-1)

Coarse 0.07

Medium 0.05

Fine 0.04

Separation:When selected, indicates that the k-point grid will be generated according to the specified k-point separation. Specify the k-point separation, in Å-1, in the associated text box.

Note: When the Separation option is selected, theMonkhorst-Pack parameters are derived to givethe specified separation between neighboring grid points.

Tip: Calculations requesting Density of states properties will also provide information for thegeneration of Fermi surfaces. In order to generate accurate Fermi surfaces the Separation optionshould be selected and a value of 0.01 1/Å or less specified.

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Custom grid parameters:When selected, indicates that the k-point grid will be generated using theMonkhorst-Pack grid parameters and the origin shift in fractional reciprocal space coordinates specifiedin theGrid parameters and Origin shift text boxes, respectively.Grid parameters: Specify theMonkhorst-Pack grid parameters in each of the lattice directions.Actual spacing: Displays the k-point separation, in Å-1, resulting from the currently specifiedMonkhorst-Pack grid parameters in each of the lattice directions.Origin shift: Specify the offset of theMonkhorst-Pack grid in fractional reciprocal space coordinates.

Note: TheGrid parameters and Origin shift controls are enabled only if the Custom grid parametersoption is selected.

Display points...: Displays the number and fractional coordinates of the reciprocal spacemesh pointsthat would be generated using the currently specified parameters.

Note: The actual set of k-points that will be used in the calculations may be altered if the symmetry ofthe system changes.

Help: Displays the Help topic in a browser.

Access methods

Menu Modules | DMol3 | Calculation | Properties | Density of states | More...

Toolbar | Calculation | Properties | Density of states | More...

Electron density selectionChoosing Electron density on the Properties tab displays options for computing several different typesof charge density. Each type of density is returned as a set of volumetric data in a .grd file.Total density:When checked, indicates that the total electronic charge density will be computed.Deformation density:When checked, indicates that the total density with the density of the isolatedatoms subtracted will be computed.Spin density:When checked, indicates that the difference between the charge density for alpha-spinand beta-spin electrons will be computed.

Note: The Spin density option is enabled only if the Spin unrestricted checkbox is checked on theSetup tab.

Grid...: Provides access to the DMol3 Grid Parameters dialog, which allows you to set the resolution andextents of the grid used to calculate the volumetric properties of the orbitals.

Tip: The default resolution of the grid is 0.2 Å. You can also modify this by editing the input files andadding the keyword Grid.

Access methods

Menu Modules | DMol3 | Calculation | Properties | Electron density

Toolbar | Calculation | Properties | Electron density

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Electrostatics selectionChoosing Electrostatics on the Properties tab displays options for computing several differentproperties related to the electrostatics of the input structure.Electrostatic potential:When checked, indicates that the total electrostatic potential will be computedand returned as a set of volumetric data in a .grd file.Electrostatic moments:When checked, indicates that the dipole moment of a molecule will becomputed.

Note: For a periodic system, thesemoments are undefined.

Nuclear electric field gradients:When checked, indicates that nuclear electric field gradient, animportant component of the nuclear magnetic shift, will be computed.Work function:When checked, indicates that work function calculations will be performed. The energyrequired to remove an electron from the bulk into the vacuum as a function of the slab distance will becalculated.

Note: This calculation is enabled for slabs only. When doing a workfunction calculation, you shouldactivate the dipole slab corrections.

Note: This calculation will yield a slightly different total energy as a result of a different chargecompensation algorithm, other properties are not affected.

Grid...: Provides access to the DMol3 Grid Parameters dialog, which allows you to set the resolution andextents of the grid used to calculate the volumetric properties of the orbitals.

Tip: The default resolution of the grid is 0.2 Å. You can also modify this by editing the input files andadding the keyword Grid.

Access methods

Menu Modules | DMol3 | Calculation | Properties | Electrostatics

Toolbar | Calculation | Properties | Electrostatics

Frequency selectionChoosing Frequency on the Properties tab displays options for computing a Hessian which is used forvibrational frequencies of themodel. The results can be used to generate a starting Hessian for ageometry optimization.The Hessian elements are computed by displacing each atom in themodel and computing a gradientvector, this builds a complete second derivativematrix. By default all atoms are displaced in thisprocedure.Calculate Raman intensities:When checked Raman intensities for the vibrational modes will becalculated.

Note: The Calculate Raman intensities option is only available for calculations on nonperiodicsystems.

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Use coarse-grained parallelization:When checked the coarse-grained parallelization is used for thenumerical displacement frequency calculation. Geometrical displacement calculations necessary forgenerating the system Hessian matrix are evenly split over all available computational nodes. Eachdisplacement is then run in a serial mode and the final Hessian elements is gathered at the end of thecalculation. This is the preferred method for larger systems with a lot of vibrational modes and a non-trivial number of computational nodes. When unchecked, the numerical displacements are calculatedsequentially, each displacement run in a parallel DMol3 process. This might be advantageous for smallersystems with fewer normal modes or for machines with a limited number of computational nodes.

Note: Coarse-grained parallelization requests will be ignored by the DMol3 server if B3LYP functional isused, if Raman intensities are requested, or if the requested number of cores is incompatible with thenumber of required displacements. In these circumstances coarse-grained parallelization is either notimplemented or inefficient.

Calculate partial Hessian:When checked only the atoms belonging to the HessianAtoms set are used togenerate the Hessian. When unchecked, the HessianAtoms set is not used for calculation of the Hessianand the Hessian is built from the displacement of all atoms.By default the Hessian is evaluated using a 2-point difference of analytic forces. Users can change this bymodifying the keyword Vibration_Steps in the input file. See the DMol3 Job Files topic for informationon how to modify the input file.More...: Opens the Partial Hessian dialog, which provides options for creating and selecting sets ofatoms for use in Hessian calculations.

Access methods

Menu Modules | DMol3 | Calculation | Properties | Frequency

Toolbar | Calculation | Properties | Frequency

Partial Hessian dialogThe Partial Hessian dialog allows you to specify and view atoms used in partial Hessian frequencycalculations.Add selected atoms to HessianAtoms set: Creates a set of atoms called HessianAtoms using thecurrently selected atoms in the active 3D Atomistic document. If a set named HessianAtoms has alreadybeen defined for the active document, any of the selected atoms that are not already members of theset will be added to it. To calculate the Hessian for only the atoms in HessianAtoms set you must checkthe Calculate partial Hessian checkbox.Select atoms in HessianAtoms set: Selects the atoms in the HessianAtoms set.Help: Displays the Help topic in a browser.

Access methods

Menu Modules | DMol3 | Calculation | Properties | Frequency | More...

Toolbar | Calculation | Properties | Frequency | More...

Menu Modules | DFTB+ | Calculation | Properties | Frequency | More...

Toolbar | Calculation | Properties | Frequency | More...

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Fukui function selectionChoosing Fukui function on the Properties tab displays options for computing the Fukui index forchemical reactivity. Each type of Fukui function is returned as a set of volumetric data in a .grd file.f(+) Nucleophilic:When checked, indicates that the f+ Fukui function, which reflects susceptibility tonucleophilic attack, will be computed.f(-) Electrophilic:When checked, indicates that the f- Fukui function, which reflects susceptibility toelectrophilic attack, will be computed.f(0) Radical:When checked, indicates that the f0 Fukui function, which reflects susceptibility to attackby radicals will be computed. This is simply the average of f+ and f-.Grid...: Provides access to the DMol3 Grid Parameters dialog, which allows you to set the resolution andextents of the grid used to calculate the volumetric properties of the orbitals.

Tip: The default resolution of the grid is 0.2 Å. You can also modify this by editing the input files andadding the keyword Grid.

Access methods

Menu Modules | DMol3 | Calculation | Properties | Fukui function

Toolbar | Calculation | Properties | Fukui function

Optics selectionChoosing Optics on the Properties tab displays options for computing optical properties for thestructure using time-dependent density functional theory (TD-DFT).Calculate: Specifies the number of lowest states to be included in the calculation of optical propertiesand the type of states. Options are:n Singletn Triplet

Note: Optics calculations can only be performed on nonperiodic systems or 3D periodics with theGamma k-point only.

Note: Oscillator strengths are available only for singlet state calculations.

Use: Specifies the TD-DFT method to use for calculating the optical properties, options are:n ALDA (default) - calculates TD-DFT excitations using the ALDA kernel with exchange-correlation terms

included.n ALDAx - calculates TD-DFT excitations using a modified ALDA kernel with the exchange term only.n RPA - no exchange-correlation response, only electrostatic response included.More...: Opens the DMol3 Optics Options dialog, which provides options for controlling thepolarizability and frequency.Optimize geometry for: Specify the excited state whose geometry should be optimized. Default = 1 (thatis, the first excited state).The optimized structure for the specified state will be saved in the <seedname>_[S,T,E]<n>_GO.xsdoutput file, where:

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n S is a singlet staten T is a triplet staten E is a spin unrestricted staten <n> is the number of the excited state

Note: The excited state's geometry can only be optimized for nonperiodic systems.

Calculate polarizability:When checked, indicates that linear polarizability will also be calculated. Thissum-over-states calculation requires all available excitations to be computed and prevents selection ofthe number of lowest states to calculate.

Note: Polarizabilities are calculated by a sum-over-states expression. This calculation can take a verylong time and requires significantly morememory than the default optics calculation.

Note: Polarizabilities calculations can only be performed on nonperiodic systems.

Access methods

Menu Modules | DMol3 | Calculation | Properties | Optics

Toolbar | Calculation | Properties | Optics

DMol3 Optics Options dialogThe DMol3 Optics Options dialog allows you to specify options for polarizability calculations. Results ofthese calculations can be found by inspecting the job's .outmol file.Calculate hyperpolarizabilities:When checked, indicates that hyperpolarizabilities will also becalculated.Calculate frequency dependent properties:When checked, indicates that processes which depend onfrequency will also be calculated. When the Calculate hyperpolarizabilities checkbox is checked, theavailable processes include:n frequency dependent linear polarizabilityn second harmonic generation (SHG)n optical rectification (OR)n electro-optic Pockels effect (EOPE)n third harmonic generation (THG)n dc-induced second harmonic generation (dc-SHG)n intensity dependent refractive index (IDRI)n electro-optic Kerr effect (EOKE)When the Calculate hyperpolarizabilities checkbox is unchecked only the frequency dependent linearpolarizability is calculated.Incident light: The wavelength of the incoming light to apply to the processes (in nm).

Note: The default value of 514.5 nm corresponds to the standard Ar laser. Other popular wavelengthsfor laser spectrometers include 632.8 nm (He-Ne), 785 nm (diode), and 1064 nm (Nd:YAG).

Help: Displays the Help topic in a browser.

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Access methods

Menu Modules | DMol3 | Calculation | Properties | Optics | More...

Toolbar | Calculation | Properties | Optics | More...

Orbitals selectionChoosing Orbitals on the Properties tab displays options for computing molecular orbitals forvolumetric rendering.HOMO:When checked, indicates that the highest occupied molecular orbital is selected for rendering.LUMO:When checked, indicates that the lowest unoccupied molecular orbital is selected for rendering.Grid...: Provides access to the DMol3 Grid Parameters dialog, which allows you to set the resolution andextents of the grid used to calculate the volumetric properties of the orbitals.Extra levels above/below the Fermi level: Specify additional orbitals above the LUMO and below theHOMO level to be computed. Entering a value in this text boxmeans that the specified number ofoccupied and virtual orbitals will be computed in addition to HOMO/LUMO, if chosen. For example,entering a value of 5 when HOMO and LUMO checkboxes are checked, results in 5 occupied and 5 virtualorbitals being computed, in addition to the HOMO and LUMO (a total of 12 orbitals).

Tip: The default resolution of the grid is 0.2 Å. You can also modify this by editing the input files andadding the keyword Grid.

Access methods

Menu Modules | DMol3 | Calculation | Properties | Orbitals

Toolbar | Calculation | Properties | Orbitals

Population analysis selectionChoosing Population analysis on the Properties tab displays options for computing various sorts ofatomic population analyses.Mulliken analysis: Select the type ofMulliken population analysis to be performed from the dropdownlist. Available options are:n None - turns offMulliken analysisn Atomic Charge - computes the total Mulliken charge on each atomn Orbital & Charge - computes the contribution to the atomic charge from each atomic orbital on each

atomn Overlap Matrix - computes the overlap population in each pair of atomic orbitals on different atomsWhenever Mulliken bond orders are calculated, DMol3will automatically computeMayer bond ordersas well.

Note: Bond orders can only be calculated for nonperiodic structures. Symmetry information shouldnot be used when calculating bond orders, i.e., theUse symmetry checkbox on the Setup tab shouldbe unchecked.

Hirshfeld analysis: Select the degree of Hirshfeld analysis to be performed from the dropdown list.Available options are:

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n None - turns off Hirshfeld analysisn Chargen Dipolen QuadrupoleESP charges:When checked, indicates that atomic-centered charges that best reproduce the DFTCoulomb potential will be computed as part of the DMol3 run.

Access methods

Menu Modules | DMol3 | Calculation | Properties | Population analysis

Toolbar | Calculation | Properties | Population analysis

DMol3 Grid Parameters dialogThe DMol3 Grid Parameters dialog allows you to set the resolution and extents of the grid used tocalculate the volumetric properties of the orbitals.Grid resolution: Specifies the resolution of the grid. Available values are:n Coarse - 0.4 Å grid intervaln Medium - 0.25 Å grid intervaln Fine - 0.15 Å grid intervalGrid interval: Alternatively, specifies a user-defined value for the grid spacing. Setting this parameter toa value other than one of those listed above will cause theGrid resolution to be set to Customized.

Tip: A smaller grid interval (i.e., finer resolution) produces a higher quality grid, but is more costly tocompute and display.

Border: Specifies the size of the border to impose about themolecular extents when creating thevolumetric grid.

Note: The values set in this dialog will be used for the computation of all volumetric properties,regardless of where the dialog was accessed from.

Help: Displays the Help topic in a browser.

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Access methods

Menu Modules | DMol3 | Calculation | Properties | Electron density | Grid...

Modules | DMol3 | Calculation | Properties | Electrostatics | Grid...

Modules | DMol3 | Calculation | Properties | Fukui | Grid...

Modules | DMol3 | Calculation | Properties | Orbitals | Grid...

Toolbar | Calculation | Properties | Electron density | Grid...

| Calculation | Properties | Electrostatics | Grid...

| Calculation | Properties | Fukui | Grid...

| Calculation | Properties | Orbitals | Grid...

Job Control tabDMol3 calculations run in the background on a server through the gateway. The Job Control tab allowsyou to select a server for the DMol3 calculation and to control some aspects of how the calculation willbe performed.

Note: The options specified on the Job Control tab only apply to new jobs. They do not affect jobsthat are already running.

Gateway location: Select a server for the DMol3 calculation from the list of available server machines.You can add servers to the list using the Server Console.Queue: Specify the queue to which the job will be submitted. Select the desired queue from thedropdown list, which displays the available queues on the chosen gateway. SeeWorking with queues foradditional details.Job description: Specify the name to be used to identify the job.A default job description is automatically assigned. An alternative description can be chosen byunchecking the Automatic checkbox and entering the new name in the Job description text box.Automatic:When checked, indicates that a job description will be selected automatically. Default =checked.Run in parallel on: Indicates that the job will be run on the selected gateway using the specified numberof computer cores. The text to the right of the Run in parallel on control indicates themaximum numberof cores available on the selected gateway.Max. memory: Specify the runtimememory per core, in MB, available to DMol3. Default = 2048 MB.File usage: Specify where to store temporary files and how often to write restart information. Availableoptions are:n Smart - Keep as much data in memory as possible, but write out restart information after each

completed geometry step. Data that does not fit into thememory allowance specified above will stillbe written to disk.

n Memory -Maximizememory use, write restart information only at the end of a job. Large arrays aretemporarily paged to disk. If a job fails with this setting, restart files will not be created.

n Disk - Keep all data on disk, including restart information.

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More...: Provides access to the DMol3 Job Control Options dialog, which allows you to set additionaloptions associated with monitoring and controlling the results of a DMol3 job.

Access methods

Menu Modules | DMol3 | Calculation | Job Control

Toolbar | Calculation | Job Control

DMol3 Job Control Options dialogTheDMol3 Job Control Options dialog allows you to set the options associated with monitoring andcontrolling the results of a DMol3 calculation on a gateway.Update structure:When checked, indicates that intermediate results will be used to update thedisplayed structure as the job progresses. Default = unchecked.Update graphs:When checked, indicates that intermediate results will be used to update the displayedgraphs as the job progresses. Default = checked.Two graphs are created for a geometry optimization or transition state optimization:n total energy vs. optimization cyclen change of energy, maximum force, plus maximum displacement vs. optimization cycle.The forces and displacements reported in this graph are computed in Cartesian coordinates.For a transition state search using a synchronous transit method, the document contains multiplegraphs. There will be a graph of energy vs. reaction coordinate for each linear or quadratic reactionpathway, as well as for each conjugate gradient minimization. Together, these graphs show how theestimate for the transition state is gradually refined.Any of these graphs may be used to animate the history of a geometry optimization or transition statesearch. See Displaying trajectory and chart data for more information.Update textual results:When checked, indicates that intermediate results will be used to updatetextual results files as the job progresses. Default = checked.

Tip: Intermediate updates are useful shortly after initiating a job to assess if it is progressing asexpected.

Update every: Specify the time interval, in seconds, between requests for intermediate updates.

Note: The rate at which new results appear is limited by the time it takes for the server to perform asingle iteration step of the chosen task. This may be significantly longer than the chosen updateinterval.

Retain server files:When checked, indicates that the folder on the server containing the job files will beretained after the job is complete. Default = unchecked.If this checkbox is left unchecked, the job files on the server will be deleted. Regardless of whether it ischecked or unchecked, copies of the results files will always be retrieved from the server, placed in theassociated project on the local machine, and displayed in the Project Explorer.Automatically view output:When checked, automatically opens the job's output files when thecalculation is complete. Files opened may include a structure document and an output file. Default =checked.

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Notify on job completion:When checked, indicates that a dialog will be displayed when the job iscomplete. Default = checked.

Tip: If you run several short jobs in one session, you may find it useful to stop the automatic displayof job completion notices and results files.

Help: Displays the Help topic in a browser.

Access methods

Menu Modules | DMol3 | Calculation | Job Control | More...

Toolbar | Calculation | Job Control | More...

DMol3 Job Files dialogThe DMol3 Job Files dialog allows you to save input files for a DMol3 calculation without running the job,or to run a job using an existing set of input files.This functionality is provided for users who need to run the DMol3 server program in standalonemode,or who wish to edit the DMol3 input files in order to gain access to features not supported by the DMol3interface.Save Files: Saves the input files required to run the DMol3 job on the server but does not submit thejob.

Note: The Save Files button is enabled only when the active document is a 3D model document.

The input files are placed in a subfolder of the current Materials Studio project directory and the primaryDMol3 input file is displayed in theMaterials Visualizer.Run Files: Runs a DMol3 job using an existing set of input files.

Note: The Run Files button is enabled only when the current document is a DMol3 input file.

The job is submitted using the settings specified on theDMol3 Job Control tab.The results files are placed in a subfolder of the current Materials Studio project directory.Help: Displays the Help topic in a browser.

Access methods

Menu Modules | DMol3 | Calculation | Files...

Toolbar | Calculation | Files...

DMol3 Analysis dialogUse the Analysis tools to analyze the results of a DMol3 calculation. The DMol3 Analysis dialog can beaccessed from theModules toolbar and theModules menu.To use any of the Analysis features, you must first perform a DMol3 calculation. When the results arereturned, open the 3D structure file (.xsd) in the Project Explorer and double-click on Analysis. Theanalysis applies to the active document.The types of analysis that can be performed include:

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n display of band structure plotsn display of density of states plotsn display of current/voltage plotsn calculate elastic constantsn display of electron density plots, including the charge, spin, and deformation densitiesn animation of the geometry optimization history for a geometry minimization or a transition state

searchn visualization of Fermi surfacesn display of Fukui function plots for electropositive, electronegative, or radical reactivityn display of optical spectran display of orbital eigenvalues and plotting ofmolecular orbitals in three dimensionsn display of the computed atomic populations from Mulliken, Hirshfeld, or electrostatic potential

analysisn display of electrostatic potential plotsn display a study table containing rate coefficientsn display of Raman spectran display of solvation propertiesn display of thermodynamic propertiesn display of transmission plotsn calculation of vibrational spectra and animation of normal modes of vibrationsHelp: Displays the Help topic for the currently selected analysis.

Access methods

Menu Modules | DMol3 | Analysis

Toolbar | Analysis

Band structure selectionSelect the Band structure option on the DMol3 Analysis dialog to display the Band structure dialog.These controls specify the DMol3 band structure calculation results file to be used and the type of bandstructure chart to be generated.Results file: Indicates the DMol3 output file associated with this calculation. This field displays the nameof the active document. You can change the active document by clicking on the desired documentwindow or by double-clicking on the document name in the Project Explorer.Energy units: Specify the energy units to be used for the dispersion graph. Available options are:n eVn HaScissors: Specify the scissors operator to be used in plotting the band structure.The scissors operator is only applied for insulating systems, which have a clear separation betweenvalence band and conduction band states. It is ignored for metallic systems.Graph style: Specify the style to be used for the band structure graph. Available options are:n Pointsn Line

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Show DOS:When checked, indicates that a density of states from the specified results file will bedisplayed, together with the band structure graph.Full DOS:When selected, indicates that the total density of states will be displayed.Partial:When selected, indicates that the partial density of states (PDOS) will be displayed.The angular momenta to be included in the PDOS display can be controlled using the s, p, d, f, and Sumcheckboxes.

Note: When the appropriate structure document is active and atoms are selected, the contribution tothe density of states from the selected atoms will be plotted. Otherwise, the contribution from allatoms is considered.

Display DOS: Specify which spin components should be plotted in the density of states graph. For aspin-polarized calculation, the supported options are:n Total - contributions from both spin-up and spin-down eigenstates are summed.n Alpha - contributions from spin-up eigenstates only.n Beta - contributions from spin-down eigenstates only.n Alpha and Beta - contributions from both spin-up and spin-down eigenstates are displayed in a

butterfly plot.n Spin - difference between contributions from spin-up and spin-down eigenstates is displayed.n Total and SpinWhen a non-spin-polarized DMol3 calculation is analyzed, only the Total option is available.Function: Specify whether to plot the untreated DOS or the integrated density of states (the number ofstates).More...: Provides access to the DMol3 DOS Analysis Options dialog, which allows the parameterscontrolling the density of states integration method to be specified.

Note: The Full, Partial, DOS display, andMore... options are enabled only if the ShowDOS checkboxis checked.

View: Displays the band structure using the options specified.

Access methods

Menu Modules | DMol3 | Analysis | Band structure

Toolbar | Analysis | Band structure

Current/Voltage selectionThe following options are available when Current/Voltage is selected from the list of properties.Results file: Indicates the DMol3 output file associated with this calculation. This field displays the nameof the active document. You can change the active document by clicking on the desired documentwindow or by double-clicking on the document name in the Project Explorer.View: Displays the current/voltage chart.

Dialogs in DMol3  | Page 135

Access methods

Menu Modules | DMol3 | Analysis | Current/Voltage

Toolbar | Analysis | Current/Voltage

Density of states selectionSelect theDensity of states option on the DMol3 Analysis dialog to display the Density of states dialog.These controls specify the DMol3 density of states calculation results file to be used and the type ofdensity of states chart to be generated.Results file: Indicates the DMol3 output file associated with this calculation. This field displays the nameof the active document. You can change the active document by clicking on the desired documentwindow or by double-clicking on the document name in the Project Explorer.Energy units: Specify the energy units to be used for the density of states graph. Available options are:n eVn HaFull DOS:When selected, indicates that the total density of states will be displayed.Partial:When selected, indicates that the partial density of states (PDOS) will be displayed.The angular momenta to be included in the PDOS display can be controlled using the s, p, d, f, and Sumcheckboxes.

Note: When the appropriate structure document is active and atoms are selected, the contribution tothe density of states from the selected atoms will be plotted. Otherwise, the contribution from allatoms is considered.

Display DOS: Specify which spin components should be plotted in the density of states graph. For aspin-polarized calculation, the supported options are:n Total - contributions from both spin-up and spin-down eigenstates are summed.n Alpha - contributions from spin-up eigenstates only.n Beta - contributions from spin-down eigenstates only.n Alpha and Beta - contributions from both spin-up and spin-down eigenstates are displayed in a

butterfly plot.n Spin - difference between contributions from spin-up and spin-down eigenstates is displayed.n Total and SpinWhen a non-spin-polarized DMol3 calculation is analyzed, only the Total option is available.Function: Specify whether to plot the untreated DOS or the integrated density of states (the number ofstates).Scissors: Specify the scissors operator to be used in plotting the density of states.The scissors operator is only applied for insulating systems, which have a clear separation betweenvalence band and conduction band states. It is ignored for metallic systems.More...: Provides access to the DMol3 DOS Analysis Options dialog, which allows the parameterscontrolling the density of states integration method to be specified.View: Displays the density of states using the options specified.

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Access methods

Menu Modules | DMol3 | Analysis | Density of states

Toolbar | Analysis | Density of states

DMol3 DOS Analysis Options dialogThe DMol3 DOS Analysis Options dialog allows you to specify the parameters controlling the density ofstates integration method.Integration method: Select themethod to be used for integrating the density of states results from thedropdown list. Supported methods are:n Smearing - Gaussian broadening is applied to the eigenvalues obtained from the DMol3 calculation.n Interpolation - eigenvalues (and partial weights for a partial density of states) from the DMol3

calculation are interpolated onto a finer k-point grid.The Interpolation method provides an improved representation of the density of states. However, it canonly be used when eigenvalues are available on a Monkhorst-Pack grid with 3 or more points in eachdirection. The k-point set for density of states calculations can be specified on the Density of states -Properties tab on the DMol3 Calculation dialog. If the Interpolation method cannot be used for theselected results, it will be absent from the dropdown list.

Note: The Interpolation integration method is only available for calculations on periodic systems.

Smearing width: Specify the Gaussian broadening to be used.

Note: This option is enabled only if the Smearing integration method is selected.

Accuracy level: Specify the quality of the interpolation to be used. Available options are:n Coarse - Interpolates onto a k-point grid of about 50 × 50 × 50.n Medium - Interpolates onto a k-point grid of about 100 × 100 × 100.n Fine - Interpolates onto a k-point grid of about 200 × 200 × 200.Instrument broadening: Specify an additional broadening to be applied to the interpolated density ofstates.

Note: The Accuracy level and Instrument broadening options are enabled only if the Interpolationintegration method is selected.

Number of points per: Specify number of points per 1 eV or per 1 Ha energy range. Use high settings togenerate charts that remain smooth after a zoom-in operation.OK: Updates the settings with any changes and closes the dialog.Cancel: Closes the dialog without updating any settings.Help: Displays the Help topic in a browser.

Dialogs in DMol3  | Page 137

Access methods

Menu Modules | DMol3 | Analysis | Density of states | More...

Modules | DMol3 | Analysis | Band structure | More...

Toolbar | Analysis | Density of states | More...

| Analysis | Band structure | More...

Elastic constants selectionSelect the Elastic constants option on the DMol3 Analysis dialog to display the Elastic constants dialog.Results file: Indicates the DMol3 output file associated with this calculation. This field displays the nameof the active document. You can change the active document by clicking on the desired documentwindow or by double-clicking on the document name in the Project Explorer.Calculate: Calculates the tensors of the elastic constants and the compliances, the bulk modulus,compressibility, Young modulus, Poisson ratio, and Lame constants for the selected run and writes theresults to a new text document, seedname Elastic Constants.txt, in the results folder.

Access methods

Menu Modules | DMol3 | Analysis | Elastic constants

Toolbar | Analysis | Elastic constants

Electron density selectionSelect the Electron density option on the DMol3 Analysis dialog to display the Electron density dialog.These controls specify the DMol3 density calculation results file to be used and the type of density fieldto be calculated. The calculation is performed on the active structure file (.xsd file).Results file: Indicates the DMol3 output file associated with this calculation. This field displays the nameof the active document. You can change the active document by clicking on the desired documentwindow or by double-clicking on the document name in the Project Explorer.Density field: Controls which type of density will be plotted. Select from the available density types inthe dropdown list. Possible options include:n charge densityn spin densityn deformation densityOnly choices that were computed as part of a DMol3 job will appear. If you do not see a particularchoice, it is because it has not been computed. Perform another calculation, specifying the desiredchoice to obtain the density. See the Properties tab and Electron density selection help topics forinformation on setting up such a calculation.View isosurface on import: Controls how the volumetric data is displayed. If this item is checked, a 3Disosurface is created when the Import button is pressed. The default value of the surface is:n charge density: 0.2 electrons/Å3 for crystals, and 0.017 electrons/Å3 for moleculesn spin density: 10% of themaximumn deformation density: 10% of themaximumIf this box is not checked, the volumetric data are imported as a 3D field.

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Once you have imported the data, refine the display using the volume visualization controls.Import: Loads the desired volumetric density data into the active document.

Access methods

Menu Modules | DMol3 | Analysis | Electron density

Toolbar | Analysis | Electron density

Energy evolution selectionUse the Energy evolution option on the DMol3 Analysis dialog to display the optimization history of aDMol3 geometry optimization. The structure file (.xsd file) used in the geometry optimization must beopen in theMaterials Visualizer to perform the energy evolution procedure.For calculations using the COSMO solvent model, a COSMO Sigma Profile chart can be generated.Two charts are created during a geometry optimization or transition state optimization:n total energy vs. optimization cycle, andn change of energy, maximum force, plus maximum displacement vs. optimization cycle.The forces and displacements reported in these charts are in Cartesian coordinates.For a transition state search using a synchronous transit method, the chart document will containmultiple charts. There will be a chart of energy vs. reaction coordinate for each linear or quadraticreaction pathway, as well as for each conjugate gradient minimization. Together, these charts show howthe estimate for the transition state is gradually refined.These charts are the same as would be generated by selecting Update graphs in the DMol3 Job ControlOptions dialog. Charts generated using Energy evolution can be generated whether or not you choseUpdate graphs in the original calculation.

Note: Each time you select Update graphs the existing chart documents are rewritten, and anychanges or annotations you havemade to the charts will be lost.

Results file: Indicates the DMol3 output file associated with this calculation. This field displays the nameof the active document. You can change the active document by clicking on the desired documentwindow or by double-clicking on the document name in the Project Explorer.View: Generates the chart documents as described above.

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Menu Modules | DMol3 | Analysis | Energy evolution

Toolbar | Analysis | Energy evolution

Fermi surface selectionThe following options are available when Fermi surface is selected from the list of properties.Results file: Select the DMol3 results file from which the optical properties information will be taken.

When more than one set of results is available, use the button to browse the current directory andappropriate subdirectories for results files.Filter: Choose how to filter the available Fermi surfaces, options are:n All - all Fermi surfaces are available.

Dialogs in DMol3  | Page 139

Show only bands crossing Fermi level:When checked only the bands which traverse the Fermi levelwill be listed in the table below.n Band - the index of the band in this rown Spin - the spin for this bandn From - lowest value of the energy for the band (in eV)n To - highest value of the energy for the band (in eV)Import: Imports the selected Fermi surface from the DMol3 results file into the current structuredocument.

Tip: In order to generate Fermi surfaces the calculation must have requested Density of statesproperties.

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Menu Modules | DMol3 | Analysis | Fermi surface

Toolbar | Analysis | Fermi surface

Fukui function selectionSelect the Fukui function option on the DMol3 Analysis dialog to display the Fukui function dialog. Thesecontrols specify the Fukui function to be plotted. The plot is based on the specified .outmol results fileand the active .xsd structure file.Results file: Indicates the DMol3 output file associated with this calculation. This field displays the nameof the active document. You can change the active document by clicking on the desired documentwindow or by double-clicking on the document name in the Project Explorer.Fukui field: Controls which type of Fukui function will be plotted. Select from the available Fukuifunctions in the dropdown list. Possible options include:n Electrophilic, f(-): the reactivity with respect to electrophilic attackn Nucleophilic, f(+): the reactivity with respect to nucleophilic attackn Radical, f(0): the reactivity with respect to radical attackIn each case, greater values indicate a greater susceptibility to attack.Only choices that were computed as part of a DMol3 job will appear. If you do not see a particularchoice, it is because it has not been computed. Perform another calculation, specifying the desiredchoice to obtain the function. See the Properties tab and Fukui function selection help topics forinformation on setting up such a calculation.View isosurface on import: Controls how the volumetric data is displayed. If this item is checked, a 3Disosurface is created when the Import button is pressed. The default value of the surface is 10% of themaximum for all types of Fukui functions.If this box is not checked, the volumetric data are imported as a 3D field.Once you have imported the data, refine the display by using the volume visualization controls.Assign Fukui charges: Imports the selected charges into the active structure document and assignspartial charges to each atom for the function selected as the Fukui field. Select the type of charges thatyou wish to import from the dropdown list. Available options are:n Mullikenn Hirshfeld

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Import: Loads the desired volumetric density data into the active document.

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Menu Modules | DMol3 | Analysis | Fukui function

Toolbar | Analysis | Fukui function

Optics selectionSelect theOptics option on the DMol3 Analysis dialog to display the Optics dialog. This provides controlsfor generating spectra, based on the specified .outmol results file and the active .xsd structure file.Results file: Indicates the DMol3 output file associated with this calculation. This field displays the nameof the active document. You can change the active document by clicking on the desired documentwindow or by double-clicking on the document name in the Project Explorer.View spectrum: Generates a chart document containing the predicted optical spectrum for thestructure being studied. The spectrum takes the form of a plot of oscillator strength in arbitrary unitsagainst wavelength expressed in nm.View grid: Generates a study table document containing a list of wavelengths (in nm) and peakoscillator strengths (in arbitrary units) for the allowed excitations used to generate the optical spectrum.

Note: Oscillator strengths are available only for singlet state calculations.

Note: Excited states calculated with unrestricted reference are a mixture of singlets and triplets.Comparing spin-restricted and spin-unrestricted results requires the results of spin-restrictedcalculations for singlet and triplet states.

Units: Specify the frequency units used for the display of optical properties, options are:n eVn cm-1n nm (default)More...: Provides access to the DMol3 Optics Analysis Options dialog.

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Menu Modules | DMol3 | Analysis | Optics

Toolbar | Analysis | Optics

DMol3 Optics Analysis Options dialogThe DMol3 Optics Analysis Options dialog allows you to specify the parameters controlling the opticscalculation method.Broadening method: Select themethod to be used for calculating the optical spectrum from thedropdown list. Supported methods are:n Gaussian - Gaussian broadening is applied to the eigenvalues obtained from the DMol3 calculation.n Lorentziann NoneSmearing width: Specify the Gaussian broadening to be used.

Dialogs in DMol3  | Page 141

Note: This option is enabled only if the Gaussian integration method is selected.

FWHM parameter: Specify the full width at half maximum, in nm, for the Lorentzian smoothingfunction. Range = 0.1 - 100 nm. Default = 20 nm.

Note: This option is enabled only if the Lorentzian integration method is selected.

Reverse wavelength axis:When checked, indicates that the values on the X axis will decrease from leftto right.Reverse intensity axis:When checked, indicates that the values on the Y axis will decrease from bottomto top.Help: Displays the Help topic in a browser.

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Menu Modules | DMol3 | Analysis | Optics | More...

| Analysis | Optics | More...

Orbitals selectionSelect theOrbitals option on the DMol3 Analysis dialog to display the Orbitals dialog. This dialogdisplays a list of orbital eigenvalues for a system and provides controls for generating 3D volumetricimages of the orbitals. The calculation is based on the specified .outmol results file and the active .xsdstructure file.

Note: TheOrbitals analysis applies only to molecular systems and to periodic structures that use theΓ-point. Calculations using multiple k-points cannot be analyzed in this way.

Results file: Indicates the DMol3 output file associated with this calculation. This field displays the nameof the active document. You can change the active document by clicking on the desired documentwindow or by double-clicking on the document name in the Project Explorer.Filter: Controls which orbitals are displayed in the table. Options include:n All: Displays eigenvalues for all the orbitals that were printed in the DMol3 output file. This includes all

of the occupied orbitals and the first ten virtual orbitals.n Available: Displays only the eigenvalues associated with orbitals that are available for volumetric

rendering. Only orbitals that were computed as part of a DMol3 job will appear. If the list of availableorbitals is empty, perform another calculation, specifying the desired orbitals on the Properties tab.

n Spin up: Displays only eigenvalues from alpha-spin (spin up) orbitals. If the calculation is closed-shell,this filter displays all orbitals.

n Spin down: Displays only eigenvalues from beta-spin (spin down) orbitals. If the calculation is closed-shell, this filter displays no orbitals.

The table displays molecular orbital eigenvalues along with information about them. The columnheadings provide the following information:

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n Field: If Yes, the orbital has volumetric data associated with it. These are the orbitals that can bedisplayed.

n N: Indicates the orbital number starting from 1 for the lowest energy orbital.n s: Indicates the spin of the orbital. For spin-restricted calculations, all orbitals are labeled +. For spin-

unrestricted calculations, alpha-spin orbitals are labeled + and beta-spin orbitals are labeled -.n Eigenvalue: Indicates the eigenvalue of each orbital in Hartree.n Type: Indicates the highest occupied molecular orbital (HOMO) and the lowest unoccupied molecular

orbital (LUMO).Only orbitals whose data were computed as part of a DMol3 job will be available for rendering. If you donot see a Yes in the Field of a particular orbital, it is because it has not been computed. Perform anothercalculation, specifying the desired orbital. See the Properties tab and Orbitals selection help topics forinformation on setting up such a calculation.View isosurface on import: Controls how the volumetric data is displayed. If this item is checked, a 3Disosurface is created when the Import button is pressed. The default is two isosurfaces at values ±0.03.If this box is not checked, the volumetric data are imported as a 3D field.Once you have imported the data, refine the display using the volume visualization controls.Import: Loads the desired molecular orbital data into the active document for volumetric display.

Access methods

Menu Modules | DMol3 | Analysis | Orbitals

Toolbar | Analysis | Orbitals

Population analysis selectionSelect the Population analysis option on the DMol3 Analysis dialog to display the Population analysisdialog. These controls import atomic charges and bond orders and assign them to the active structurefile (.xsd).Results file: Indicates the DMol3 output file associated with this calculation. This field displays the nameof the active document. You can change the active document by clicking on the desired documentwindow or by double-clicking on the document name in the Project Explorer.Assign charges to structure: Imports the selected charges into the active structure document andassigns partial charges to each atom. Select the type of charges that you wish to import from thedropdown list. Available options are:n Mullikenn Hirshfeldn ESPAssign spins to structure: Imports the selected spins into the active structure document and assignspartial spins to each atom. Select the type of spins that you wish to import from the dropdown list.Available options are:n Mullikenn HirshfeldAssign bond orders to structure: Imports the selected bond orders into the active structure documentand assigns them to each bond. Select the type of bond orders that you wish to import from thedropdown list. Available options are:

Dialogs in DMol3  | Page 143

n Mayern Mulliken

Note: The import options above are available only when the appropriate types of charges, spins, andbond orders have been generated as part of the DMol3 calculation.

Tip: You can see the charges, spins, and bond orders in the active structure document by labeling theatoms and bonds according to their charge, spin, or order.

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Menu Modules | DMol3 | Analysis | Population analysis

Toolbar | Analysis | Population analysis

Potentials selectionSelect the Potentials option on the DMol3 Analysis dialog to display the Potentials dialog. These controlsspecify the type of potential field to be generated. The volumetric image calculation is based on thespecified .outmol results file and the active .xsd structure file.Results file: Indicates the DMol3 output file associated with this calculation. This field displays the nameof the active document. You can change the active document by clicking on the desired documentwindow or by double-clicking on the document name in the Project Explorer.Potential field: Controls which type of potential will be plotted. The only option available is Electrostaticpotential (Coulomb).Only choices that were computed as part of a DMol3 job will appear. If you do not see a particularchoice, it is because it has not been computed. Perform another calculation, specifying the desiredchoice to obtain the function. See the Properties tab and Electrostatics selection help topics forinformation on setting up such a calculation.View isosurface on import: Controls how the volumetric data is displayed. If this item is checked, a 3Disosurface is created when the Import button is pressed. The default value of the surface is ±10 kcal/mol(0.016 au).If this box is not checked, the volumetric data are imported as a 3D field.Once you have imported the data, refine the display using the volume visualization controls.Import: Loads the desired molecular orbital data into the active document for volumetric display. If thestructure is a slab with a region of vacuum and theWork function checkbox was checked, a Chartdocument, named <seedname> Potential Profile.xcd is also displayed containing a plot of thepotential averaged in the planes perpendicular to the surface normal. This chart document also containsthe value of work function calculated as a difference between the potential level in a vacuum and theFermi energy.

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Menu Modules | DMol3 | Analysis | Potentials

Toolbar | Analysis | Potentials

Raman spectrum selectionThe following options are available when Raman spectrum is selected from the list of properties.

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Results file: Select the DMol3 results file from which the Hessian will be taken. This field displays thename of the active document. You can change the active document by clicking on the desired documentwindow or by double-clicking on the document name in the Project Explorer.Function: Specify whether to calculate the Intensity or the Activity of the vibrational mode.Temperature: If the intensity of the vibrational mode is being calculated set the temperature in Kelvin.Incident light: If the intensity of the vibrational mode is being calculated specify the wavelength of theincident light in nm. The default value of 514.5 nm corresponds to a standard Ar laser. Other popularwavelengths for laser Raman spectrometers include 632.8 nm (He-Ne), 785 nm (diode), and 1064 nm(Nd:YAG).Smearing: Specify the type of broadening (Gaussian or Lorentzian) and width to be used. DefaultLorentzian broadening with width = 20.0 cm-1.Units: Specify the units for the X axis of the spectrum, options are:n meVn THzn cm-1Reverse wavenumber axis:When checked, indicates that the values on the X axis will decrease fromright to left.Reverse intensity axis:When checked, indicates that the values on the Y axis will decrease from bottomto top.Once a Hessian has been imported, vibrational mode frequencies and, if ATP tensors were calculated,absorption intensities can be displayed in the form of a list of values or graphically as a vibrationalspectrum using the Vibrational Analysis tool.View: Displays the selected Raman spectrum.

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Menu Modules | DMol3 | Analysis | Raman spectrum

Toolbar| Analysis | Raman spectrum

Reaction kinetics selectionSelect the Reaction kinetics option on the DMol3 Analysis dialog to display the Reaction kinetics dialog.Results file: Indicates the collection document containing the reaction ingredients. This field displaysthe name of the active document. You can change the active document by clicking on the desireddocument window or by double-clicking on the document name in the Project Explorer.

Note: Reaction kinetics calculation can be performed only if the collection document contains well-defined reaction ingredients: the reactant(s), the product(s), and the transition state. All thestructures must have Hessians and total energy calculated. Reactant(s) and product(s) systems mustbe in the ground state - that is all the eigenfrequencies must be real and non-negative.The transitionstatemust be a valid saddle point with one and only one imaginary frequency for which eigenvectorsrepresent the reaction path.

From: To: Specify the temperature range for the output of the calculated rate coefficient.Apply tunneling correction:When checked, indicates that the reaction rate coefficient will be calculatedtaking into account the tunneling correction.

Dialogs in DMol3  | Page 145

Threshold correction: Specify the value to be added to the DFT reaction threshold. This correctioncompensates for the underestimation of reaction barriers at the DFT level of theory.Vibrational frequencies scaling: Specify the value of the scaling coefficient to be applied to calculatedvibrational frequencies before evaluation of vibrational partition functions.Calculate: Calculate and display a study table containing rate coefficients for the forward and reversereactions.

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Menu Modules | DMol3 | Analysis | Reaction kinetics

Toolbar | Analysis | Reaction kinetics

Solvation properties selectionSelect the Solvation properties option on the DMol3 Analysis dialog to display the options for displayingCOSMO properties.Results file: Indicates the DMol3 output file associated with this calculation. This field displays the nameof the active document. You can change the active document by clicking on the desired documentwindow or by double-clicking on the document name in the Project Explorer.Import: Controls which type of solvation field will be displayed and loads the desired volumetric densitydata into the active document. Available options are:n COSMO surface (default) - displays the surface created from COSMO charges.n COSMO point charges - displays points corresponding to COSMO charges.View sigma chart on import: Controls how the volumetric data is displayed. If this item is checked, a 3Disosurface is created when the Import button is clicked.Once you have imported the data, refine the display using the volume visualization controls.

Note: Both the COSMO surface and points can have the COSMO potential mapped onto them. Theycan be displayed using the volume visualization controls.

Access methods

Menu Modules | DMol3 | Analysis | Solvation properties

Toolbar | Analysis | Solvation properties

Choose COSMO File dialogThe Choose COSMO File dialog allows you to import COSMO solvent files from the current project orfrom local and network locations.Select a solvent file you would like to import from the project document chooser. The selected file will bedisplayed in the Solvent 1 or Solvent 2 dropdown list for the Solvation properties selection of the DMol3Analysis dialog.

Note: The document chooser will only show COSMO files (.cosmo).

Import...: Provides access to a file browser which enables you to navigate to and select COSMO solventfiles from local or network locations. The selected file will be imported into the current project and

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displayed in the Solvent 1 or Solvent 2 dropdown list for the Solvation properties selection on the DMol3Analysis dialog.Help: Displays the Help topic in a browser.

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Menu Modules | DMol3 | Analysis | Solvation properties| Browse...

Toolbar | Analysis | Solvation properties | Browse...

Structure selectionPressing theUpdate button on the Structure dialog restores the view of the active 3D model documentbased on the data in the last-saved version of the file. If you havemademodifications to a structure onscreen, use theUpdate button to restore the geometry to that saved in the file. If you havemanuallyedited and saved the output file (.outmol), pressing theUpdate button causes Materials Studio toreload the structure, which you can then use for analysis.

Note: Every DMol3 calculation generates a structure containing the final geometry. For most types ofcalculation the final geometry will be different from the initial geometry. If an energy calculation isperformed the final geometry is the same as the initial geometry, unless the structure is snapped tosymmetry, in which case the final geometry will be only slightly different from the initial geometry.

Results file: Indicates the DMol3 output file associated with this calculation. This field displays the nameof the active document. You can change the active document by clicking on the desired documentwindow or by double-clicking on the document name in the Project Explorer.Update: Updates the structure of the active document with the geometry contained in the .outmol file.TheUpdate button also reimports the Hessian into themodel, if one exists.

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Menu Modules | DMol3 | Analysis | Structure

Toolbar | Analysis | Structure

Thermodynamic properties selectionWhenever a DMol3 calculation includes a vibrational analysis, you can compute and displaythermodynamic properties as a function of temperature. These include the enthalpy, entropy, freeenergy, and heat capacity. Themethod of computation is described in Thermodynamic calculations.Results file: Indicates the DMol3 output file associated with this calculation. This field displays the nameof the active document. You can change the active document by clicking on the desired documentwindow or by double-clicking on the document name in the Project Explorer.View: Generates and displays a chart of the enthalpy, entropy, free energy, and heat capacity as afunction of temperature.

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Menu Modules | DMol3 | Analysis | Thermodynamic properties

Toolbar | Analysis | Thermodynamic properties

Dialogs in DMol3  | Page 147

Transmission selectionThe following options are available when Transmission is selected from the list of properties.Results file: Indicates the DMol3 output file associated with this calculation. This field displays the nameof the active document. You can change the active document by clicking on the desired documentwindow or by double-clicking on the document name in the Project Explorer.View: Displays the transmission function.

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Menu Modules | DMol3 | Analysis | Transmission

Toolbar | Analysis | Transmission

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DMol3 keywordsThis section documents all keywords that are recognized by DMol3, including many that are notaccessible from the DMol3 setup dialog. Commands are listed in alphabetical order on the Contents tab.

Tip: For information on DMol3 keywords, please refer to theMaterials Studio Online Help.

The .input fileThe .input file is a simplified command input file that consists of keywords followed by values (real,integer, or character). These keywords and their values specify flags for the calculation, such as the typeof basis set or themaximum number of self-consistent iterations to be employed.Using the .input file to run DMol3 in standalonemode is outlined in Running DMol3 in standalonemode.

Format for documenting DMol3 standalone commandsThe keyword topics provide detailed descriptions of each of the commands available in the standaloneversion. For each command, documentation is divided into subsections. Conventions used indocumenting the commands are described below, along with a short description of the intent of eachsubsection.The Syntax subsection begins with the command syntax presented in as generic a form as possible.Several type style conventions are used to distinguish different kinds of words. For example:command_keyword [value_keyword, ..., value_number, ...]Words (or letters) in bold and not italicized indicate the names of keywords that must be typed asshown.

Note: Keywords must be typed as shown, but are case-insensitive. They may be typed in lower-,upper-, or mixed case.

Note: Keyword options must be separated by spaces. Tab characters are not supported.

A hash mark (#) at the beginning of a line indicates a comment line. It can also be used to temporarilycomment-out a command.Words in bold italics indicate options that must be replaced with appropriate text, as indicated in thetable of allowed values that follows the syntax line for each command.The values appropriate to each keyword are also listed and may be (as appropriate) numbers orenumerated constants:n Numbers can be represented in integer, floating-point, or exponential form. DMol3 converts the

number to the appropriate form, depending on the context.n Mutually exclusive options are represented by enumerated constants identified by names The names

of enumerated constants must not be enclosed in quotation marks.Optional item(s) are enclosed in round brackets( ), and, if there is more than one, the items areseparated by commas.Ellipses (...) indicate that a kind of item may be repeated.The brackets, commas, and ellipses themselves are used for documentation only and should not beincluded in the real command.

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DMol3 ReferencesA list of published papers describing calculations using DMol3 can be found on theMaterials Studiowebsite: http://accelrys.com/products/materials-studio/publication-references/dmol3-references/.Ackland, G. J. "Embrittlement and the Bistable Crystal Structure of Zirconium Hydride", Phys. Rev. Lett.,80, 2233-2236 (1998).Allis, D. G.; Prokhorova, D. A., Korter, T. M. J. Phys. Chem. A, 110, 1951 (2006).Almlöf, J.; Faegri., K, Jr.; Korsell, K. J. Comput. Chem., 3, 385 (1982).Andzelm, J.; Kölmel, Ch.; Klamt, A. "Incorporation of solvent effects into the density functionalcalculations ofmolecular energies and geometries", J. Chem. Phys., 103, 9312-9320 (1995).Andzelm, J.; Wimmer, E.; Salahub, D. R. "Spin density functional approach to the chemistry of transitionmetal clusters: Gaussian-type orbital implementation", in The Challenge of d- and f-Electrons: Theoryand Computation, Salahub, D. R.; Zerner, M. C., Eds., ACS Symp. Ser., ser. 394 (1989).Auckenthaler, T.; Blum, V.; Bungartz, H.-J.; Huckle, T.; Johanni, R.; Krämer, L.; Lang, B.; Lederer, H.;Willems, P. R.; "Parallel solution of partial symmetrix eigenvalue problems from electronic structurecalculations", Parallel Computing, 37, 783-794 (2011).Baerends, E. J.; Ellis, D. E.; Ros, P. Chem. Phys., 2, 41 (1973).Bagno, A.; Scorrano, G. J. Phys. Chem., 100, 1545 (1996).Bakalarski, G.; Grochowski, P.; Kwiatkowski, J. S.; Lesyng, B.; Leszczynski, J. "Molecular and electrostaticproperties of the N-methylated nucleic acid bases by density functional theory", Chem. Phys., 204, 301-311 (1996).Baker, J. "An algorithm for the location of transition states", J. Comput. Chem., 7, 385 (1986).Baker, J. "Geometry optimization in Cartesian coordinates: Constrained optimization", J. Comput.Chem., 13, 240 (1992).Baker, J. "Techniques for geometry optimization: A comparison of Cartesian and natural internalcoordinates", J. Comput. Chem., 14, 1085 (1993).Baker, J.; Bergeron, D. "Constrained optimization in Cartesian coordinates", J. Comput. Chem., 14, 1339(1993).Baker, J.; Hehre, W. J. "Geometry optimization in Cartesian coordinates: The end of the Z-matrix?", J.Comput. Chem., 12, 606 (1991).Banerjee, A.; Adams, N.; Simons, J.; Shepard, R. "Search for stationary points on surfaces", J. Phys.Chem., 89, 52 (1985).Bayly, C. I.; Cieplak, P.; Cornell, W. D.; Kollman, P. A. "Awell-behaved electrostatic potential basedmethod using charge restraints for deriving atomic charges: the RESP model", J. Phys. Chem., 97, 10269-10280 (1993).Becke, A. D. J. Chem. Phys., 88, 2547 (1988).Becke, A. D. J. Chem. Phys., 84, 4524 (1986).Becke, A. D. "Density-functional thermochemistry. III. The role of exact exchange", J. Chem. Phys., 98,5648-5652 (1993).Ben-Naim, A.; Marcus, Y. "Solvation thermodynamics of nonionic solutes", J. Chem. Phys., 81, 2016(1984).Bengtsson, L. Phys. Rev. B, 59, 12301 (1999).Bergner, A.; Dolg, M.; Kuechle, W.; Stoll, H.; Preuss, H.Mol. Phys., 80, 1431 (1993).

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