Please download program

CTCC

June 16-19 2011

Oscarsborg, Norway

Program and abstracts

1

ESCMQC ’11

European Seminar on

Computational Methods in Quantum Chemistry

2011

The 15th Strasbourg Seminar

June 16Ð19 2011

Oscarsborg Fortress, Dr¿bak, Norway

Organizing Committee

JŸrgen Gauss, Trygve Helgaker (chair), Fred Manby

Secretaries

Anne Marie ¯veraas and John Vedde

Technical Assistant

Simen Reine

2

ESCMQC ’11

3

ESCMQC ’11

Dear participant,

The organizing committee has great pleasure in welcoming you to Oscarsborg For-tress in Dr¿bak, Norway, for the 15th European Seminar on Computational Methods in Quantum Chemistry (ESCMQC), devoted to the development of new computational methods and techniques for molecular and condensed-phase systems. At Oscarsborg, you will hear about the latest developments in theory and computational techniques from some of the foremost workers in the field. In keeping with the tradition of these seminars, which have been organized triennially since the first meeting in Strasbourg in 1969, a preference is given to young speakers. To broaden the scope of these semi-nars and to stay in line with recent developments, we have deviated slightly from the traditional emphasis on molecular quantum chemistry by devoting more time to den-sity-functional theory and condensed-phase methods.

During the next three days, about 90 participants from 20 countries will give a total of 38 oral presentations and 25 poster presentations. It is our hope that these presenta-tions and our discussions will stimulate us all towards new directions and develop-ments in our field.

JŸrgen Gauss, Trygve Helgaker and Fred Manby

Organizing committee of ESCMQC 2011

Sponsor:

ESCMQC 2011 is sponsored by the Centre for Theoretical and Computational Chemistry (CTCC), a Centre of Excellence established by the Research Council of Norway in 2007 and shared between the University of Troms¿ and the University of Oslo. You are invited to visit the home page http://www.ctcc.no/ or, even better, to visit the CTCC research groups for a shorter or longer period, noting that the CTCC has an extensive program for visiting scholars.

4

ESCMQC ’11

5

ESCMQC ’11

Thursday afternoon June 16

13:00 Registration opens

15:00 Light meal (served in the lecture hall)

16:30 Opening

T. Helgaker, University of Oslo, Norway

Session I: New beginnings (16:40Ð18:25) Chair: Dage Sundholm, University of Helsinki, Finland

16:40 Ali Alavi, University of Cambridge, UK (L01)

Quantum Monte Carlo approach to the full CI problem

17:20 Edward F. Valeev, Virginia Tech, USA (L02)

Quantum chemistry beyond atomic orbitals and Slater determinants

18:00 Jonas JusŽlius, University of Troms¿, Norway (L03)

Massively parallel quantum chemistry using multiwavelets

18:25 Coffee

Session II: Molecular properties and spectroscopy (18:55Ð19:45) Chair: Michal Jaszunski, Polish Academy of Sciences, Warsaw, Poland

18:55 Cristina Puzzarini, University of Bologna, Italy (L04)

Benchmarking quantum chemistry with rotational spectroscopy or benchmarking rotational spectroscopy with quantum chemistry?

19:20 Sonia Coriani, University of Trieste, Italy (L05)

Near-edge X-ray absorption fine structure from coupled cluster damped response theory using an asymmetric Lanczos-chain driven algorithm

20:00 Dinner

6

ESCMQC ’11

Friday morning June 17

07:30 Breakfast

Session III: Density functional theory (09:00Ð10:40) Chair: Andreas Gšrling, University of ErlangenÐNuremburg, Germany

09:00 Paul Ayers, McMaster University, Hamilton, Canada (L06)

Two-point weighted density approximations for the kinetic energy and exchangeÐcorrelation energy

09:40 Paola Gori-Giorgi, VU University Amsterdam, The Netherlands, (L07)

Strong spatial correlations in density functional theory

10:10 David J. Tozer, Durham University, UK (L08)

Dispersion, static correlation and delocalisation errors in DFT: an electrostatic theorem perspective

10:40 Coffee

Session IV: Variational coupled-cluster theory and more (11:10Ð12:30) Chair: JŸrgen Gauss, University of Mainz, Germany

11:10 Peter J. Knowles, Cardiff University, UK (L09)

Approximate variational coupled cluster theory

11:40 Tatiana Korona, University of Warsaw, Poland (L10)

Expectation-value coupled cluster theory for molecular propertiesÑtheory and implementation

12:05 Michael Hanrath, University of Cologne, Germany (L11)

Efficient evaluation of projected and expectation values of powers of the Hamiltonian for coupled cluster wavefunctions using an equivalence class decomposition of WickÕs theorem

13:00 Lunch

7

ESCMQC ’11

Friday afternoon June 17

Session V: Optical activity (14:30Ð16:05)

Chair: Antonio Rizzo, IPCF-CNR, Pisa, Italy

14:30 Kenneth Ruud, University of Troms¿, Norway (L12)

Vibronic effects in chiroptical spectra

15:10 T. Daniel Crawford, Virginia Tech, USA (L13)

Localized coupled cluster wave functions for mixed magnetic/electric properties

15:40 Heike Fliegl, University of Helsinki, Finland (L14)

Hydrogen-bond strengths by magnetically induced currents

16:05 Coffee

Session VI: Range separation in DFT (16:35Ð17:40) Chair: Hans J¿rgen Aa. Jensen, University of Southern Denmark, Denmark

16:35 Trond Saue, CNRS and University of Toulouse, France (L15)

Four-component relativistic long-range-MP2Ðshort-range-DFT

17:15 Alexandrina Stoyanova, CNRS and University of Strasbourg, France (L16)

Exploring exact exchange schemes in multideterminant range-separated density functional theory

17:40 Coffee

Session VII: Explicit correlation (18:00Ð18:55) Chair: Ludwik Adamowicz, University of Arizona, USA

18:00 David P. Tew, University of Bristol, UK (L17)

Explicitly correlated coupled cluster theory: robust approximations and localization

18:30 Toru Shiozaki, University of Stuttgart, Germany (L18)

Multireference explicitly correlated F12 theories

19:00 Dinner

20:30 Poster session

8

ESCMQC ’11

Saturday morning June 18

07:30 Breakfast

Session VIII: Density matrix renormalization and more (09:00Ð10:55) Chair: Roland Lindh, Uppsala University, Sweden

09:00 Takeshi Yanai, Institute of Molecular Science, Japan (L19)

Advanced multireference methods for molecular strongly-correlated electronic states

09:40 Yuki Kurashige, Institute of Molecular Science, Japan (L20)

DMRG-CASPT2 theory for large-scale multi-reference problems

10:05 Lan Cheng, University of Mainz, Germany (L21)

Analytical energy gradients in relativistic quantum chemistry: theory and implementation for the spin-free exact two-component theory

10:30 Simen Kvaal, University of Oslo, Norway (L22)

Multiconfigurational time-dependent Hartree method for describing particle loss due to absorbing boundary conditions

10:55 Coffee

Session IX: Density functional theory (11:25Ð12:55)

Chair: Paul Ayers, McMaster University, Hamilton, Canada

11:25 Andreas Gšrling, University of ErlangenÐNuremberg, Germany (L23)

RPA correlation functional based on the exact exchange kernel of TDDFT

12:05 Andrew M. Teale, University of Oslo, Norway (L24)

Dispersion interactions in density-functional theory: an adiabatic connection analysis

12:35 Christoph R. Jacob, Karlsruhe Institute of Technology, Germany (L25)

Unambiguous optimization of effective potentials in finite basis sets

13:00 Lunch

9

ESCMQC ’11

Saturday afternoon June 18

Session X: The condensed phase (14:30Ð16:20) Chair: Fred Manby, University of Bristol, UK

14:30 So Hirata, University of Illinois at Urbana-Champaign, USA (L26)

Thermodynamic limit and size-consistent design

15:10 Joost VandeVondele, University of Zurich, Switzerland (L27)

Ab initio MD of large condensed phase systems with hybrid density functionals

15:50 Denis Usvyat, University of Regensburg, Germany (L28)

Local correlation methods for periodic systems

16:20 Coffee

Session XI: Large systems (16:50Ð18:50) Chair: Peter J. Knowles, Cardiff University, UK

16:50 Frank Neese, University of Bonn, Germany (L29)

Recent developments in pair natural orbital based single reference correlation methods

17:30 Branislav Jansik, Aarhus University, Denmark (L30)

Developments in the DivideÐExpandÐConsolidate (DEC) method for linear scaling coupled cluster calculations

18:00 Christian Ochsenfeld, University of Munich, Germany (L31)

Nuclei-selected NMR shieldings: a sublinear-scaling quantum-chemical method

18:25 Carsten MŸller, Free University of Berlin, Germany (L32)

Application of wave function based electron correlation methods to weakly bound systems

20:00 Conference dinner

10

ESCMQC ’11

Sunday morning June 19

07:30 Breakfast and checkout

Session XII: Multireference coupled-cluster theory (09:00Ð10:25) Chair: Christof HŠttig, Ruhr-University Bochum, Germany

09:00 Mih‡ly K‡llay, Budapest University of Technology and Economics, Hungary (L33)

Development and benchmark studies of state-specific multi-reference coupled-cluster theories

09:30 Andreas Kšhn, University of Mainz, Germany (L34)

Internally contracted multi-reference coupled-cluster theory: the latest news

10:00 Francesco A. Evangelista, University of Mainz, Germany (L35)

An orbital-invariant internally contracted multireference coupled-cluster approach

10:25 Coffee and checkout

Session XIII: Environment and solvation (11:05Ð12:35) Chair: Magdalena Pecul, University of Warsaw, Poland

11:05 Benedetta Mennucci, University of Pisa, Italy (L36)

Modeling environment effects in quantum chemistry

11:45 Luca Frediani, University of Troms¿, Norway (L37)

Solvation at surfaces: a fully quantistic model including non-electrostatic interactions. Energetics and molecular properties

12:10 Benoit Champagne, University of Namur, Belgium (L38)

Predicting the optical properties of molecules and aggregates

12:35 Closing

13:00 Lunch

11

ESCMQC ’11

Speakers in alphabetical order with references to abstracts:

Alavi [L01]: Quantum Monte Carlo approach to the Full CI problem

Ayers [L06]: Two-point weighted density approximations for the kinetic energy and exchangeÐcorrelation energy

Champagne [L38]: Predicting the optical properties of molecules and aggregates

Cheng [L21]: Analytical energy gradients in relativistic quantum chemistry: theory and implementation for the spin-free exact two-component theory

Coriani [L05]: Near-edge X-ray absorption fine structure from coupled cluster damped response theory using asymmetric Lanczos-chain driven algorithm

Crawford [L13]: Localized coupled cluster wave functions for mixed magnetic/electric properties

Evangelista [L35]: An orbital-invariant internally contracted multireference coupled-cluster approach

Fliegl [L14]: Hydrogen-bond strengths by magnetically induced currents

Frediani [L37]: Solvation at surfaces: a fully quantistic model including non-electrostatic interactions. Energetics and molecular properties

Gori-Giorgi [L07]: Strong spatial correlations in density functional theory

Gšrling [L23]: RPA correlation functional based on the exact exchange kernel of TDDFT

Hanrath [L11]: Efficient evaluation of projected and expectation values of powers of the Hamiltonian for coupled cluster wave functions using an equivalence class decomposition of WickÕs theorem

Hirata [L26]: Thermodynamic limit and size-consistent design

Jacob [L25]: Unambiguous optimization of effective potentials in finite basis sets

Jansik [L30]: Developments in the DivideÐExpandÐConsolidate (DEC) method for linear scaling coupled cluster calculations

JusŽlius [L03]: Massively parallel quantum chemistry using multiwavelets

K‡llay [L33]: Development and benchmark studies of state-specific multi-reference coupled-cluster theories

Knowles [L09]: Approximate variational coupled cluster theory

Kšhn [L34]: Internally contracted multi-reference coupled-cluster theory: the latest news

Korona [L10]: Expectation value coupled cluster theory for molecular propertiesÑtheory and implementation

Kurashige [L20]: DMRG-CASPT2 theory for large-scale multi-reference problems

12

ESCMQC ’11

Kvaal [L22]: Multiconfigurational time-dependent Hartree method for describing particle loss due to absorbing boundary conditions

Mennucci [L36]: Modeling environment effects in quantum chemistry

MŸller [L32]: Application of wave function based electron correlation methods to weakly bound systems

Neese [L29]: Recent developments in pair natural orbital based single reference correlation methods

Ochsenfeld [L31]: Nuclei-selected NMR shieldings: a sublinear-scaling quantum-chemical method

Puzzarini [L04]: Benchmarking quantum chemistry with rotational spectroscopy or benchmarking rotational spectroscopy with quantum chemistry?

Ruud [L12]: Vibronic effects in chiroptical spectra

Saue [L15]: Four-component relativistic long-range-MP2Ðshort-range-DFT

Shiozaki [L18]: Multireference explicitly correlated F12 theories

Stoyanova [L16]: Exploring exact exchange schemes in multideterminant range-separated density functional theory

Teale [L24]: Dispersion interactions in density-functional theory: an adiabatic connection analysis

Tew [L17]: Explicitly correlated coupled cluster theory: robust approximations and localization

Tozer [L08]: Dispersion, static correlation and delocalisation errors in DFT: an electrostatic theorem perspective

Usvyat [L28]: Local correlation methods for periodic systems

Valeev [L02]: Quantum chemistry beyond atomic orbitals and Slater determinants

VandeVondele [L27]: Ab initio MD of large condensed phase systems with hybrid density functionals

Yanai [L19]: Advanced multireference methods for molecular strongly-correlated electronic states

13

ESCMQC ’11

Poster presenters in alphabetical order with references to abstracts:

Adamowicz [P01]: Development of high-end correlated methods at Arizona

Atsumi [P02]: NMR shieldings of an excimer

Biancardi [P03]: Thiazole orange as a light-switch probe: a combined quntum-mechanical and spectroscopic study

Carissan [P04]: Treatment of π electrons using anisotropic pseudopotentials

Hanauer [P05]: Formal aspects and applications of internally contracted multireference coupled cluster theory

Jagau [P06]: Treatment of excited states in state-specific multireference coupled-cluster theory

Jaszunski [P07]: Coupled cluster and DFT calculations of 14N nuclear quadrupole coupling constants

Jonsson [P08]: A first-principles theory for the frequency-dependent magnetizability

Kauch [P09]: Theoretical prediction of the spinÐspin coupling constants of silver intercalated between nucleic bases

Knecht [P10]: Pushing the limits in parallel multi-configurational electronic structure theories

Kristensen [P11]: The MP2 molecular gradient for large molecular systems using the DivideÐExpandÐConsolidate approach

Kvaal [P12]: Time-dependent coupled cluster with variational orbitals

Lehtola [P13]: Quantum chemical calculations of isotropic Compton profiles

Losilla [P14]: BUBBLES: accurate numerical electrostatics for molecular systems

Lourenço [P15]: SCC-DFTB study of chrysotile nanotube

MŸck [P16]: Calculation of spin-orbit splittings in open-shell systems via multireference coupled-cluster theory

Onishi [P17]: A theoretical study on hydrogen transport mechanisms in StTiO3 perovskite

Pecul [P18]: Chiralooptical properties of hydrogen bond-forming species in aqueous solution

Ruusuvuori [P19]: Stability of clusters containing water, pyridine and ammonia

Schwalbach [P20]: Relativistic corrections via sixth-order direct perturbation theory

Steindal [P21]: Parallelization of quantum mechanis/molecular mechanics for higher-order response functions

Stopkowicz [P22]: Relativistic corrections via fourth-order direct perturbation theory at the MP2 level

Sundholm [P23]: Efficient construction of Fock matrices using a numerical integration scheme

Tellgren [P24]: Molecular electron correlation in strong magnetic fields

Woywod [P25]: A systematic approach to the calculation of Rydberg states

Abstractsof

Lectures

Quantum Monte Carlo approach to the Full CI problem

Ali AlaviUniversity of Cambridge

Abstract

The Full CI problem of quantum chemistry can be cast as a stochastic process involving an annihilating population of positive and negative walkers that inhabit Slater determinant space [1]. The population of walkers evolve according to a simple set of rules (akin to a “game of life”), which are derived from the underlying imaginary-time Schrödinger equation, such that the long-time distribution of the walkers matches the exact ground-state eigenvector. We show that this algorithm has a remarkable emergence characteristic, akin to symmetry-breaking phase transitions in classical statistical mechanical systems.

The sign problem posed by Hamiltonian matrix elements of positive and negative sign is solved through a combination of walker annihilation and a “survival of the fittest” criterion [2] (the latter greatly reducing the dependence of the algorithm on walker annihilation).

We will give examples of the algorithm at work in real systems in sizeable basis sets, ranging from atoms, anions and diatomic molecules (C2,N2,O2,F2, CN and NO).

Finally, we discuss the scaling of the algorithm with the number of electrons and orbitals[3].

[1] G.H. Booth, A.J.W. Thom and Ali Alavi, J. Chem. Phys., 131 , 054106, (2009).[2] Deidre Cleland, G.H. Booth, and Ali Alavi, J. Chem. Phys., 132 , 041103, (2010).[3] Deidre Cleland, George Booth, and Ali Alavi, J. Chem. Phys., 134 , 024112, (2011)

ESCMQC-11 - Lectures

L1

Quantum Chemistry Beyond Atomic Orbitals and Slater Determinants

Edward F. Valeev, Florian Bischoff, Liguo Kong, Jinmei Zhang

Department of Chemistry, Virginia Tech, Blacksburg, VA, USA

Atomic orbitals and Slater determinants have supported the development of

accurate quantum chemical theory since 1930s. They both are the pillars of the well-

established ”technology” of quantum chemistry that is used to rationalize and guide

many experimental studies of today. However, augmenting and/or dismantling both

of these concepts may be necessary for truly predictive electronic structure methods.

First, I will describe our work on the explicitly correlated (R12) electronic struc-

ture methods that go beyond purely orbital approximation and describe the corre-

lation of pairs of electrons directly in terms of the interelectronic distances. The

R12 methods attain higher precision (smaller basis set error) than the standard

wave function methods by the virtue of a more efficient description of the Coulomb

correlation at short interelectronic distances. Our focus will be primarily on the

development of R12 methods for modeling multiple electronic states.

In the second part I will discuss methods that do not use atomic orbitals. Atomic

basis sets are ubiquitous in electronic structure studies of molecules and are becom-

ing popular for solids. In search for more universal and robust numerical repre-

sentations we are exploring adaptive spectral-element basis sets that in principle

allow to compute wave functions with guaranteed high precision. Our focus will be

on computing two-electron correlated wave functions in such bases. To make such

computations feasible it is essential to use low-rank (separated) representations for

both operators and functions. We will present pilot Hartree-Fock and (hopefully)

MP2 computations with such an approach.

Figure 1: Multiresolution structure of the orbitals of the water molecule. The darkest

volume elements have the highest separation ranks.


L2

Massively parallel quantum chemistry using multiwaveletsJonas Jusélius, Stig Rune Jensen and Luca FredianiUniversity of Tromsø, N-9037 Tromsø, Norway

We present a fully numerical, real-space method for density functional theoryand Hartree–Fock calculations on molecular systems. Using a tensorial multi-wavelet (MW) basis, efficient and automatic grid adaptation is achieved with rig-orous error control. This allows for calculations with a defined error bound on thewavefunction and energy, and for calculations without the use of effective corepotentials. The Hartree–Fock and Kohn–Sham equations are solved by reformu-lating the problem as an integral equation with Green’s function kernels. In a MWbasis, such operators become naturally narrow-banded allowing for an efficientimplementation which scales linearly with the system size.In contrast to traditional methods with atom centered basis sets, a fully numeri-cal representation of the wavefunction and density requires a much larger num-ber of parameters for any sizable system. A major challenge in the developmentof numerical methods is overcoming the computational barriers and the memorybottlenecks associated with very large number of parameters. By utilizing mod-ern computer architectures and distributing both the represented functions andthe computational workload to a large number of computational hosts, both chal-lenges can be addressed simultaneously. In the current implementation we cantreat molecular systems with up to 5000 atoms, using approximately 4000 proces-sors per orbital. Additionally, by using a coarse grained algorithm up to 100000processors could potentially be utilized.


L3

Benchmarking Quantum Chemistry with RotationalSpectroscopy or Benchmarking RotationalSpectroscopy with Quantum Chemistry?

Cristina PuzzariniDipartimento di Chimica ”G. Ciamician”, Universita di Bologna, I-40126 Bologna, Italy

Jurgen GaussInstitut fur Physikalische Chemie, Universitat Mainz, D-55099 Mainz, Germany

Quantum chemistry has nowadays reached such an advanced level that highly accurate

results can be achieved for energies and properties of small to medium-sized molecules.

For these high-level calculations the requirements are efficient treatment of electron cor-

relation via coupled-cluster theory, basis-set extrapolation techniques, incorporation of

core correlation, relativistic as well as vibrational effects together with the use of suitable

additivity schemes.

Nevertheless, despite all the progress made so far, it is still essential to benchmark the

results from quantum-chemical calculations. Data from rotational spectroscopy are ideally

suited for this purpose, as this technique provides, in particular for small molecules in

the gas phase, highly accurate results. On the other hand, however, measurements and

analyses of rotational spectra are not often straightforward. State-of-the-art quantum-

chemical computations are therefore needed to guide the investigation and in particular

to assist in the determination of the spectroscopic parameters of interest. Quantum

chemistry in this way allows to verify (“benchmark”) results from rotational spectroscopy.

A statistical analysis of the accuracy of theoretically predicted rotational constants will

be presented as an example for the benchmark of quantum chemistry via rotational spec-

troscopy [1]. On the other hand, the determination of the hyperfine parameters of di-

halogencarbenes (CF2 and CCl2) will show the need of “benchmarking” results from

experiments [2].

Based on all the considerations given above, the answer to the “title question” turns out

to be not clear-cut. What we suggest instead is to exploit a fruitful interplay of theory

(quantum chemistry) and experiment (rotational spectroscopy). The power of such an

interplay will be demonstrated by a few examples. In particular, the determination of

an absolute 17O NMR scale via the analysis of the rotational spectrum of H217O [3] and

the investigation of the rotational spectrum of fluoroiodomethane, CH2FI [4], for which

relativistic effects turned out to be essential for the accurate theoretical predictions of the

spectroscopic parameters involved.

[1] C. Puzzarini, M. Heckert, and J. Gauss, J. Chem. Phys. 128, 194108 (2008).[2] C. Puzzarini, S. Coriani, A. Rizzo, and J. Gauss, Chem. Phys. Lett. 409, 118 (2005).[3] C. Puzzarini, G. Cazzoli, M.E. Harding, J. Vazquez, and J. Gauss, J. Chem. Phys. 131,234304 (2009).[4] C. Puzzarini, G. Cazzoli, J.C. Lopez, J.L. Alonso, S. Stopkowicz, L. Cheng, and J. Gauss, J.Chem. Phys., in press (2011). Doi:10.1063/1.3583498


L4

Near-Edge X-ray Absorption Fine Structure from Coupled Cluster Damped Response Theory using an Asymmetric Lanczos-chain

driven algorithm

S. Coriani1,2,3, O.Christiansen 2, T. Fransson4, P. Norman4

1Dipartimento di Scienze Chimiche e Farmaceutiche,

Università degli Studi di Trieste, Trieste, I-34127, ITALY 2Department of Chemistry, Aarhus University, Aarhus, DK-8000, DENMARK,

3Centre for Theoretical and Computational Chemistry, Department of Chemistry, University of Oslo, N-0315, NORWAY

4Department of Physics, Linköping University, Linköping, SE-58183, SWEDEN,

ABSTRACT Coupled cluster methods are considered among the most accurate tools in electronic structure theory. Nonetheless limited attempt seems to have been made to extend their applicability to the description of the core-excitation phenomena that are behind largely used spectroscopic techniques like x-ray absorption spectroscopy and x-ray circular dichroism. We present here an implementation of damped response theory based on an asymmetric Lanczos algorithm for the CCS, CC2 and CCSD approximations, and apply it to the simulation of the K-edge x-ray absorption spectra of various closed-shell systems, including Neon, CH4, H2O, HF and CO. The effect of triple excitations on the excitation energies is estimated by means of the CCSDR(3) approximation, and relativistic effects are accounted for using the Douglas-Kroll approach. Results are compared with experiment as well as results obtained with other computational methods.


L5

Two-Point Weighted Density Approximations for the Kinetic Energy and Exchange-Correlation Energy

Paul Ayers1

1Department of Chemistry & Chemical Biology; McMaster University; Canada

Many of the problems in density-functional theory can be mitigated by carefully designing an exchange-correlation hole with the proper mathematical properties. This leads to generalized and extended versions of the venerable weighted density approximation (WDA). In this talk, I will show how well WDA can work for the kinetic energy, exchange energy, and exchange-correlation energy. One advantageous feature of the WDA is that it allows one to deal with fractionally occupied sites in a better way than conventional functionals. (For example, the H2 dissociation problem is entirely solved.) The traditional criticism of WDA has been its high computational cost. These costs are mitigated by new algorithms using a new limited-memory quasi-Newton method that was designed especially for this application.


L6

Strong spatial correlations in Density Functional Theory

P. Gori-Giorgi1, M. Seidl2, G. Vignale3 1 Department of Theoretical Chemistry and Amsterdam Center for Multiscale Modeling, FEW, Vrije Universiteit, De Boelelaan 1083, 1081HV Amsterdam, The Netherlands 2 Institute of Theoretical Physics, University of Regensburg, D-93040 Regensburg, Germany 3 Department of Physics and Astronomy,University of Missouri, Columbia, Missouri 65211, USA * Corresponding author [email protected]

In the last four years, the mathematical structure of the strong-interaction limit of density functional theory has been uncovered [1-3], and exact information on this limit has started to become available. The aim of this talk is to give a perspective on how this new piece of exact information can be used to treat situations that are problematic for standard Kohn–Sham DFT. One way to use the strong-interaction limit, more relevant for solid-state physical devices, is to define a new framework to do practical, non-conventional, DFT calculations in which a strong-interacting reference system is used instead of the traditional non-interacting one of Kohn and Sham [4]. Another way to proceed, more related to chemical applications, is to include the exact treatment of the strong-interaction limit into approximate exchange–correlation energy density functionals in order to describe difficult situations such as the breaking of the chemical bond [5]. The possibility of tightening the Lieb-Oxford bound will be also discussed [6].

Keywords: density functional theory, spatial correlations, exchange-correlation functionals

[1] M. Seidl, P. Gori-Giorgi, and A. Savin Phys. Rev. A 75 042511 (2007) [2] P. Gori-Giorgi, G. Vignale, and M. Seidl, J. Chem. Theory Comput. 5, 743 (2009) [3] P. Gori-Giorgi, M. Seidl, and A. Savin, Phys. Chem. Chem. Phys. 10, 3440 (2008) [4] P. Gori-Giorgi, M. Seidl, and G. Vignale, Phys. Rev. Lett. 103, 166402 (2009) [5] P. Gori-Giorgi and M. Seidl, Phys. Chem. Chem. Phys. 12, 14405 (2010) [6] E. Rasanen, M. Seidl, and P. Gori-Giorgi Phys. Rev. B, to appear.


L7

DISPERSION, STATIC CORRELATION AND DELOCALISATIONERRORS IN DFT: AN ELECTROSTATIC THEOREM PERSPECTIVE

David J Tozer1 and Austin D Dwyer

1 Department of Chemistry, Durham University, South Road, Durham, DH1 3LE UKE-mail: [email protected]

The problems of dispersion [1,2], static correlation [3] and delocalisation [3] errors inDFT are considered from the unconventional perspective of the force on a nucleus in astretched diatomic molecule. The electrostatic theorem of Feynman [4] is used to relateerrors in the forces to errors in electron density distortions, which in turn are related toerroneous terms in the Kohn-Sham equations. For H2, the exact dispersion force arises dueto a very small density distortion; the DFT static correlation error leads to a significantlyoverestimated force due to an exaggerated distortion. For H+

2 , the DFT delocalisationerror leads to an underestimated force due to an underestimated distortion; the forcecan become repulsive, giving the characteristic maximum in the potential energy curve.Increasing the fraction of long-range exact orbital exchange in the functional increasesthe distortion, which is detrimental for static correlation but favourable for delocalsationerror. It is hoped that the physical insight provided by the analysis will stimulate furthertheoretical developments into these problems.

[1] S Kristyan and P Pulay, Chem. Phys. Lett. 229 (1994) 175.[2] MJ Allen and DJ Tozer, J. Chem. Phys. 117 (2002) 11113.[3] AJ Cohen, P Mori-Sanchez, and W Yang, Science 321 (2008) 7982.[4] RP Feynman, Phys. Rev. 56 (1939) 340.


L8

Approximate Variational Coupled Cluster Theory

Bridgette Cooper,1,2 Andrew Jenkins,1 James B. Robinson,1 Peter J. Knowles1

1School of Chemistry, Cardiff University, United Kingdom2Department of Physics, Imperial College London, United Kingdom

A modification is presented of the variational configuration interaction func-

tional in the first-order interacting space for molecular electronic structure. The

modified functional is a fully-linked expression, that by construction is extensive

and invariant to transformations of the underlying orbital basis, and is exact for an

ensemble of separated 2-electron subsystems. The method is then extended by in-

cluding additional terms in the functional that can be computed with O(N6) work,

and which make it agree at low order with variational coupled-cluster with dou-

ble excitations (VCCD). This method demonstrates accuracy that exceeds that of

the standard coupled-cluster (CCD) method, in particular in situations where the

reference Slater determinant is not a good approximation.

We also discuss the inclusion of the effect of single orbital excitations, either

through minimisation of the approximate VCCD functional with respect to the

orbitals, or through an explicit generalisation of the functional to approximate

VCCSD.

A further extension generalises the use of the functional to a multiconfigurational

reference wavefunction.

[1] P. J. Knowles and B. Cooper, J. Chem. Phys., 133 (2010) 224106


L9

Expectation-value coupled cluster theory for molecular properties –

theory and implementation

Tatiana Korona

Faculty of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warsaw, Poland

Although usually molecular properties in coupled cluster theory are defined as

derivatives of the coupled cluster energy with respect to a field strength (or equiva-

lently with the Lagrangian approach) [1], an alternative model, where these proper-

ties are obtained as expectation values of the normalized coupled cluster wave func-

tion, can also be formulated [2]. Recently, a generalization of the latter approach to

second-order properties has been proposed [3]. Since in coupled cluster theory the

Hellmann-Feynman theorem is not fulfilled, the Lagrangian and expectation-value

methods for properties do not lead to equivalent results, but they both converge the

full configuration-interaction solution with an increasing maximum excitation level

of cluster operators. Recently expectation-value coupled cluster theory (currently

limited to single and double excitations) has been implemented into the molpro

package of ab initio programs. The first- [4] and second-order [5] properties like mul-

tipole moments, frequency-dependent polarizabilities, and dispersion coefficients of

intermolecular interactions can be obtained within the XCCSD and somewhat sim-

pler XCC2 [6] models. For the first-order properties also the local-correlated version

of the XCCSD approach is available. Some illustrative applications of these new

methods will be presented.

Bibliography:

[1] P. Jørgensen and T. Helgaker, J. Chem. Phys. 89, 1560, 1989

[2] B. Jeziorski, R. Moszynski, Int. J. Quantum Chem. 48, 161, 1993

[3] R. Moszynski, P. S. Zuchowski, B. Jeziorski, Coll. Czech. Chem. Commun. 70,

1109, 2005

[4] T. Korona, B. Jeziorski, J. Chem. Phys. 125, 184109, 2006

[5] T. Korona, M. Przybytek, B. Jeziorski, Mol. Phys. 104, 2303, 2006

[6] T. Korona, PCCP, 12, 14977, 2010


L10

Efficient Evaluation of Projected and Expectation Values of

Powers of the Hamiltonian for Coupled Cluster Wavefunctions

Using an Equivalence Class Decomposition of Wick’s Theorem

Michael Hanrath

Institute for Theoretical Chemistry, University of Cologne

Greinstrasse 4, 50939 Cologne, Germany

An efficient implementation of the evaluation of

• 〈Φ0|e−T (HN)neT Φ0〉, n = 1, 2, . . .

• 〈Φ0|eT †(HN)neT Φ0〉, n = 1, 2, . . .

in an arbitrary excitation level coupled cluster framework is reported. The algebraic engine

does not rely on standard diagrammatic evaluation techniques but uses a two step process:

(i) an equivalence class decomposed version of Wick’s theorem delivering pre-factors and

signs efficiently [1] and (ii) a term simplification engine based on topological methods

[2]. The resulting expressions are factorized [3] and contracted [4] by previously published

approaches. The new implementation outperforms a previous full CI based implementation

[5] significantly. First applications and numerical results are reported.

References

[1] M. Hanrath, ”Eliminating Redundancy in Wick’s Theorem”, manuscript in preparation

[2] M. Hanrath and A. Engels-Putzka, ”Simplification of Expressions of Antisymmetric

Tensor Products by Topological Methods”, manuscript in preparation

[3] A. Engels-Putzka and M. Hanrath, J. Chem. Phys. 134 (2011) 124106

[4] M. Hanrath and A. Engels-Putzka, J. Chem. Phys. 133 (2010) 64108

[5] M. Hanrath, Chem. Phys. Lett. 466 (2008) 240


L11

Vibronic effects in chiroptical spectra

Na Lin1, Harald Solheim1, Marcel Nooijen2 and Kenneth Ruud1

1 Centre for Theoretical and Computational Chemistry

Department of Chemistry, University of Tromsø

9037 Tromsø, Norway

2 Department of Chemistry, University of Waterloo

Waterloo, Ontario N2L 5E3

Canada

In the talk, I will present results from recent work in our group on the study of

vibronic effects on chiroptical spectra. I will in particular address the challenging

problem of isotopically induced chirality in the circular dichroism spectrum of 2(R)-

deuteriocyclopentanone, in which additional complications arise due to the presence of

two almost isoenergetic conformations of the isotopically substituted molecule. Dif-

ferent models for describing the vibronic problem will be discussed.

In addition, I will discuss the calculation of vibronic effects for magnetic-field

induced chiroptical spectroscopy, and in particular for the study of magnetic circular

dichroism. For magnetic circular dichroism, different approaches must be applied for

the study of electronic transitions dominated by the A and the B terms, respectively.

Although focussing largely on the B, the problems associated with treating theA term

will also be addressed.


L12

Localized Coupled Cluster Wave Functions for Mixed Magnetic/ElectricProperties

T. Daniel Crawford

Department of Chemistry, Virginia Tech, Blacksburg, Virginia 24061, U.S.A

[email protected]

Chiral enantiomers — pairs of dissymmetric molecules that are merely mirror images of one another— often exhibit dramatically different chemical behavior when reacting in chiral environments, andthe need to distinguish between such enantiomers drives much of the multibillion-dollar researchefforts of the pharmaceutical industry. Enantiomeric pairs also exhibit mirror-image responses tocircularly polarized electromagnetic fields in absorption (dichroism), refraction (birefringence), andscattering: if the left hand of a chiral compound strongly absorbs right-circularly-polarized light, theright-hand enantiomer will strongly absorb the left-handed light, and vice versa. However, suchresponses are useful for the identification of the handedness of a chiral sample only if a reliablereference is available. This lecture will focus on our recent work to establish high-level quantumchemical methods such as coupled cluster theory as just such a reference. In particular, we willdiscuss our efforts to develop reduced-scaling response methods based on the coupled clusterframework for treating larger molecules and thus more realistic simulations of chiral chemistry.While great progress has been reported in the last two decades for local-correlation treatmentsof molecular structure and energetics, the obstacles for extension of such techniques to molecu-lar response properties have been much more difficult to overcome. We report new progress incombining localized-orbital and optimized-orbital concepts to obtain gauge invariance in magnetic-field-dependent properties.


L13

HYDROGEN-BOND STRENGTHS BY MAGNETICALLY INDUCED CURRENTS

Heike Fliegl1, Olli Lehtonen1, Dage Sundholm1 and Ville R. I. Kaila2

1Department of Chemistry, University of Helsinki, A. I. Virtasen aukio 1, P.O. Box 55, FI-00014 Helsinki, Finland

2Laboratory of Chemical Physics, National Institute of Diabetes and Digestive and Kidney Diseases, National Institutes of Health, Bethesda,

Maryland 20892-0520, USA

A “non-invasive” computational method to estimate the strength of individual hydrogen bonds using magnetically induced currents is presented.[1] The magnetically induced current strengths across H-bonds are obtained on density functional theory level for a representative test set of molecular systems using the gauge including magnetically induced current method (GIMIC).[2] It is found that magnetically induced current strengths across H-bonds correlate linearly with the H-bond energy. This finding is used to study individual H-bond strengths in Watson-Crick DNA base pairs and H-bonded water chains in carbonic anhydrase, without breaking the H-bonding connectivity of the system.

[1] H. Fliegl, O. Lehtonen, D. Sundholm and V. R. I. Kaila, Phys. Chem. Chem. Phys., 13, 434 (2011)[2] J. Jusélius, D. Sundholm and J. Gauss, J. Chem. Phys., 121, 3952 (2004)


L14

4-component relativistic long-range MP2-short-range-DFT

Ossama Kullie1 and Trond Saue2

1) Institute de Chimie de Strasbourg, CNRS et Université de Strasbourg, Laboratoire de ChimieQuantique, 4 rue Blaise Pascal, 67070 Strasbourg, France

2) Laboratoire de Chimie et Physique Quantique (UMR 5626), CNRS/Université de Toulouse 3(Paul Sabatier), 118 route de Narbonne, 31062 Toulouse, France.

e-mail: [email protected]

We report the implementation of long-range second-order Møller-Plesset perturbation theorycoupled with short-range density functional theory (MP2-srDFT), for the first time based on the4-component relativistic Dirac-Coulomb Hamiltonian [1]. The new code resides in a develop-ment version of the DIRAC10 package [2]. The range separation of the two-electron interactionis based on the error function, such that the long-range interaction, to be handled by wave func-tion theory, corresponds to the potential of finite electrons with a Gaussian charge distribution.We argue that the interelectronic distance associated with the range-separation parameter shouldaccordingly be determined from a Gaussian rather than a hard-sphere model.

As a first application of our relativistic MP2-srDFT implementation we calculate spectro-scopic constants of the complete series of homoatomic rare gas dimers — from helium to thesuperheavy element 118 — where bonding is dominated by dispersion forces.

We find that the MP2-srDFT method is less sensitive to the basis set quality than pure MP2,but for the heavier rare gas dimers the computational cost is approximately the same as forpure MP2 if one seeks convergence with respect to both basis set and the number of correlatedelectrons. The inclusion of a short-range DFT contribution allows to dampen the tendency ofpure MP2 to overbind the heavier dimers, but it is diffcult to find an optimal range-separationparameter for the whole series of diatomics. Interestingly, MP2-srLDA shows better performancethan MP2-srPBE for the selected molecules.

References[1] O. Kullie and T. Saue. Chem. Phys., (2011). in press.

[2] DIRAC, a relativistic ab initio electronic structure program, Release DIRAC10 (2010), writ-ten by T. Saue, L. Visscher and H. J. Aa. Jensen, with contributions from R. Bast, K. G. Dyall,U. Ekström, E. Eliav, T. Enevoldsen, T. Fleig, A. S. P. Gomes, J. Henriksson, M. Iliaš,Ch. R. Jacob, S. Knecht, H. S. Nataraj, P. Norman, J. Olsen, M. Pernpointner, K. Ruud,B. Schimmelpfennnig, J. Sikkema, A. Thorvaldsen, J. Thyssen, S. Villaume, S. Yamamoto(see http://dirac.chem.vu.nl).


L15

Exploring exact exchange schemes in multideterminant range-separated densityfunctional theory

A. Stoyanova1, E. Fromager1, A. Teale2 and T. Helgaker2

1Laboratoire de Chimie Quantique,Institut de Chimie, CNRS / Universite de Strasbourg,

4 rue Blaise Pascal, 67000 Strasbourg, France.2Center for Theoretical and Computational Chemistry,

Department of Chemistry, University of Oslo,P.O. Box 1033, Blindern N-0315, Norway

We explore the introduction of multideterminant (MD) short-range exact exchange (srEXX)within the framework of range-separated density functional theory (srDFT). The range separa-tion in srDFT of the regular two-electron Coulomb interaction into long- and short-range partshas permitted the combination of a wave-function-theory (WFT)-based treatment of the long-rangestatic and dynamic electron correlation effects with srDFT approximate functionals describing theshort-range dynamical electron correlation. Current srDFT functionals (of LDA/GGA-type), how-ever, do not enable an accurate description of multiconfigurational and multireference systems [1, 2].For example, the dissociation energies of the molecules H2, N2, and H2O were found to be too highcompared to experimental values which has been attributed to the approximate short-range densityfunctionals [1]. One possible remedy for that shortcoming, which will be discussed here, is theintroduction of short-range exact exchange within srDFT. For the purpose of introducing srEXXin srDFT, the multideterminant srEXX energy functional defined in Refs. [3, 4] has been adopted.The problem of calculating the ground-state WFT-srEXX energy can be recast into the optimizationof a local potential by means of an optimized effective potential (OEP) method which is adaptedto the MD srDFT[3]. In order to optimize the local potential, we opt for the OEP scheme of Yangand Wu [5] where the local potential is expanded in terms of a basis of Gaussian functions. Thisapproach has already been implemented by A. Teale in the DALTON program package for the case ofKS-DFT EXX [6]. In this talk, we present the optimization procedure for the effective potential forboth variational (HF, MCSCF) and non-variational (CC, MP2 ) WFT methods. The formulationof a general Lagrangian-based formalism for the computation of the ground-state WFT-srEXX en-ergy for both non- and variational WFT methods is also considered. In the srEXX schemes, theMD wave function which is obtained by means of WFT describes the ground state of a fictitiouslong-range-only interacting Hamiltonian which contains the local potential to be optimized. As aresult, the attractive features of srDFT such as faster basis set convergence and shorter configurationexpansion of the wave function are preserved.

[1] E. Fromager, J. Toulouse and H. J. Aa. Jensen, J. Chem. Phys. 126, 074111 (2007).[2] E. Fromager, F. Real, P. Wahlin, U. Wahlgren, and H. J. Aa. Jensen, J. Chem. Phys. 131, 054107 (2009).[3] P. Gori-Giorgi and A. Savin, Int. J. Quant. Chem. 109, 1950 (2009).[4] J. Toulouse, P. Gori-Giorgi, and A. Savin, Theor. Chem. Acc. 114, 305 (2005).[5] W. Yang and Q. Wu, Phys. Rev. Lett. 89, 143002 (2002).[6] A. M. Teale and D. J. Tozer Phys. Chem. Chem. Phys. 7, 2991 (2005).


L16

Explicitly correlated coupled cluster theory: robust

approximations and localization

David P. Tew∗, Andreas Kohn, and Christof Hattig

Abstract

i) A comprehensive perturbational analysis of the explicitly correlated CCSD Lagrangian is re-

ported that explains the success and limitations of the simplified models CCSD(F12), CCSD-F12x

and CCSD(2)F12. We present an improved model CCSD(F12*) that has essentially the same

accuracy as CCSD(F12) but with an efficiency comparable to CCSD-F12b.

ii) Localization in the framework of pair natural orbitals is explored at the explicitly correlated

MP2-F12 level of theory. Our results demonstrate that very small virtual active spaces, 20-50

orbitals per significant pair, return more than 98% of the basis set limit correlation energy. The

extension of pair natural orbital ideas to the complementary auxiliary basis set for the RI also

affords enormous truncation of the auxiliary orbital space without significant loss of accuracy.

1


L17

Multireference Explicitly Correlated F12 Theories

Toru Shiozaki and Hans-Joachim Werner

Institut für Theoretische Chemie, Universität Stuttgart, Pfaffenwaldring 55, D-70569 Stuttgart, Germany

We will present the recent development of CASPT2-F12 and MRCI-F12 methods [1,2], which achieve much improved basis-set convergence compared to the conventional CASPT2 and MRCI methods by including internally contracted configurations that depend explicitly on the electron-electron distances. The multistate extension allows for application to systems with near degeneracy (such as avoided crossings and conical intersections) and for complicated electronic structures of excited states [3]. MRACPF-F12 has been also developed [2]. All the methods are implemented in the developer version of the MOLPRO package [4]. Numerical results for some benchmark systems, including the ozone excited states and OH + H2 reaction, will be presented to illustrate the superior basis-set convergence of the multireference F12 theories. The importance of the F12 treatment in d-electron correlated systems will be also discussed [5]. [1] T. Shiozaki and H.-J. Werner, J. Chem. Phys. (Comm.) 133, 141103 (2010). [2] T. Shiozaki, G. Knizia, and H.-J. Werner, J. Chem. Phys. 134, 034113 (2011). [3] T. Shiozaki and H.-J. Werner, J. Chem. Phys. in press (2011). [4] MOLPRO, version 2010.2, a package of ab initio programs, H.-J. Werner, P. J. Knowles, G. Knizia, F. R. Manby, M. Schütz and others, see http://www.molpro.net. [5] T. Shiozaki, K. R. Shamasundar, and H.-J. Werner, in preparation


L18

Advanced multireference methods for molecular strongly-correlated electronic states

Takeshi Yanai

Institute for Molecular Science, Okazaki, JAPAN

[email protected]

We will present our recent progress in the development of efficient multireference

approaches based on the density matrix renormalization group (DMRG) method and its

partner dynamical correlation models. of the

DMRG algorithm to ab initio quantum chemistry calculations, we use it to describe a

substantial amount of static correlation accurately with large active space for multireference

calculations, e.g. CAS(28e,32o) or even larger. Developing our efficient implementation of

the DMRG method, we recently demonstrated its significant applicability to challenging

multireference chemistry, involving strongly-correlated electronic states of transition metal

complexes and -conjugated molecules. For the latter, we will show some novel findings in

spin structures of polycarbenes (orgnaic magntic molecules) and graphene-nanoribbons

(future organic semiconductors). These electronic structures associated with complex

multireference electron correlation are thought to be a key to understand interesting

quantum phenomena arising in organic materials and biomolecules.

Dynamic correlation needs be taken into account to deliver a quantitative accuracy in

calculations, and is regarded as weak correlation that should be handled perturbatively in

light of efficiency. We have developed a joint theory of the DMRG method and a canonical

transformation (CT) idea to calculate the dynamic correlation on top of multireference

description with large active space. Our CT theory constructs a renormalization structure of

the high-level dynamic electron correlation in an effective Hamiltonian where the bare

Hamiltonian is transformed by the unitary exponential correlation operator. We will discuss

some theoretical aspects and applications of the DMRG-CT theory to quasi-degenerate

electronic states in chemistry.


L19

DMRG-CASPT2 theory for large-scale multi-reference problems Yuki Kurashige* and Takeshi Yanai

(Institute Molecular Science, Japan) The large-scale multi-reference problem, i.e. the exponential dependence of the conventional multi-reference theories on the size of the active space is one of the major problems remaining with quantum chemistry. Recently, effective approaches based on the density matrix renormalization group (DMRG) algorithm have been vigorously developed by several groups.1-4 The DMRG algorithm is an approximate method for diagonalizing large many-body Hilbert space, i.e. the FCI in quantum chemical language. Although the applications had been limited to FCI calculations for small molecules in the early stage of the developments, the developments of DMRG-SCF5-7 opened up new possibilities for the practical applications because only the non-dynamical correlation involving a relatively small number of orbitals needs to be treated by the DMRG. Of course, the remaining dynamical correlation is necessary for a quantitative description or even qualitative description in some cases. In this presentation, we will present a second-order perturbation theory with a DMRG-SCF reference function, in which the generalized Fock operator is employed as the zeroth-order Hamiltonian. In fact, it is equivalent to the CASPT2 in the case where the size of renormalized state M is large enough, and thus we call it as DMRG-CASPT2. It was applied to the potential energy function of Cr dimer with ‘double d-shell’ active orbitals.

1 G.K.-L. Chan and M. Head-Gordon, J. Chem. Phys. 116, 4462 (2002). 2 K.H. Marti, I.M. Ondík, G. Moritz, and M. Reiher, J. Chem. Phys. 128, 014104 (2008). 3 D. Zgid and M. Nooijen, J. Chem. Phys. 128, 014107 (2008). 4 Y. Kurashige and T. Yanai, J. Chem. Phys. 130, 234114 (2009). 5 D. Zgid and M. Nooijen, J. Chem. Phys. 128, 144116 (2008). 6 D. Ghosh, J. Hachmann, T. Yanai, and G. K.-L. Chan, J. Chem. Phys. 128, 144117 (2008). 7 T. Yanai, Y. Kurashige, E. Neuscamman, and G.K.-L. Chan, J. Chem. Phys. 132, 024105 (2010).

!"#$%%

!"#&%%

!'#$%%

!'#&%%

!&#$%%

&#&%%'#(%% '#)%% '#*%% "#&%% "#"%% "#(%% "#)%% "#*%% +#&%% +#"%%

!E(e

V)

Cr - Cr (Å)

,-./#%

01!234456789):(.+;"<'=>%

01!234453789?:$.(;+<"='@>%

42A86"B'"CD'"EF5GG!.H4I675:@JKL&#"M#N#%

42A86"B'"CD'"EF5GG!.H4I375:@JKL&#"M#N#%

O01P!42A86"B'"CD"*EF5GG!.H4I67%

O01P!42A86"B'"CD"*EF5GG!.H4I37%


L20

Analytical energy gradients in relativistic quantum chemistry: theory and implementation for the spin-free exact two-component theory

Lan Cheng and Jürgen Gauss

Institut für Physikalische Chemie, Universität Mainz, D-55099 Mainz, Germany

We report the implementation of analytical gradients within the spin-free exact two-component (X2c) theory for relativistic calculations of first-order electrical properties and equilibrium geometries using HF-SCF, MP2, and coupled-cluster methods. In the used X2c-1e scheme [1,2,3], the one-electron Dirac Hamiltonian in its matrix representation is block-diagonalized by means of a single unitary transformation and the resulting electronic two-component Hamiltonian is used together with untransformed two-electron interactions in subsequent calculations. The implementation is based on available and well-developed non-relativistic analytical derivative techniques [4], since only the one-electron Hamiltonian integrals and the corresponding derivative integrals need to be modified. Applicability and accuracy of the presented scheme are demonstrated in benchmark calculations of first-order electrical properties in comparison to non-relativistic and spin-free four-component calculations. We also present results of equilibrium geometries for various copper compounds as a first application of nuclear forces computed analytically at the X2c-1e level.

[1] K. G. Dyall, J. Chem. Phys. 115, 9136 (2001)

[2] M. Ilias and T. Saue, J. Chem. Phys. 126, 064102 (2007)

[3] W. Liu and D. Peng, J. Chem. Phys. 131, 031104 (2009)

[4] I. Shavitt and R. J. Bartlett, Many-Body Methods in Chemistry and Physics: MBPT and Coupled-Cluster Theory (Cambridge University Press, Cambridge, 2009), Chap. 11.


L21

Multiconfigurational time-dependent Hartree method for describing particle lossdue to absorbing boundary conditions

Simen Kvaal1, 2,∗ and Sølve Selstø2, †

1Matematisches Institut, Universitat Tubingen, Auf der Morgenstelle 10, D-72076 Tubingen, Germany2Centre of Mathematics for Applications, University of Oslo, N-0316 Oslo, Norway

Absorbing boundary conditions on the form of complex absorbing potentials (CAPs) are routinely intro-duced in the molecular Schrodinger equation in order to limit the computational domain, to study reactivescattering events, etc. Intuitively, the CAP removes particles from the system, consistent with the probabil-ity interpretation of the square norm‖ΨN‖2 of theN-particle wave-function.

However, it is well-known that a pure wave-function description doesnot allow the modeling and prop-agation of theremnantsof a system of which some particles are removed by the absorbing boundary – asevere limitation. This is easily seen from the fact that‖ΨN‖2 is normalized to the probability of findingall N particles somewhere in the domain. This is zero if a particle with certainty has left.

It was recently shown [S. Selstø and S. Kvaal, J. Phys. B: At. Mol. Opt. Phys.43 (2010), 065004]that a master equation of Lindblad form resolves this dilemma, allowing the consistent description of theevolution of the system withN, N−1, N−2, etc, particles due to absorbing boundary conditions. TheN-particle wave-function is replaced by a density operator in Fock space, where the number of particlescan vary. The CAP attains amathematicalinterpretation as a dissipative mechanism, producingN′ < Nparticle systems.

An exposition of this Lindblad-type master equation is given. In particular it is shown that the masterequation follows uniquely and solely from the choice of the CAP and the probability interpretation of‖ΨN‖2. Even though Lindblad-type equations are often phenomenological, this is not the case here: thedescription is fully microscopic, allowing theN′ < N particle systems to be constructed as the systeminteracts with the CAP. The evolution of the originalN-particle system alone is of course unchanged byusing the master equation instead of the Schrodinger equation with a CAP.

The de facto standard methods forab initio many-particle quantum dynamics is today the family ofmulticonfigurational time-dependent Hartree methods (MCTDH). We derive the so-called Type II densityoperator MCTDH approximation of the present master equation, arriving at simple equations of motionfor the density operator matrix elements and the single-particle functions that are closely related to theoriginal wave-function MCTDH. In particular, they are equivalent if the remnants of the absorption processis ignored, and existing computer codes can be re-used to a high degree for implementations of the masterequation.

A preprint version of this work can be retrieved fromhttp://arxiv.org/abs/1102.3899.

∗Electronic address:[email protected]†Electronic address:[email protected]


L22

RPA correlation functional based on the exact exchange kernel of TDDFT

A. Gorling and A. Heßelmann

Lehrstuhl fur Theoretische Chemie, Universitat Erlangen-Nurnberg Egerlandstr. 3,

91054 Erlangen, Germany

Several variants of EXX-RPA (exact-exchange random phase approximation) correla-

tion functionals are presented. The functionals are obtained with the exact frequency-

dependent exchange kernel [1,2] of time-dependent density-functional theory [3,4] via

the fluctuation dissipation theorem [5]. The functionals yield more accurate electronic

energies for molecules in their equilibrium geometry than standard correlation func-

tionals [6]. Moreover, the EXX-RPA correlation functionals can take into account

static correlation and therefore correctly dissociate electron pair bonds without the

need to resort to symmetry breaking in spin space [6]. They thus combine accuracy

at equilibrium bond distances and in dissociation processes with a correct descrip-

tion of spin, something all commonly employed correlation functionals fail to do.

Due to the capability of treating static correlation, i.e., multireference states, the

applicability of EXX-RPA methods is broader than that of standard coupled cluster

methods. The reason why EXX-RPA correlation functionals yield distinctively and

qualitatively better results than RPA approaches based on Hartree-Fock and time-

dependent Hartree-Fock is explained. Different approaches to evaluate the EXX-RPA

correlation functionals computationally and their efficiency and scaling with system

size are discussed.

Literature:

[1] A. Gorling, Phys. Rev. A 57, 3433 (1998); Int. J. Quant. Chem. 69, 265 (1998).

[2] Y.-H. Kim and A. Gorling, Phys. Rev. B 66, 035144 (2002).

[3] A. Heßelmann, A. Ipatov, and A. Gorling, Phys. Rev. A 80, 012507 (2009).

[4] A. Heßelmann and A. Gorling, J. Chem. Phys 134, 034120 (2011).

[5] A. Heßelmann and A. Gorling, Mol. Phys., 109 359 (2010).

[6] A. Heßelmann and A. Gorling, Phys. Rev. Lett., 106 093001 (2011).


L23

Dispersion Interactions in Density–Functional Theory:An Adiabatic Connection Analysis

A. M. Tealea), M. D. Strømsheima), S. Coriania,b), T. Helgakera)

a) Centre for Theoretical and Computational Chemistry, University of Oslo, P. O. Box1033, Blindern, N-0315, Oslo, Norway

b) Dipartimento di Scienze Chimiche, Università degli Studi di Trieste, Via LicioGiorgieri 1, I-34127 Trieste, Italy

In recent years the Kohn–Sham formulation [1] of density functional theory (DFT)has become the workhorse of electronic structure theory and is now routinely applied tomedium and large systems in a variety of disciplines spanning chemistry, physics and(increasingly) biology. The continued success and applicability of the theory relies onthe development of more accurate and robust approximations to describe the energy aris-ing from quantum-mechanical interactions of electrons in terms of their density. A largenumber of exchange–correlation approximations have been developed, however, seriousproblems remain, limiting the accuracy to which systems having nearly degenerate elec-tronic configurations or long-ranged interactions may be described.

Recently, we have begun to study the way in which accurate exchange–correlationapproximations should behave in these situations by calculating the density functionalusing systematically refine-able wave function approaches [2, 3, 4]. This has been facil-itated by Lieb’s formulation of DFT [5], which provides a convenient practical route tostudy the exchange–correlation contributions using any wave-function model [6, 7]. Inparticular, the study of the transition from a system of non-interacting electrons with thecorrect density to the physical interacting system with the same density, along the adia-batic connection [8, 9, 10, 11], provides insight into the nature of the exchange–correlationcontributions and can help to rationalize the behaviour of a variety of existing approxima-tions [3, 4]. Here we will illustrate the particularly difficult case of long-ranged dispersioninteractions using the prototypical (He)2 dimer. Prospects for utilizing the approach out-lined for the development of new approximations and calibration of existing ones will bediscussed.

[1] W. Kohn and L .J. Sham, Phys. Rev. 140, A1133 (1965)[2] A.M. Teale, S. Coriani, T. Helgaker, J. Chem. Phys. 130, 104111 (2009)[3] A.M. Teale, S. Coriani, T. Helgaker, J. Chem. Phys. 132, 164115 (2010)[4] A.M. Teale, S. Coriani, T. Helgaker, J. Chem. Phys. 133, 164112 (2010)[5] E.H. Lieb, Int. J. Quantum. Chem. 24, 243 (1983)[6] F. Colonna and A. Savin, J. Chem. Phys. 110, 2828 (1999)[7] Q. Wu and W. Yang, J. Chem. Phys. 118, 2498 (2003)[8] J. Harris and R. O. Jones, J. Phys. F: Met. Phys. 4, 1170 (1974)[9] D.C. Langreth and J.P. Perdew, Sol. St. Comm. 17, 1425 (1975)[10] O. Gunnarsson and B.I. Lundqvist, Phys. Rev. B 13, 4274 (1976)[11] D.C. Langreth and J.P. Perdew, Phys. Rev. B 15, 2884 (1977)


L24

Unambiguous Optimization of Effective Potentials in Finite Basis Sets

Christoph R. Jacob

Karlsruhe Institute of Technology (KIT), Center for Functional Nanostructures,Wolfgang-Gaede-Str. 1a, 76131 Karlsruhe, Germany

E-Mail: [email protected]

The success of density-functional theory relies on the availability of suitable ap-proximations for the exchange-correlation energy functional. With orbital-dependentexchange-correlation functionals, the Kohn–Sham potential has to be evaluated with theoptimized effective potential (OEP) method [1]. The closely related problem of deter-mining the local the yields a given target electron density is also of interest in a numberof different contexts: By using accurate electron densities from high-level calculations,it can be used to obtain accurate exchange–correlation potentials that can serve as guid-ance for constructing improved approximations (see, e.g., [2]). Furthermore, a numeri-cally stable procedure would be of great use in embedding schemes combining differentquantum-chemical levels of accuracy [3].

However, if a finite basis set is introduced for the Kohn–Sham orbitals, the OEP pro-cedure turns into an ill-posed problem, because within a finite orbital basis set, many dif-ferent local potentials yield the same target density [4]. Even tough different approachesto overcome this obstacle have been been proposed, such as the use of balanced basissets [5] or a regularization procedure [6], we believe that this problem has so far not beensolved satisfactorily. Either they restrict the possible choices of basis sets and requirevery large orbital basis sets, or they lead to smooth potentials even in cases where theexact potential (obtained in numerical, basis set free calculations) is not smooth.

Here, a new approach to the OEP problem based on projection techniques is presented,which unambiguously selects the potential that would yield the target electron density alsowithin an infinite orbital basis set and thus systematically approaches the exact (basis setfree) solution [7]. The proposed scheme is numerically stable and allows one to vary thebasis set for the orbitals and potential independently. This way, it is possible to approachthe basis set limit for the potential for any given (possibly unbalanced) orbital basis set.Our scheme can be applied both for reconstructing the local potential yielding a giventarget density and for EXX-OEP calculations [8]. Finally, its application within wavefunction theory (WFT) in DFT embedding schemes will also be discussed.

[1] J. D. Talman, W. F. Shadwick, Phys. Rev. A, 1976 14, 36; A. Gorling, Phys. Rev. A,46, 3753; Q. Wu and W. Yang, J. Chem. Phys. 2003, 118.

[2] A. M. Teale, S. Coriani, T. Helgaker, J. Chem. Phys., 2010, 132, 164115.[3] S. Fux, Ch. R. Jacob, J. Neugebauer, L. Visscher, M. Reiher, J. Chem. Phys., 2010,

132, 164101; O. Roncero et al., J. Chem. Phys., 2008, 129, 184104.[4] V. N. Staroverov, G. E. Scuseria, and E. R. Davidson, J. Chem. Phys. 2006, 124,

141103.[5] A. Heßelmann, et al., J. Chem. Phys., 2007, 127, 054102.[6] T. Heaton-Burgess, F. A. Bulat, and W. Yang, Phys. Rev. Lett., 2007, 98, 256401.[7] Ch. R. Jacob, to be submitted, 2011.[8] D. R. Rohr, Ch. R. Jacob, in preparation, 2011.


L25

Thermodynamic limit and size-consistent design

So Hirata Department of Chemistry, University of Illinois at Urbana-Champaign,

600 South Mathews Avenue, Urbana, Illinois 61801, U.S.A.

Why is energy extensive and is an application of statistical thermodynamics to chemistry valid? It has taken 40 years for the finest mathematicians to complete the proof of the extensivity of energy or, equivalently, the existence of thermodynamic (in-finite-volume) limit of energy density. I will offer an alternative, more accessible proof of the extensivity of energy for electrically neutral, metallic and nonmetallic crystals by establishing the same for its individual energy components, namely, the kinetic, Cou-lomb, exchange, and correlation energies. On this basis, I will address size-consistent design of electronic and vibrational many-body methods. Our findings are summarized as follows: The significance of the distinct use of the intermediate and standard normal-ization for extensive and intensive operator amplitudes, respectively; The extensive and intensive diagram theorems, which serve as the foolproof criteria for determining size consistency of a method for extensive and intensive quantities; The extensive-intensive operator consistency theorem, which stipulates the precise balance between the deter-minant spaces reached by extensive and intensive operators in a size-consistent excit-ed-state method. This work is financially supported by University of Illinois, U.S. National Science Foundation (CHE-1118616 CAREER and OCI-1102418), and U.S. Department of En-ergy (DE-FG02-11ER16211). S.H. is a Camille Dreyfus Teacher-Scholar and an Alum-ni Research Scholar.


L26

Ab initio MD of large condensed phase systems with hybrid density functionals

Joost VandeVondele, University of Zurich

Traditionally, ab initio molecular dynamics (AIMD) of condensed phase systems is performed using local density functionals (GGAs). The use of GGAs allows for MD simulations containing a thousand atoms, and static calculations on systems containing millions of atoms. Hybrid functionals, which include a non-local component such as Hartree-Fock exchange, remained prohibitively expensive until recently. Here, we present a linear scaling approach to hybrid DFT that is suitable for condensed phase MD simulations. The approach is based on the use of a truncated Coulomb operator. A massively parallel implementation allows AIMD simulations to be performed with good time to solution. Furthermore, a new approximation to Hartree-Fock exchange will be presented that allows for a significant reduction in computational cost using an approximate density matrix method (ADMM). ADMM exploits the fact that Hartree-Fock exchange can be evaluated rapidly for systems with small basis sets or sparse density matrices, and uses an exchange functional to correct for the difference between the approximate and exact density matrix. This approach captures the most important features of hybrid functionals, such as an improved band gap and reduced self interaction error, while it is similar to a GGA calculation in cost. The methods will be illustrated with applications to vibrational spectroscopy in the condensed phase, and calculations on dye sensitized solar cells.


L27

Local correlation methods for periodic systems

Denis UsvyatInstitute of Physical and Theoretical Chemistry, Universitat Regensburg, Universitatsstrasse 31, D-93040 Regensburg

(Germany)

In extended systems dispersion plays an important and often decisive role for the physically relevant quantities, likethe binding energy, relative stability, etc. Unlike the standard DFT, which has so far been the most common tool forelectronic structure calculations for solids, the recently developed periodic local MP2 method [1] includes the short-and long-range electron correlation on the same footing. This allows for a balanced treatment of dispersion as wellas other contributions to binding. Linear scaling of the computational cost of the method with unit cell size makesit applicable to relatively complicated periodic systems. Performance of the method is analyzed on the examples ofcubic vs hexagonal boron nitride [2] and adsorption of argon on MgO (100) surface.

Reliable and accurate periodic excited state methods are even scarcer than those for the ground state. The firststep to the correlated treatment of excitons – the periodic local CIS method [3] – is presented. For the excitationenergies it appears to be equivalent to the first-order variational coupled cluster linear response formalism [4], whichis also sketched.

[1] C. Pisani, L. Maschio, S. Casassa, M. Halo, M. Schutz, and D. Usvyat, J. Comp. Chem. 29, 2113 (2008).[2] M. Halo, C. Pisani, L. Maschio, S. Casassa, M. Schutz, and D. Usvyat, Phys. Rev. B 83, 035117 (2011).[3] M. Lorenz, D. Usvyat, and M. Schutz, J. Chem. Phys. 134, 094101 (2011).[4] D. Kats, D. Usvyat, and M. Schutz, Phys. Rev. A (2011 (accepted)).


L28

Recent developments in pair natural orbital based single reference correlation methods

Frank Neese

Lehrstuhl für Theoretische Chemie

Universität Bonn

Institut für Physikalische und Theoretische Chemie

Wegelerstr. 12, D-53115 Bonn, Germany

Present day computational chemistry is dominated by density functional theory (DFT). There is no doubt that DFT is a very successful theory that offers a spectacularly good price performance ratio. Nevertheless, there are still a number of problems in DFT and it is not clear how to solve them simultaneously and systematically. It has become evident over the past three decades that single reference coupled cluster methods offer high and systematic accuracy for a wide variety of molecular properties although at high – often too high – computational cost. It seems natural to try to seek for efficient approximations to the very intricate coupled cluster equations that would allow application to large molecules without loosing the intrinsic accuracy of the approach. Linear scaling local correlation methods as first suggested by Pulay and Saebo and further developed and efficiently implemented by Werner, Schütz and co-workers offer one possible route to the problem.[1] We have recently investigated alternative local correlation methods on the basis of pair natural orbitals (PNOs) and the coupled electron pair approximation (CEPA). An efficient production level code was developed and integrated into the ORCA program. In the talk various aspects of local PNO based correlation methods (open shells, parallelization, new functionals) will be discussed.


L29

Developments in the Divide–Expand–Consolidate (DEC) method forlinear scaling Coupled Cluster calculations.

Branislav Jansık ,1 Kasper Kristensen,1 Poul Jørgensen,1 Marcin Zio lkowski,1

Thomas Kjærgaard,1,2 Simen Reine,2

1Lundbeck Foundation Center for Theoretical Chemistry, Department of

Chemistry, Aarhus University, Denmark2Centre for Theoretical and Computational Chemistry, Department of Chemistry,

University of Oslo, Norway

We present recent developments in the Divide-Expand-Consolidate (DEC) cou-

pled cluster (CC) model, where a CC calculation on a full molecular system is carried

out in terms of calculations on small orbital fragments of the total molecular system.

The fragmentation does not involve non–physical bond cuts and represents only an

efficient way of dividing the calculation on a full molecular system into calculations

on small orbital fragments. The sizes of the orbital fragment spaces are optimized

during the calculation in a black box manner to ensure that that the fragment ener-

gies are determined to a preset threshold. This in turn defines the total correlation

energy as a sum of fragment energies to a preset threshold compared to a full molec-

ular calculation. The number of independent fragment calculations scales linearly

with the system size, and the method is therefore linearly scaling and embarrassingly

parallel.

The fragmentation of orbital spaces relies on using a set of local Hartree-Fock

(HF) orbitals. We use our recently developed orbital localization strategy where

powers of the orbital variances are minimized to yield a set of local occupied and

virtual HF orbitals.

DEC calculations are presented for the energy using second order Møller-Plesset

perturbation (MP2) theory and the coupled cluster singles doubles (CCSD) models

to demonstrate the performance of the DEC model. Calculations of the molecular

gradient for the DEC-MP2 will also be presented.


L30

Nuclei-Selected NMR Shieldings: A Sublinear-Scaling

Quantum-Chemical Method

Christian Ochsenfeld

Theoretical Chemistry, University of Munich (LMU)

D-81377 Munich, Germany

http://www.cup.uni-muenchen.de/pc/ochsenfeld/

We present a reformulation that allows for the direct calculation of NMR shieldings

for selected nuclei at Hartree-Fock (HF) and Density-Functional Theory (DFT) levels

[1]. Our method shows a computational effort scaling only sublinearly with molecular

size within the rate-determining steps, as it is motivated by the physical consideration

that the chemical shielding is dominated by its local environment. The key feature of

our method is to avoid the conventionally performed calculation of all NMR shieldings

scaling linearly with system size [2-4], but instead to solve directly for specific nuclear

shieldings. This has important implications not only for the study of large molecules,

but also for the simulation of solvent effects and molecular dynamics, since often just a

few shieldings are of interest. Our theory relies on two major aspects both necessary to

provide a sublinear scaling behavior: First, an alternative expression for the shielding

tensor is derived, which involves the response density matrix with respect to the nuclear

magnetic moment instead of the response to the external magnetic field. Second, as

unphysical long-range contributions occur within the description of distributed gauge

origin methods that do not influence the final expectation value, we present a reformu-

lation suitable for truncation, so that an early onset of the sublinear-scaling behavior

can be achieved. Applications to molecular systems with more than 1000 atoms will be

shown.

[1] M. Beer, J. Kussmann, C. Ochsenfeld; J. Chem. Phys. 134, 074102 (2011)

[2] C. Ochsenfeld, J. Kussmann, F. Koziol; Angew. Chem. Int. Ed. 43, 4485 (2004)

[3] J. Kussmann, C. Ochsenfeld; J. Chem. Phys. 127, 054103 (2007)

[4] M. Beer, C. Ochsenfeld; J. Chem. Phys. 128, 221102 (2008)


L31

Application of wave function based electron correlation methods to weakly bound systems

C. Müller, E. Voloshina, B. Paulus

Institut für Chemie und Biochemie, Freie Universität BerlinTakustrasse 3, Berlin, 14195, Germany

The correct treatment of weakly bound systems, such as physisorbed molecules on surfaces or molecular crystals is a challenging problem in theoretical solid state chemistry. In these systems, electron correlation is of crucial importance. Hence, Hartree-Fock or standard DFT functionals often fail to produce reliable adsorption energies or cohesive energies. On the other hand, common implementations of wave function based post-Hartree-Fock methods, such as Møller-Plesset Perturbation (MP2) or Coupled Cluster (CC) theory, suffer from an unfortunate scaling with system size, and are difficult to adopt to periodic systems.

In our investigations we have combined the Method of Increments [1,2], which is one type of local correlation method, with embedded cluster calculations to investigate physisorption of CO [3-5], NO [6], N2O [7], H2O [8] and H2S [9] on different surfaces of ionic (CeO2, MgF2), semi-metallic (graphene) and even metallic (Mg) materials at the MP2 and CCSD(T) levels. In addition to the speed up in computational time we gain new insights in the nature of the molecule-surface interaction in these systems.

In a related study we demonstrate how the method of increments can be facilitated to the investigation of noble-gas crystals or molecular crystals. For the two examples, Ar fcc [10] and solid CO2 [11], we examine different cluster models and show how they can be combined with periodic calculations to overcome limitations and restrictions in periodic implementations of MP2.

[1] H. Stoll, Chem. Phys. Lett. 191 (1992) 548; J. Chem. Phys. 97 (1992) 8449; Phys. Rev. B 46 (1992) 6700.[2] B. Paulus, Phys. Rep. 428 (2006) 1.[3] C. Müller, B. Herschend, K. Hermansson and B. Paulus, J. Chem. Phys. 128 (2008) 214701.[4] C. Müller, B. Paulus, K. Hermansson, Surf. Sci. 603 (2009) 2619.[5] L. Hammerschmidt, C. Müller and B. Paulus, in preparation.[6] C. Müller and B. Paulus, in preparation.[7] C. Müller, K. Hermansson and B. Paulus, Chem. Phys. 362 (2009) 91.[8] E. Voloshina, K. Rosciszewski and B. Paulus, in preparation.[9] B. Paulus and K. Rosciszewski, Int. J. Quant. Chem. 109 (2009) 3055. [10] C. Müller, D. Usvyat and H. Stoll, Phys. Rep. B, submitted.[11] C. Müller and D. Usvyat, in preparation.


L32

Development and benchmark studies of state-specificmulti-reference coupled-cluster theories

Mihály Kállaya, Sanghamitra Dasa, and Debashis MukherjeebaDepartment of Physical Chemistry and Materials Science, Budapest University

of Technology and Economics, Budapest P.O.Box 91, H-1521 HungarybIndian Association for the Cultivation of Science, Calcutta 700032, India

Recently we have reported the general implementation of the state-specificmulti-reference coupled-cluster (SS-MRCC) theory proposed by Mukherjee andco-workers [J. Chem. Phys. 110, 6171 (1999)]. In several benchmark calcula-tions we have also demonstrated that the performance of the original SS-MRCCansatz in the minimal truncation scheme, viz. at the singles and doubles (SD)level (SS-MRCCSD), is often not satisfactory for multiple bond dissociation ifcanonical MCSCF orbitals are used. Here we analyze the reason for this behav-ior and demonstrate that the SS-MRCCSD approach does not involve the directcoupling of all the model functions with a given virtual function belonging to theuncontracted multi-configuration CISD space. It also does not involve, even in thelinear power of a cluster operator Tµ, the direct coupling of the virtual functionsχlµ , which are up to doubly excited with respect to a model function φµ to theother virtual functions of the MRCISD space which can be generated by tripleand quadruple excitations from φµ. We propose two possibilities to overcome thisproblem. First, we argue that inclusion of a selection of triples and quadruplesinvolving at most two inactive orbital excitations from every φµ would amelioratethe shortcoming of the incomplete coupling of the triply and quadruply excitedvirtual functions which can couple with the singly and doubly excited ones. Sec-ond, we argue that the strength of the coupling and thereby the error caused bythe missing coupling decreases if localized active orbitals are used. Excellent re-sults on potential energy surfaces of small molecules involving single, double, andtriple bond dissociation bear out our expectations.


L33

Internally Contracted Multi-Reference Coupled-Cluster Theory: The Latest News

M. Hanauer, A. KöhnInstitut für Physikalische Chemie, Universität Mainz, 55099 Mainz, Germany

For single-reference systems, coupled-cluster theory provides a hierarchy of methods with systemat-ically increasing accuracy and is hence one of the keystones for quantitative quantum chemistry [1].However, the generalization of the coupled-cluster ansatz to multi-reference systems (e.g. biradicals,transition metal compounds) is still an open question and to date no agreement on the most promisingroute has been reached [2].In this contribution, we present our recent work [3] on the implementation and analysis of the inter-nally contracted multi-reference coupled-cluster (icMRCC) approach. Although early work on thisidea dates back to the early 80s [4], we found that the approach has so far not been fully exploited,likely due to the complexity of the equations. A more rigorous analysis is now feasible with the aidof automated implementation tools. More recent numerical realizations of the theory were based ona CI-like expansion of the intermediates [5], the present implementation proceeds via the factorizedterms and exhibits the correct computational scaling with system size.In particular, we discuss the orbital invariance of the approach, the construction of a unique excitationmanifold, and the structure of the equations, as well as possible truncation schemes. Comparison ismade to related approaches in the present literature. Numerical examples are presented for icMR-CCSD and icMRCCSDT. These comprise of, e.g., the application to the vibrational frequencies ofozone and the singlet-triplet splitting of benzynes.

[1] see e.g. Helgaker, Tew, Klopper, Mol. Phys. 106, 2107 (2008)[2] see e.g. Jeziorski, Monkhorst, Phys. Rev. A 24, 1668 (1981), Mahapatra, Datta, Mukherjee,

J. Chem. Phys. 110, 6171 (1999), Hanrath, J. Chem. Phys. 123, 084102 (2005), Nooijen,Shamasundar, Collect. Czech Chem. Comm. 70, 1082 (2005), Evangelista, Gauss, J. Chem.Phys. 133, 044101 (2010)

[3] Hanauer, Köhn, J. Chem. Phys., accepted[4] Banerjee, Simons, Int. J. Quantum Chem. 19, 207 (1981); J. Chem. Phys. 76, 4548 (1982)[5] Evangelista, Gauss, J. Chem. Phys. 134, 114102, 2011; Olsen, unpublished

1


L34

An Orbital-Invariant Internally Contracted Multireference Coupled Cluster Approach

F. A. Evangelista1, J. Gauss1

1Institut für Physikalische Chemie, Johannes Gutenberg-Universität Mainz, Jakob-Welder-Weg 11, Mainz, 55128, Germany

State-specific multireference coupled cluster (MRCC) theories based on the ansatz of Jeziorski and Monkhorst [1,2] have recently emerged as promising generalizations of the single-reference CC approach for degenerate and near-degenerate electronic states. The key aspect of these theories is the focus on one electronic state, which effectively eliminates the intruder state problem encountered in multiroot theories. However, MRCC methods based on the Jeziorski-Monkhorst ansatz are subject to two major limitations: (i) computations with large active spaces are impractical because the memory and computational costs scale linearly with the number of reference determinants, and (ii) there is a degree of arbitrariness in the MRCC results that stems from the lack of invariance of the energy with respect to rotations of active orbitals [3]. In order to address these two issues we have considered a MRCC approach based internally-contracted wave function ansatz. We report the first implementation of the internally contracted multireference coupled cluster method with singles and doubles (ic-MRCCSD) [4]. The quality of the ic-MRCCSD method is benchmarked in computations of the potential energy curve of the BeH2 model system, the dissociation of HF, and the symmetric double dissociation of water. For all systems, the ic-MRCCSD results are superior with respect to the Mukherjee MRCC approach with singles and doubles (Mk-MRCCSD) [2]. When comparison is available, ic-MRCCSD is found to be competitive with the MRexpT and CASCC approaches and superior to canonical transformation theory [5]. Approximations of the ic-MRCCSD approach based on a truncated Baker-Campbell-Hausdorff expansion converge quickly to the full theory. Two commutators are sufficient to recover a total energy within 0.5 mEh of the full ic-MRCCSD method along the entire potential energy curve. In the case of a complete model space, we also formally prove and numerically test the invariance of the energy with respect to rotation of active orbitals. [1] B. Jeziorski and H. Monkhorst, Phys. Rev. A 24, 1668 (1981). [2] U. Mahapatra, B. Datta, and D. Mukherjee, Mol. Phys. 94, 157 (1998). [3] F. A. Evangelista and J. Gauss, J. Chem. Phys. 133, 044101 (2010). [4] F. A. Evangelista and J. Gauss, J. Chem. Phys. 134 , 114102 (2011). [5] M. Hanrath, J. Chem. Phys. 123, 84102 (2005); P. Piecuch, N. Oliphant, and L. Adamowicz, J. Chem. Phys. 99, 1875 (1993); T. Yanai and G. K.-L. Chan, J. Chem. Phys. 124, 194106 (2006).


L35

MODELING ENVIRONMENT EFFECTS IN QUANTUM CHEMISTRY

Benedetta Mennucci

Department of Chemistry, University of Pisa, via Risorgimento 35,

56126, Pisa, ITALY

The development of models that account for environment effects (commonly indicated as solvation models) reflects to some extent the development of molecular modeling itself. The computer simulation of molecular processes and properties in fact necessarily requires the inclusion of the effects of the solvent (or, more in general, of the environment) if a direct link with the experimental observation is searched. A similar, if not more stringent, request applies to any computational study aimed at predicting behaviours of new materials, at designing new molecules or supramolecular systems with desired characteristics, at interpreting physical phenomena and chemical processes at a molecular level. In this talk I’ll present and discuss the recent advances achieved in the integration of QM descriptions of molecular systems with continuum solvation models of increasing accuracy. The main theoretical aspects related to this integration will be discussed with particular reference to applications to electronically excited states. In parallel, an analysis of how specific physical characteristics of different types of environment can be taken into account will be presented. Examples of recent applications of the same models will be given and discussed in the light of the above theoretical and physical issues.


L36

Solvation at surfaces: a fully quantistic model includingnon-electrostatic interactions. Energetics and molecular properties.

Luca FredianiCTCC, University of Tromsø, N-9037, Tromsø, Norway

The main component of any solvation model is the solute-solvent electrostaticinteraction, which is effectively modeled through a continuum approach. Otherinteractions are often neglected, partially due to a lucky cancellation effect. How-ever, for solvation at surfaces the non-electrostatic interactions become essentialin describing the physics of the system. We present a fully quantum-mechanicalcontinuum solvation model including the effect of dispersion and repulsion inter-actions. We show that when all interactions are properly accounted for the ener-getics of the phase transfer is correctly described. In addition, a fully quantum-mechanical model will be capable of describing the effect of non-electrostaticinteractions on molecular properties such as excitation energies and polarizabili-ties.

Figure 1. Solvation energy of acetone at the water surface. Fullsolvation energy (red, full) and non-electrostatic contributions(green, dashed) are reported. Energies are in KCal/mol and dis-tances in Angstrom. Bulk water on the left side. Acetone moleculeoriented as depicted

1


L37

Predictingtheopticalpropertiesofmoleculesandaggregates

BenoîtCHAMPAGNELaboratoiredeChimieThéorique,UnitédeChimie‐PhysiqueThéoriqueetStructuraleFacultésUniversitairesNotre‐DamedelaPaix(FUNDP)RuedeBruxelles,61,B‐5000Namur(BELGIUM),[email protected]

Designingnewdyesandpigmentsfortargetedapplicationsisasubstantialtaskwheretheoreticalmethodscanplayakeyrole.Todothat,fastandreliablemethodsforcomputingandinterpretingtheiropticalpropertiesshouldbeelaborated. Before tackling molecules in aggregated forms, a preliminary step consists often incharacterizing themolecules in solution, i.e. in simulating their UV/vis absorption spectra.Indeed, a lack of agreement between the simulated and – easily – recorded spectra tellsdirectlythatthemethodisnotreliableforaddressingthecrystals.Thisfirstissueishoweveralready complicated because an absorption spectra is not only characterized by transitionenergiesbutalsobytransitionintensitiesandbandshapes. Ourfirststeptowardsthisgoalwas therefore the implementation of the Doktorov recursive scheme to determine thevibronic structure of organic chromophores. This was combined with an investigation ofseveral“traditional”methodstoevaluatetheexcitationenergies[1]andoscillatorstrengths[2].Inmanycases,TDDFTwithahybridexchange‐correlationfunctionalcanleadtoaprettynicereproductionoftheshapeoftheexperimentalspectrumaswellasofthebatho‐orhypso‐chromaticshiftsuponstructuralvariations,asevidencedforcyaninesandmerocyanines[1]. The second aspect, the crystal packing effects, is also important and can changecompletely the shape of the absorption spectra. Generally, the approach consists indetermining exciton andgas to crystal shifts by considering thewhole3D crystal structureandthenofinjectingitinthemultimodevibronictheory[3].Inparticular,wehavecombinedthe latter approach with TDDFT to simulate the absorption spectrum of coupled identicalmonomers. Different levels of approximations have been considered: one where thevibrational excitations strictly accompany the electronic excitations and one that includesvibrationalexcitationsforboththegroundandtheexcitedelectronicstates[4].

[1] B.Champagne,M.Guillaume, andF.Zutterman,TDDFT Investigationof theOpticalPropertiesofCyanineDyes,Chem.Phys.Lett.425,105(2006);M.Guillaume,B.Champagne,andF.Zutterman,InvestigationoftheUV/visibleAbsorptionSpectraofMerocyanineDyesusingTDDFTMethod, J.Phys.Chem.A110,13007(2006).

[2] M. Miura, Y. Aoki, and B. Champagne, Assessment of TimeDependent Density Functional Schemes forComputing the Oscillator Strengths of Benzene, Phenol, Aniline, and Fluorobenzene, J. Chem. Phys. 127,084103(2007).

[3] A.M.Kelley,Amultimodevibronictreatmentofabsorption,resonanceRaman,andhyperRayleighscatteringofexcitonicallycoupledmoleculardimers, J.Chem.Phys.119,3320(2003).

[4] J.Guthmuller,F.Zutterman,andB.Champagne,Predictionofvibroniccouplingandabsorption spectraofdimers from timedependent density functional theory: the case of a stack streptocyanine, J. Chem.Theor.Comput.4,2094 (2008); J.Guthmuller,F.Zutterman,andB.Champagne,Multimode simulationofdimerabsorption spectra and exciton coupling energies from first principle calculations: Application to the3,4,9,10perylenetetracarboxylicdiimidedimer,J.Chem.Phys.131,154302(2009).


L38

Abstractsof

Posters

Development of high-end correlated methods at Arizona.

Ludwik AdamowiczDepartment of Chemistry and Biochemistry

University of ArizonaTucson, Arizona 85721, U.S.A.

Abstract

In this presentation I will reviewing the work recently performed in my group at the Universityof Arizona on the development of very accurate ab initio methods for the calculations of small- andmedium-size atoms and molecules. The following methods will be described:

• The gradient-based variational approach for Born-Oppenheimer (BO) calculations of poten-tial energy curves (PEC) and surfaces (PES) of small molecular systems with explicitly cor-relate Gaussian functions. The method was recently employed to calculate the most accurateand complete adiabatic PES of H+

3 . The rovibrational frequencies obtained using the PESfacilitated assignment of the newly measured H+

3 lines in the visible region of the spectrum.

• The gradient-based variational non-BO approach for calculating stationary states of atomsand diatomic molecules with explicitly correlated Gaussian functions. An example of calcula-tions leading to refinement of experimental energy levels of 2D Rydberg states of the Li atomwill be shown.

• The state-selective multireference couple-cluster method with single and double excitationsemploying an active space obtained in a CASSCF calculation (the CASCCSD method). Anexample of calculations of the ground-state PEC of the N2 molecule will be shown.

1

ESCMQC11 - Posters

P1

NMR shieldings of an excimer

Michiko Atsumi,a Daniel Roca-Sanjuán,

a Hans Jørgen Aagaard Jensen,

b

Trygve Helgaker,c and Roland Lindh

a

a Department of Physical and Analytical Chemistry, Quantum Chemistry,

Uppsala University, Uppsala, Sweden

b Department of Physics and Chemistry, University of Southern Denmark, Odense, Denmark

c Centre for Theoretical and Computational Chemistry, Department of Chemistry,

University of Oslo, Oslo, Norway

Multiconfigurational self-consistent field (MCSCF) methods have been used to

study the nuclear shieldings at the lowest excited singlet state of nucleobase excimers

(excited dimers). The optimized structure of excimers were reported by Roca-Sanjuán et

al.[1] by complete active space self-consistent field (CASSCF)/complete active space

plus second-order perturbation theory (CASPT2) level of theory.

Since there are no experimental results of nuclear constants in excited state excimer,

the primary calculation has been carried out for the nuclear shieldings of uracil at

ground state. Using the same method, excimer results for the ground state and two

lowest excited states were also obtained. The state-average CASSCF calculations and

geometry optimizations were done by Molcas 7. A preliminary version of Dalton 2011

was employed for state-specific CASSCF and nuclear shielding calculations.

The atomic natural orbital (ANO) type basis set has been used for all atoms.

Reference

[1] D. Roca-Sanjuán, G. Olaso-González, I. González-Ramírez, L. Serrano-Andrés and M.

Merchán J. Am. Chem. Soc., 2008, 130 (32), 10768

ESCMQC11 - Posters

P2

THIAZOLE ORANGE AS A LIGHT-SWITCH PROBE:

A COMBINED QUANTUM-MECHANICAL AND

SPECTROSCOPIC STUDY

Alessandro Biancardi, Tarita Biver, Alberto Marini,

Benedetta Mennucci, Fernando Secco

Dipartimento di Chimica e Chimica Industriale, via Risorgimento 35, 56126 - Pisa (IT)

email: [email protected]

A Density Functional Theory (DFT) study of the absorbance and fluorescence emission

characteristics of the cyanine Thiazole Orange (TO) in solution and when intercalated in

DNA was carried out in combination with spectrophotometric and spectrofluorometric

experiments under different conditions (temperature, concentration, solvent viscosity).

T-jump relaxation kinetics of the TO monomer-dimer conversion enabled the

thermodynamic parameters of this process to be evaluated. The overall data collected

provided information on the features of the “light-switch” by the fluorescent TO and the

comparison between experimental and calculated photo-physical properties allowed to

explain and rationalize both shifts and quenching/enhancing effects on fluorescence due

to solvation, dimerisation and intercalation in the DNA.

ESCMQC11 - Posters

P3

mailto:[email protected]

Treatment of π electrons using anisotropicpseudopotentials

Jean Drujon and Yannick Carissan

Université Paul Cézanne - iSm2, UMR-CNRS-6263 Campus St. JérômeService D42 - 13397 Marseille - France

The division of a system into active and inactive electrons is a key problem in theoretical

chemistry : the choice of the QM/MM frontier, the active space in CASSCF calculations,

the choice of atomic pseudopotentials are examples of this dilemma. It is a crucial question

when dealing with effective group potentials from which this work derives1.

Because we are interested in π − π interactions and excitation energies of π electronic

systems, we want to reproduce accurately the electronic properties of π electrons and use

the smallest possible system. This was achieved with model hamiltonians2and the electronic

structure of such systems is still studied these days.3

We have used the symmetry properties of π orbitals and atomic pseudopotentials in order

to treat explicitly only 1 electron per carbon atom. We replace a sp2

carbon by a pseudo

carbon made of (i) one nucleus of charge Z=1, (ii) one s pseudopotential with a high eigenvalue

which shifts up the 1s and 2s atomic orbitals, (iii) two s pseudopotentials along the z axis,

slightly away from the nucleus, which stabilize the pz orbital (px and py are unchanged). This

later potential plays the role of α in the Hückel model. Additionally, one p pseudopotential

is inserted between two adjacent sp2

carbons in order to reproduce properly the energy of a

π interaction, similarly to the Hückel parameter β.

The extraction of the pseudopotential parameters were done on the ethylene molecule

and transferred to linear polyenes up to C10H12. At the MRCI level for the first excitation

energy, and the ionization potential, our model compares with full electron calculations with

a maximum deviation of 0.2 eV. Furthermore, we used this model to compute the first

excitation energy of sandwich complexes of the kind M(C8H8)2, M = Ce, Th and obtained

an agreement of 0.2 eV with previous calculations4.

These results are encouraging for further studies on larger systems and weaker interac-

tions.

1Carissan, Y., Bessac, F., Alary, F., Heully, J.-L. and Poteau, R. (2006), International Journal of Quantum

Chemistry, 106: 727–733.2M. Said, D. Maynau, and J. P. Malrieu, Journal of the American Chemical Society, 1984, 106(3), 580–587

3Junjing Gu, Yonghui Lin, Ben Ma, Wei Wu and Sason Shaik Journal of Chemical Theory and Compu-

tation 2008 4 (12), 2101-21074W. Liu, M. Dolg and P. Fulde J. Chem. Phys. 107(9) 1997, p3584

1

ESCMQC11 - Posters

P4

Formal Aspects and Applications of

Internally Contracted Multireference Coupled Cluster Theory

Matthias Hanauer and Andreas Kohn

Institut fur Physikalische Chemie, Universitat Mainz, D-55099 Mainz, Germany

E-mail: [email protected]

The internally contracted multireference coupled cluster (icMRCC) method offers ahighly accurate description of both static and dynamic correlation. Compared to theJeziorski-Monkhorst ansatz [1] (which uses one cluster operator for each reference deter-minant), the icMRCC ansatz parameterizes the wave function more efficiently by lettinga single exponential operator act upon the multideterminantal reference:

|Ψ〉 = eT |Ψ0〉 = eT∑

µ

|Φµ〉cµ, with T =∑

ρ

τρtρ.

Two major difficulties arise from this ansatz: First, the set of excited functions τρ|Ψ0〉contains linear dependencies which need to be eliminated. We have studied four possibleways to construct a unique excitation manifold and have found that three of them are notsize consistent [2]. The sole exception is a procedure that enforces orthogonality betweenexcitations of different operator ranks such as between singles and doubles. We showhow this can be done in practice while preserving orbital invariance, which is anotherimportant feature of the icMRCC method [3]. The second difficulty is the occurrenceof a large number of terms in the amplitude equations due to non-commutativity of thecluster excitations. We deal with the problem by deriving the equations and factorizingeach term in an automated fashion. This results in the correct computational scaling.For the challenging ozone molecule, icMRCCSDT yields an equilibrium structure and har-monic vibrational frequencies in excellent agreement with CCSDTQ. Further applicationsof icMRCC theory include potential energy surfaces of LiF and N2, and singlet-tripletsplittings of benzynes.

[1] B. Jeziorski, H. J. Monkhorst, Phys. Rev. A 24 (1981) 1668.[2] M. Hanauer, A. Kohn, J. Chem. Phys., accepted.[3] F. A. Evangelista, J. Gauss, J. Chem. Phys. 134 (2011) 114102.

ESCMQC11 - Posters

P5

TREATMENT OF EXCITED STATES IN STATE-SPECIFICMULTIREFERENCE COUPLED-CLUSTER THEORY

Thomas-C. Jagau, Jurgen Gauss

Institut fur Physikalische Chemie, Johannes Gutenberg-Universitat Mainz,Jakob-Welder-Weg 11, D-55128 Mainz, Germany


Single-reference coupled-cluster (CC) theory has evolved into a standard tool for high-accuracy quantum-chemical calculations, but it carries one major drawback: TruncatedCC schemes fail for multireference cases like bond-breaking situations, organic biradicals,and many transition-metal compounds, where strong static electron correlation is present.To treat such systems, several multireference coupled-cluster (MRCC) methods have beenproposed, but they are still far from routine application. Among the multitude of MRCCapproaches, the state-specific variant suggested by Mukherjee et al. [1,2] (Mk-MRCC)holds a lot of promise, especially as it rigorously preserves size-extensivity.

In this presentation, we focus on the treatment of electronically excited states inMRCC theory suitable for molecules that exhibit strong multireference character in theirground state. The conceptually simplest access to excited states in the framework ofMk-MRCC theory consists in converging the equations to the state of interest. However,this route suffers from a severe disadvantage: Since Mk-MRCC is a state-specific theory,all information on the connection of two electronic states is lost when converging theequations to either state. To overcome this inherent problem, two distinct approachesmay be pursued, namely the application of response theory [3] to the Mk-MRCC wave-function for the ground state or the construction of an equation-of-motion (EOM) typewavefunction [4] for the excited state. By means of these methods, excitation energies,transition moments, and further excited state properties become accessible for systemswith multireference character.

We present the necessary theory to determine excitation energies at the Mk-MRCClevel of theory within the singles and doubles approximation (Mk-MRCCSD). It is shownthat response theory and the earlier developed EOM ansatz [5] lead to the same expres-sions for excitation energies. We illustrate the usefulness of our scheme by exemplaryresults for excitation energies of chemically interesting molecules.

[1] U. S. Mahapatra, B. Datta, and D. Mukherjee, Mol. Phys. 94 (1998), 157.[2] U. S. Mahapatra, B. Datta, and D. Mukherjee, J. Chem. Phys. 110 (1999), 6171.[3] O. Christiansen, P. Jørgensen, and C. Hattig, Int. J. Quantum Chem. 68 (1998), 1.[4] J. F. Stanton and R. J. Bartlett, J. Chem. Phys. 98, 7029 (1993).[5] S. Chattopadhyay, U. S. Mahapatra, and D. Mukherjee, J. Chem. Phys. 112 (2000), 7939.

ESCMQC11 - Posters

P6

�� !��" �#��$�#%'& (*) �+�� ,�$-.��,��/��0�#� �

��#��" ��12��3�

46587�9;:=<�>=?*@�A�B�>DCE<F?*@G�HJI8KMLONQPRHOSEN6TVU�WYX8HOP�Z;[FNQLF\=]_^�KMLFZ`KaWcb8L�ZdHfehgji=kl TnmhTMop[�iMKrqcS�ZtsMHOL�[�ZQNQ\=]

I lvu ^wKMLFZQKxWcb8L�ZdHfehgji=kl TnmhTMop[�iMKzy{]6|~}{e�}My*�w��bE� l Z;Sj]+��T l KMS�m� 9;�f��@��8@~<�>=�6�7�<�?E9

��Sj[FNQZQNQbjN�HzTVUa��L`�*K{S�ZQ��WYX8HOP�Z;[FNQLF\D]��T l Z;[ Xx�#� K*m*HOP�\�TVUwg3�fZdHOS��FHF[ ]

��KM[dI�L�nK=i{K��h�8]�}{�{e{|h|D��KML�[OKMop]��T l KMS3m=] �¡¢P�K{Z lv£ P�Z`�OX~K l ¤ �h¥!Z`�OX~T u H mMb u I l

¦ :§:©¨3@~ª�9t7�:�«O��:¬�:=®¯:=7�¬3:=7��D:w°�±³²d´fµ·¶��@~¬�B��®Y°~�t:§�D°8��®��;9t7�5¸�=°87�< «f@~7j«F<¹9t7º@'<�:=BF9;:=<»°�±¼<�ª@��t�ª�°8�t:D�=��;:=<=½3�M@~�;�=��t@�«O:D¬¸@*«.«F��:³�=°8�3®��t:D¬¸�D�t��< «O:=B+�;:D¾8:D�¢½�°87�«O�3:R�;:D¾~:=��°~±!@~®�®�B�°{¨�9;ª@�«F9t°87c¿�À/°~B+Á�Â_µ�½Á6µ6Â6½/Â_Á¼Ã©Â_µ�@~7�¬wÂ_Á¼Ãnµ6Â6½3Ä#:��<F:�«F��:��=°~��®��t:D¬Å�=�;��<�«F:=BÆ<F9;7�58�;:=< ÇÈ@~7�¬�ÇV¬�°8��É3�t:=<�Ä+9;«F��@»7�°87�9Ê«O:DBO@*Ç«O9Ê¾8:.®Y:DB�«F��BFÉ�@*«O9;¾~:Æ«OBF9;®��t:D<��=°8B�BF:=�©«O9;°87EË ÂÆÂÆÌ3ÍÏÎdÐ.ÑVËÒ@�®�®�BF°8@~�f�p½�@�7�¬�Ä#:�@�7�@~�;CE<�:+«F��:.É�@~<F9;<�<F:D«#¬�:nÇ®¯:=7�¬�:D7��=:#°~±E«O��:ÓBF:D<F��Ê«O<=¿!À�°8B�@~>=9;BF9;¬�9t7�:�½{¬�9Q@�>=9tB�9t7�:�@~7�¬R�DCE�=�;°8®�BF°~®�CE��DC8@~7�9;¬�:ÓÄ#:Ó��<F:�«O��:�ÂÆÂÆÌ3ÍÏÎdÐ.Ñ@~®�®3BF°j@~�f�c½,É��3«¹<�ª@~�;�t:DB�É�@�<F9t<�<F:©«O<=½Ó@~73¬x±d°8B�«F��:§�Q@�BF58:D<�«»< «O��¬39t:=¬ºª�°8�;:=�=�3�t:=<ÈË�¶��9;7E�3�=�t9;¬�9t73:�@�7�¬��:n¨�@�ª�9;7�:nËÔÄ�:³®�B�:=<F:D7j«�ÂÆÂÆÌ3ÍÕBF:D<F��Ê«O<=¿

ÐÆ��:¹¬�9ÊÖc:DBF:D7��=:D<RÉ¯:D«ÈÄ#:=:D7��D°8ª�®3�3«O:D¬×@�7�¬Ø:©¨�®Y:DBF9;ª�:D7�«O@~�Ù¾�@~�;��:=<�±d°~B6«O��:¹É¯:=< «RÉ�@~<F9;<�<F:©«O<³��<�:=¬@~B�:_ÚRÛ8ÜÝ@�«Þ«O��:�ÂÆÂÆÌ3ÍÔ�;:D¾8:D�E@~7�¬0¬3:=�=B�:M@~<�:_7�°~«F9t�D:M@~É��ÊC³@�«Þ«O��:�ÂÆÂÆÌ3ÍÏÎdÐ.ÑÞ�t:©¾8:D�¢¿ÞÐÆ��:�ß�µ6à�Â�É¯°87�¬3<@~B�:�@�7�:©¨��D:=®3«F9t°87EË$9t7�«O��9;<+�M@~<�:R«F��:�¶��@�¬�BF��®¯°8�;:R�D°8��®��;9t7�5Ï�D°87�<�«O@~7j«O<6@~BF:�¾8:DB�Cw<Fª�@~�;�¢½3�3:=7��D:�«O�3:¬�9ÊÖc:DBF:=73�=:=<.É¯:D«ÈÄ#:=:=7w«O��:D°8B�Cw@�7�¬�:©¨�®Y:DBF9;ª�:D7�«.É¯:=�D°8ª�:³�t@~BF58:DB³Î��3®w«F°�á8Ü�Ñn¿

¦ :¸�D°87�<F9;¬�:=B�@~�;<F°Ø«O��:w®Y:DB�±d°8B�ª@�7��=:�°~±6¬�:=7�<�9;«ÈC�±d��7��©«O9;°87�@~�_«F��:=°8B C�ÎJÍ�À!Ð.Ñn½,�=°8ª�®�@~B�9t7�5z«O�3:BF:D<F��Ê«O<!±d°~BÙ¬�9ÊÖc:DBF:D7�«�¬�:=7�<�9;«ÈCR±d��7��©«O9t°~7�@~�t<�Ä+9;«F�0«O�3:_�=°8�3®��t:D¬»�=�;��<�«F:=B!¾�@~�;��:=<Ù°~±�«O��:�<O@~ª�:��D°87�<�«O@~7j«O<D¿� °8< «�°�±Y«F��:.±d�37��D«F9t°87�@��t<,®�B�°h¾E9;¬�:+BF:=<��;«F<#< CE<�«O:Dª@*«O9t�=@~�t�ÊC»9;ª�®�B�°{¾8:=¬ÏÄ+9;«F��B�:=<�®Y:D�D«Ó«O°³«O��:.Á6@�B�«OB�:=:nÇÀ�°��f?zÎJÁ6À�Ñ#¾~@��t��:D<=½3Ä+9Ê«O�z²d´nµâ�=°8��®3�t9t735¹�=°87�< «f@~7j«F<¼9;7§ßEµ�àRÂÒÉ¯°87�¬�<+É¯:=9t735�@�5j@~9t7�@�7¸:n¨3�D:=®3«F9t°87c¿

ESCMQC11 - Posters

P7

A first-principles theory for the frequency-dependent magnetizability

Marco Anelli, Dan Jonsson, Kenneth Ruud

Centre for Theoretical and Computational Chemistry, Department of Chemistry,

University of Tromsø, 9037 Tromsø, Norway

Materials with a negative index of refraction are substances in which either

one or both of the permittivity and the permeability of the medium is negative.

Whereas the permittivity of the medium is well defined and related to the frequency-

dependent polarizability, the dispersion behaviour of the permeability is not as well

defined. The relation between the macroscopic permeability and the microscopic

quantity describing the interaction with the magnetic component of the electro-

magnetic field, the frequency-dependent magnetizability, is in contrast poorly un-

derstood. Indeed, even the definition of the frequency-dependent magnetizability

appear unsatisfactory.

A theory for the frequency-dependent magnetizability has been presented by Raab

and de Lange [1], and these authors have also considered the frequency-dependent

permeability [2]. However, the expression derived for the frequency-dependent mag-

netizability is based on a number of assumptions, making the theory somewhat

unsatisfactory.

In this talk, we will discuss our recent analysis of the frequency-dependent magne-

tizability, and propose a new way of deriving the frequency-dependent permittivity,

inverse permeability and magnetizability starting from the single-photon scattering

amplitude.

References

[1] R. E. Raab and O. L. de Lange. Mol. Phys. 104, 1925 (2006)

[2] R. E. Raab and O. L. de Lange. Proc. Royal Soc. 461, 595 (2005)

ESCMQC11 - Posters

P8

Theoretical prediction of the spin-‐spin coupling constants of silver

intercalated between nucleic bases

and Magdalena Pecul

Faculty of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warszawa The indirect nuclear spin-‐spin coupling constants of Ag intercalated between imidazole rings in DNA chains have been calculated by means of density functional theory with zeroth order regular approximation hamiltonian (DFT-‐ZORA).

Figure 1. Structure of the model system

Atom of silver placed between two imidazole rings has been chosen as a model, on which various functionals and basis sets have been tested. It has been modeled how the coupling constant is affected by different types of geometry deformations and by the presence of the solvent (simulated by polarizable continuum model and explicitly present water molecules). The calculations for systems containing two and three imidazole pairs have also been made. The coupling path has been visualized using coupling energy density (CED).

The computed spin-‐spin coupling constant is 80-‐92Hz and changes little with the computational model. It is in good agreement with the experimental value (about 92Hz). Bigger models allowed us to compute the coupling constant between two atoms of silver which gave result of approximately 1Hz. The coupling constant J(N,Ag) was surprisingly unaffected by the presence of solvent and geometry deformations. Such behavior is explained by visualization analysis.

ESCMQC11 - Posters

P9

Pushing the limits in parallelmulti-con�gurational electronic

structure theories

Stefan Knecht1, Hans Jørgen Aa. Jensen1, Jeppe Olsen2 and Trond Saue3

1Department of Physics and Chemistry, University of Southern Denmark, Campusvej 55, DK-5230

Odense M, Denmark

2Lundbeck Foundation Center for Theoretical Chemistry, Department of Chemistry, Aarhus University,

Langelandsgade 140, DK-8000 Aarhus C, Denmark

3Laboratoire de Chimie et Physique Quantiques - UMR5626, Université Paul Sabatier - Bât. 3R1b4,

118 route de Narbonne 31062 Toulouse Cedex 09, France

In the past both non-relativistic and relativistic quantum chemistry hassteadily bene�t from signi�cant advances in computer technologies. Thenowadays common access to massively parallel computer architectures pro-vides an excellent starting point for the challenge of designing and devel-opping e�cient parallel algorithms. In this contribution we introduce ourrecent progress regarding a new set of parallel non-, scalar- as well as 4-component relativistic MCSCF computer codes which are being implementedin the open-source Dalton [1] and Dirac [2] program packages, respectively.As a �rst application we investigate to what extent the variational inclusionof spin-orbit interaction modi�es the electronic structure, in particular thebond order, of the uranium dimer U2. For this purpose, we will analyze ourresults in the light of a computational study by Gagliardi and Roos suggestingthat U2 has a quintuple bond [3]. In these calculations scalar relativistic ef-fects were included variationally through the second-order Douglas-Kroll-HeÿHamiltonian, whereas spin-orbit coupling was treated perturbatively throughthe SO-RASSI approach [4].

References

[1] Dalton, a molecular electronic structure program, development version,http://www.daltonprogram.org/

[2] Dirac, a relativistic ab initio electronic structure program, development ver-sion, http://wiki.chem.vu.nl/dirac/index.php/Dirac_Program

[3] L. Gagliardi and B. Roos. Nature, 433, 848, (2005).

[4] P. Å Malmqvist, B. O. Roos, and B. Schimmelpfennig. Chem. Phys. Lett., 357,230, (2002).

ESCMQC11 - Posters

P10

The MP2 molecular gradient for large molecular systems using

the Divide-Expand-Consolidate approach

Kasper Kristensen, Simen Reine, Thomas Kjærdgaard,

Branislav Jansik, Ida-Marie Høyvik, and Poul Jørgensen

Lundbeck Foundation Center for Theoretical Chemistry,

Department of Chemistry, University of Aarhus, DK-8000 Arhus C, Denmark

(Dated: April 28, 2011)

Abstract

The divide-expand-consolidate (DEC) coupled-cluster approach is used to express the MP2

molecular gradient in a form, which can be applied for large molecular systems. All four-index

quantities (local electron correlation effects) are manipulated by considering only small fragments

of the total orbital space to circumvent the scaling wall of standard MP2 calculations, whereas

two-index quantities are treated at the full molecular level. The errors introduced compared to

a full molecular MP2 gradient calculation are controlled by a fragment optimization threshold

(FOT), which determines the sizes of the orbital fragments. Calculations for a series of polyalanine

α-helixes show that the full molecular MP2 gradient can be reproduced to a desired accuracy using

relatively small orbital fragments. For example, for polyalanine(4) the standard deviation of the

cartesian components of the DEC-MP2 molecular gradient compared to the full molecular MP2

gradient decreases from 0.30 to 0.048 mHartree/bohr when the FOT is lowered from 10−4 to 10−5.

1

ESCMQC11 - Posters

P11

Time-dependent coupled cluster with variational orbitals

Simen Kvaal1, 2,∗1Matematisches Institut, Universitat Tubingen, Auf der Morgenstelle 10, D-72076 Tubingen, Germany

2Centre of Mathematics for Applications, University of Oslo, N-0316 Oslo, Norway

The curse of dimensionality is the main challenge for many-particle quantum mechanics. It is especiallyhampering forab initio solutions of the time-dependent Schrodinger equation. Today, thede factostandardmethod is the multi-configurational time-dependent Hartree method (MCTDH) and its variants. Thesemethods are successful for more particles than, say, a standard time-dependent full CI approach, sincethe single-particle functions/orbitals that are used to build the basis functions are variationally determinedalong with the basis expansion coefficients, lowering the needed Hilbert space dimension.

MCTDH-type methods “postpone” the curse of dimensionality to a higher particle number, but does noteliminate it. The time-dependent basis is still growing combinatorially fast, i.e.,

dim(H ) =(

LN

), L = # of orbitals,N = # of particles.

For the time-independentSchrodinger equation, the popular coupled-cluster method (CCM) overcomesthe curse of dimensionality in the sense that the dimension of the nonlinear ansatz manifold (a subset of thefull CI space) grows only polynomially withL andN,

dim(MCCSD) ∝ N2(L−N)2.

It is also size-consistent, and is today one of the most widely-used method in both chemistry and nu-clear physics as it can treat many more particles than full CI. Fordynamicalcalculations, however, it hasbeen limited to response theory using stationary single-particle functions. This limits the use of the time-dependent CCM to systems that are localized in space, and performs badly on studies of, say, ionization ofatoms and molecules, where today the MCTDH method is the standard.

The CCM can be derived using the bi-variational principle [J. Arponen, Ann. Phys. (1983),151, 311–382]which generalizes the usual variational principle. Introducing the single-particle functions as variationalparameters as well as the CCM amplitudes, a polynomially scaling highly adaptive generalization of theCCM can be derived. We perform this derivation and point out some properties of the resulting equationsof motion. Most important is perhaps that the method represents an interpolation between the simple time-dependent Hartree-Fock method (for no amplitudes at all, using only the reference determinant as ansatz)and the MCTDH method for fermions on the other (no truncation of the amplitudes, i.e., full CI space withvariational orbitals).

∗Electronic address:[email protected]

ESCMQC11 - Posters

P12

QUANTUM CHEMICAL CALCULATIONS OF ISOTROPIC COMPTON PRO-FILES

J. Lehtola†, M. Hakala†, J. Vaara‡ and K. Hämäläinen†

†Department of Physics, P. O. Box 64, FI-00014 University of Helsinki, Finland‡Department of Physics, P. O. Box 3000, FI-90014 University of Oulu, Finlandemail: [email protected]

Artist’s impression of Comptonscattering from the water dimer.

c� Jyrki Hokkanen, CSC.

Compton scattering is a process in which a pho-ton scatters inelastically from an electron in thesample, exchanging a large amount of energyand momentum. The scattering cross sectioncan be shown to be proportional to the Comp-ton profile, which measures the projection of themomentum density of the electrons in the tar-get onto the scattering vector. In systems wherethere are no preferred orientations (e.g., gasesand liquids) the profile is isotropic.

Compton scattering experiments using x-raysfrom synchrotron sources can be used to obtaininformation about the ground state momentumdensity (electron density in momentum space)[1]. This information can be used in structurestudies. However, one must be able to modelthe Compton profile to see how it is affected bychanges in the atomic and molecular structure.

In the presentation we will give an overview of the results of our recent study[2], inwhich we developed an algorithm to calculate the isotropic Compton profile and per-formed calculations on water and helium monomers and dimers using density functionaltheory (DFT), Hartree-Fock and post-Hartree-Fock methods such as Møller-Plesset andCoupled Cluster theory, using Dunning-type ((d-)aug-)cc-p(C)VXZ basis sets.

We discuss requirements for accurate computation of the Compton profile, both with re-spect to the basis set used and the level of theory used in the formation of the densitymatrix, the convergence criterion being determined by the accuracy of state-of-the-artexperiments.

[1] M. J. Cooper, Rep. Prog. Phys. 48 (1985) 415.M. J. Cooper et al., X-ray Compton Scattering, 2004, Oxford University Press.

[2] J. Lehtola and M. Hakala and J. Vaara and K. Hämäläinen, Phys. Chem. Chem. Phys.,DOI:10.1039/C0CP02269A.

ESCMQC11 - Posters

P13

Bubbles: accurate numerical electrostatics for molecular

systems

S. A. Losilla, D. Sundholm

Department of Chemistry, University of Helsinki, A. I. Virtasen aukio 1,P.O. Box 55, FI-00014 University of Helsinki, FINLAND

Numerical approaches to electronic structure problems always face the problem of representing

nuclear cusps. Pseudopotentials are the most common workaround, at the cost of accuracy. If the

core electrons are treated explicitly, very large numbers of points are required in those regions,

making calculations of middle-sized systems prohibitively expensive. We have recently developed a

numerical framework where electronic molecular functions are described using a mixed representa-

tion, with low-order spherical-harmonic expansions at every nucleus (bubbles) and a 3D Cartesian

grid (cube):

f(r) =∑A

∑lm

fAlm(rA)Ylm(θA, φA) + f∆(r)

The bubbles (fAlm)can be chosen so that the cube (f∆) is smooth and small, drastically reducing

the number of points required for an accurate representation.

Calculating the electrostatic potentials caused by a given electron charge density represented

in this manner is easy, as it can be done in an additive manner through direct integration of the

Coulomb potential. The contribution from the bubbles can be obtained at a very low cost. For the

cube, we use an algorithm previously developed by our group[1, 2, 3].

An algorithm for calculating accurate interaction energies has been also developed. The integral

of the product of a charge density times a potential cannot performed directly, because few of the

arising terms retain spherical symmetry and the advantages are lost. However, a new set of bubbles

for the resulting product function can be constructed to recasting the problem into integrating one

function over all space.

Likewise, the interaction energy between a charge density and a nuclear potential requires careful

treatment, due to the singularities at the nuclear positions. We have also developed that is able to

overcome this problem.

For interaction energies (both electron-electron and electron-nuclear), the accuracy obtained is

in the order of a mili-hartree for second-row elements including all electrons, using a moderate-sized

Cartesian grid. All these operations can be e�ciently parallelized, and certain crucial steps could

exploit the potential of GPGPUs.

References

[1] D Sundholm. Universal method for computation of electrostatic potentials. J. Chem. Phys.,122:194107, 2005.

[2] Jonas Jusélius and Dage Sundholm. Parallel implementation of a direct method for calculatingelectrostatic potentials. J. Chem. Phys., 126:094101, 2007.

[3] S. A. Losilla, D. Sundholm, and J. Juselius. The direct approach to gravitation and electrostaticsmethod for periodic systems. The Journal of Chemical Physics, 132(2):024102, 2010.

ESCMQC11 - Posters

P14

SCC-DFTB Study of Chrysotile Nanotube

M. P. Lourenço1, C. de Oliveira1, A. F. Oliveira3, L. Guimarães2, H. A. Duarte1

1Universidade Federal de Minas Gerais, Campus Pampulha, MG, Brasil 2 Universidade Federal de São João Del Rei, Campus Dom Bosco, MG, Brasil

3 Physikalische Chemie, Technische Universität Dresden, Mommsenstr, Dresden, Germany

Lizardite and chrysotile are the most abundant minerals of the serpentine group and share the same chemical formula Mg3Si2(OH)2. Lizardite has a flat-layered structure and chrysotile, the less abundant, occurs as cylindrically or spirally wrapped nanotubes (Fig.1)[1]. Recents studies indicate that chrysotile could be used as support for the immobilization of metalloporphyrins as well as adsorbent of ions and molecules[2]. Chrysotile has been the target for designing advanced materials with enhanced properties. In this work the self consistent charge – Density Functional Tight Binding (SCC-DFTB) method was used to study stability, electronic and mechanical properties of chrysotile. The Slater-Koster parameters for MgX (X = Mg, Si, O, H) have been calculated and the SCC-DFTB calculations compared with respect to the DFT calculations. The bond lengths and angles are in good agreement with DFT results, with an error around 0.05Å and 3 degrees, respectively. Chrysotile nanotubes with different quiralities and sizes have been calculated and their stability compared with respect to the lizardite. The SCC-DFTB calculations were performed using the deMon-nano and DFTB+ codes. Keywords: Clay Mineral, DFT, SCC-DFTB, electronic and mechanical properties.

a)

b) c)

Figure 1. Structures of lizardite (2D) (a), chrysotile (2D) (b) and (3D) (c). Work supported by INCT-Mineral Resource, Water and Biodiversity – ACQUA, CNPq, FAPEMIG. [1] D. A. Philipe, Y. Yves, D. Raffaella, D. Roberto, J. Chem. Phys. 131, 204701 (2009). [2] S. Nakagaki, F. Wypych, J. Coll. Int. Sci., 315, 142 (2007). [3] A. F. Oliveira, G. Seitfert, T. Heine, H. A. Duarte, J. Braz. Chem. Soc. 20, 1193 (2009). [email protected], Universidade Federal de Minas Gerais, Campus Pampulha, MG, Brasil

ESCMQC11 - Posters

P15

mailto:[email protected]

CALCULATION OF SPIN-ORBIT SPLITTINGS IN OPEN-SHELLSYSTEMS VIA MULTIREFERENCE COUPLED-CLUSTER THEORY

Leonie Anna Muck and Jurgen Gauss



The treatment of spin-orbit coupling in degenerate open-shell systems (e. g.Π -statesin linear molecules) requires a multideterminantal description. We adapted two variantsof multireference coupled-cluster (MRCC) theory for the computation of spin-orbit split-tings, namely state-universal MRCC and the state-specific Mukherjee’s MRCC,[1] whichare both based on the Jeziorski-Monkhorst ansatz.Spin-orbit interactions are treated via degenerate perturbation theory, which means thatspin-orbit splittings are computed as a first derivative of the MRCC energy. The La-grangian technique is applied for the derivation of analytical gradient expressions to beused for the spin-orbit splittings.[2] The implementation in the quantum-chemical pro-gram package CFOUR [3] is based on a density-matrix formulation of gradient theory. Asspin-orbit operator we use an effective one-electron operator derived from the full operatorin the Breit-Pauli formulation. The mean-field approach employed here was suggested byHeß and Marian [4] and first implemented by Berning et al.[5]Implementing this scheme, the reliable computation of spin-orbit splittings becomes acces-sible for molecules with degenerate open-shell states. The treatment of spin-orbit effectsis indispensable for the high-accuracy calculation of spectra and thermochemical energies.We plan on connecting the implementation with scalar-relativistic calculations (e. g. di-rect perturbation theory [6] and the spin-free Dirac-Coulomb approach), which will leadto a thorough treatment of relativistic effects.Furthermore, the treatment of spin-orbit coupling could shed light on theoretical problemsin MRCC theory. There is the concern that in state-specific MRCC theory the referencedeterminants might not be sufficiently coupled. Due to the symmetry properties of thespin-orbit operator, spin-orbit splittings can be interpreted as a direct measure for thecoupling of the reference determinants. The comparison of spin-orbit splittings obtainedfrom various Jeziorski-Monkhorst based MRCC methods could be a further piece in thepuzzle of finding the ultimate solution to MRCC theory.

[1] U. S. Mahapatra, B. Datta and D. Mukherjee, Mol. Phys. 94 (1998) 157-171.

[2] E. Prochnow, F. A. Evangelista et al, J. Chem. Phys. 131 (2009) 064109/1-12.

[3] see www.cfour.de

[4] B. Heß, C. M. Marian et al, Chem. Phys. Lett. 251, 365-371 (1996).

[5] A. Berning, M. Schweizer et al, Mol. Phys. 98 (2000), 1823-1833

[6] W. Kutzelnigg, Relativistic Electronic Structure Theory: Fundamentals, Elsevier Amsterdam

2002, Chap. 12, Pt. I, p. 664

ESCMQC11 - Posters

P16

A theoretical study on hydrogen transport mechanism in SrTiO3 perovskite

Taku Onishi1-2, Trygve Helgaker3

1Department of Chemistry for Materials, Graduate School of Engineering, Mie University, Japan

2The Center of Ultimate Technology on nano-Electronics, Mie University, Japan

3The Centre for Theoretical and Computational Chemistry (CTCC), Department of Chemistry,

University of Oslo, Norway


Abstract

Proton-conductive materials have recently attracted much interest, driven by the search for efficient

protonic electrolytes in solid oxide fuel cells (SOFCs). Hybrid-DFT calculations have been

performed to clarify the hydrogen transport mechanism in SrTiO3 perovskite. From a

molecular-orbital analysis, we discuss the changes in chemical bonding involving the conductive

hydrogen atom, as well as proton conduction paths. In addition, we consider nitrogen doping at the

oxygen site. It is concluded that doped nitrogen exists as the part of NH2- ion, enhancing proton

conductivity.

References

[1]T. Onishi, Int. J. Quant. Chem. 109, 3659, 2009.

[2]T. Onishi, Int. J. Quant. Chem. 110, 2912, 2010.

[3]T. Onishi and T. Helgaker, Int. J. Quant. Chem., submitted.

ESCMQC11 - Posters

P17

Chiralooptical properties of hydrogen bond-forming species in aqueous solution

Magdalena Pecul1,2, Maciej Kamiński1, Anna Rybicka1, Andrzej Kudelski1

1 Faculty of Chemistry, University of Warsaw, Pasteura 1, 02-093 Warszawa, Poland. 2 Centre for Theoretical and Computational Chemistry, Department of Chemistry, University of Tromsø, N-9037 Tromsø, Norway Interaction of chiral molecules with time-dependent electromagnetic field is a fascinating common field of spectroscopy and structural chemistry. Measurements of optical rotation (OR), electronic circular dichroism (CD), vibrational circular dichroism (VCD) and Raman optical activity (ROA) provide valuable information on the molecular conformation and chemical environment, which is a consequence of particular sensitivity of chiralooptical properties to electron cloud deformation. However, it also means that chiralooptical properties exhibit also unusually large solvent effects, and, since the chiralooptical spectra are usually measured in solution, it is essential to account for them in quantum chemical calculations. In this work, CD, VCD and ROA spectra have been calculated for aqueous solution of lactamide [1,2], β-amino acid phenylisoserine [3] and α-amino acid cysteine [4]. The influence of aqueous solution have been modeled by means of polarizable continous model and using classical molecular dynamics. It has been found that PCM is quite a cost effective model (even for hydrogen bond-forming species), while obtaining meaningful results from MD simulations requires very time-consuming calculations. VCD and ROA spectra of cysteine have been analysed with respect to the amount of conformational information derived from them. The spectra obtained from quantum chemical calculations have been compared with experimental VCD and ROA spectra measured at the Faculty of Chemistry, University of Warsaw. The experimental spectra have been simulated by means of linear combination of the spectra obtained for individual conformers, and conformational ratios have been derived [4]. References [1] K. H. Hopmann, K. Ruud, M. Pecul, A. Kudelski, M. Dracinsky, P. Bour, J. Phys. Chem. B, 2011, 115, 4128. [2] A. Rybicka, M. Pecul, in preparation. [3] M. Pecul, J. Rode, J. Dobrowolski, J. Sadlej, in preparation. [4] M. Kamiński, A. Kudelski, M. Pecul, in preparation. Email corresponding author: [email protected]

ESCMQC11 - Posters

P18

Xx

Stability of Clusters Containing Water, Pyridine and Ammonia

K. Ruusuvuori, T. Kurtén, M.J. McGrath, I.K. Ortega, H. Vehkamäki and M. Kulmala

Department of Physics, P.O. Box 64, FI-00014, University of Helsinki, Finland Even though the majority of atmospheric nucleation is believed to happen via neutral pathways [1]-[2], ion-induced nucleation may play some part, especially in regions where air ion or ion cluster concentrations are relatively high. There are several molecular ion species in the atmosphere, but Schulte and Arnold [3] have identified protonated pyridine as the most abundant molecular ion in the middle troposphere over Europe. Several atmospheric reaction channels have been proposed which could lead to large positive cluster ions containing eg. water, pyridine and ammonia [4]. Thus, understanding the properties of nitrogen containing organic molecules is important and with the help of quantum chemical calculations, we can gain useful insight on the details of ion-induced nucleation. Our objective is to study H+(NH3)1(C5H5N)1(H2O)n clusters with n=1-5, and see how the stability of the clusters behaves as a function of the amount of water molecules in the cluster. We have started the study of the structure of clusters containing (protonated) pyridine, ammonia and 1-5 water molecules. Optimized geometries for the single pyridine ion, ammonia and water molecules were obtained with Gaussian 03 [5] using density functional theory at the B3LYP/3-21G level. These geometries were used as “building blocks” for generating cluster geometries. Cluster geometries were generated randomly within the limits of cluster definitions (i.e. the generated configurations were always true clusters, according to the Stillinger criterion) and checked for uniqueness. Energies for the generated cluster configurations were calculated with CP2K [6] using the density functional based tight binding (DFTB) method. For each case of H+(NH3)1(C5H5N)1(H2O)n, 10 000 random geometries were generated, out of which 50 lowest energy geometries were selected for each H+(NH3)1(C5H5N)1(H2O)n. These geometries were then optimized with CP2K using the DFTB method. The next step is to study these optimized geometries and select the most promising ones (eg. the ones with the most hydrogen bonds) for geometry optimization and energy calculations using higher level methods. [1]Kulmala, M., Riipinen, I., Sipilä, M., Manninen, H.E., Petäjä, T., Junninen, H., Dal Maso, M., Mordas, G., Mirme, A., Vana, M., Hirsikko, A., Laakso, L., Harrison, R.M., Hanson, I., Leung, C., Lehtinen, K.E.J. and Kerminen, V.-M., Science, 318, 89-92 (2007) [2]Mirme, S., Mirme, A., Minikin, A., Petzold, A., Hõrrak, U., Kerminen, V.-M. and Kulmala, M., Atmos. Chem. Phys., 10, 437–451 (2010) [3]Schulte, P. and Arnold, F., Geophys. Res. Lett., 17, 1077–1080 (1990) [4]Beig, G. and Brasseur, G.P., J. Geophys. Res., 105, 22671–22684 (2000) [5]Frisch, M.J. et al. (2004) Gaussian 03, Revision E.01, Gaussian, Inc., Wallingford CT [6]http://cp2k.berlios.de/

ESCMQC11 - Posters

P19

RELATIVISTIC CORRECTIONS VIASIXTH-ORDER DIRECT PERTURBATION THEORY

Werner Schwalbach, Stella Stopkowicz, Lan Cheng, and Jurgen Gauss



The sixth-order relativistic correction (with respect to c−1) to the electronic energy is de-rived using direct perturbation theory (DPT) [1,2]. The required expressions and implementa-tion are based on the formulation of DPT in terms of derivative theory [3], thus enabling thecalculation of the DPT6 energy correction as a third derivative of the energy with respect toλ = c−2.

The convergence of the DPT expansion for energy as well as of the relativistic correctionsfor dipole moments and electric field gradients is analyzed via calculations for the hydrogenhalides HX with X = F, Cl, Br, I and At at the Hartree-Fock level of theory.

[1] A. Rutkowski, J. Phys. B: At. Mol. Phys. 19 (1986) 149.[2] W. Kutzelnigg, Z. Phys. D 11 (1989) 15.[3] S. Stopkowicz, J. Gauss, J. Chem. Phys., 13488 (2011) 064114.

ESCMQC11 - Posters

P20

Parallelization of quantum mechanics/molecular mechanics forhigher-order response functions

A. H. Steindala), J. M. Olsen(b), K. Ruuda), L. Frediania) and J. Kongstedb)

a) Centre for Theoretical and Computational Chemistry, Department of Chemistry,University of Tromsø, NO-9037 Tromsø, Norway

b) Department of Physics and Chemistry, University of Southern Denmark, DK-5230Odense M, Denmark

It is well known that the main limitation to quantum chemical calculations is posed bythe lack of computational resources. In many cases only a fraction of the system is cru-cial, whereas the remainder is only important for its environmental effects on the centralpart. In these cases we may use a so-called “focused model”, where the environmentaleffects are modeled by molecular mechanics (MM) whereas the quantum mechanic (QM)portion contains only that part of the system requiring a more accurate description of theelectronic structure. Today’s quantum chemistry programs also rely on well-parallelizedcodes to run efficient on modern supercomputers.

We will present a parallel implementation of the quantum mechanics/molecular me-chanics (QM/MM) for Hartree-Fock and density functional theory calculations of ener-gies and linear, quadratic, and cubic response functions. The contributions to the QMsystem due to the MM system have been implemented using a master-slave approach. Avery good scaling of the code has been achieved, as shown by calculations on a small (awater molecule in a bulk of water molecules) and a medium sized system (green fluores-cence protein).

ESCMQC11 - Posters

P21

Relativistic Corrections via Fourth-Order Direct Perturbation Theory at the MP2 level

Stella Stopkowiczand Jurgen GaussInstitut fur Physikalische Chemie, Universitat Mainz, D-55099 Mainz, Germany

When aiming for high-accuracy in quantum-chemical calculations, relativistic effects need to

be considered already when dealing with systems containing light elements. For this purpose,

perturbative techniques such as direct perturbation theory (DPT) [1] present an attractive option.

While DPT in lowest-order, i.e. DPT2, already has evolved to a standard tool for the calculation

of relativistic corrections to energies, higher-order treatments are so far scarce. For this reason, we

extend in this contribution the DPT treatment to the next higher order (DPT4). To facilitate the

implementation, the theory is developed using analytical derivative theory within a non-relativistic

framework. In this general formulation, wave function and operators are expanded with respect

to the relativistic perturbationλrel = c−2, with c being the speed of light. The DPT4 correction is

then given as a second derivative of the energy with respect toλrel = c−2. Scalar-relativistic as well

as spin-orbit contributions can be separated using Dirac’s identity and calculated using the usual

one-component formulations. To investigate the characteristics of relativistic contributions at the

correlated level MP2 results are presented with spin-orbit contributions neglected in the correlation

treatment.

[1] W. Kutzelnigg,Relativistic Electronic Structure Theory. Part I. Fundamentals, (Elsevier, Am-

sterdam, 2002), p. 664, chapter 12

ESCMQC11 - Posters

P22

Efficient construction of Fock matrices using anumerical integration scheme

Mooses Mehine, Sergio Losilla Fernadez, Dage Sundholm

Department of Chemistry, University of Helsinki

P.O. Box 55 (A.I. Virtanens plats 1), FIN-00014 Helsinki, Finland

An efficient method to numerically calculate the Fock matrix is presented. The

Coulomb operator is re-expressed as an integral using the well-known identity

1r12

= 2√π

∫∞0e−t

2r212dt and then made discrete for a numerical calculation. This

separates the x, y and z dependencies transforming the two-electron integral to

〈ij|kl〉 =∑

pwpXijkl(tp)Yijkl(tp)Zijkl(tp). The Fock-matrix contributions for

each p-value can be calculated independently and integrated numerically as

Fij =∑

pwpFpij, where F p

ij =∑

kl〈ij|tp|kl〉ρkl. The two-dimensional overlap in-

tegrals can easily be computed directly when needed. Thus, no two-electron inte-

grals have to be precomputed and stored. The aim is not to calculate analytically

exact results, which are analogously gained through the Rys quadrature, but Fock

matrices of enough accuracy for electronic structure calculations. Preliminary cal-

culations indicate that it is possible to achieve an accuracy of 10−12 hartree and

better for the two-electron integral using the numerical approach. The calculations

also suggest that a division of integrals into different classes based on the values

of the GTO exponents and the values of the distances between the GTO centers

might be necessary.

ESCMQC11 - Posters

P23

Electron correlation in strong magnetic fields

Kai Karvann Lange1, Erik I. Tellgren1, Mark R. Hoffmann2, and Trygve Helgaker1

1Centre for Theoretical and Computational Chemistry,

University of Oslo, P.O.Box 1033 Blindern, N-0315 Oslo, Norway and

2Chemistry Department, University of North Dakota,

Grand Forks, North Dakota 58202, USA

(Dated: June 7, 2011)

Abstract

Though London orbitals are widespread in perturbative calculations of various response proper-

ties, the London program package is unique in being a quantum-chemical code for non-perturbative

London-orbital calculations on molecular systems in strong magnetic fields. Here we report on the

development of a CAS-CI (FCI) and CAS-SCF module within this program package and show

some preliminary applications.

1

ESCMQC11 - Posters

P24

A systematic approach to the calculation of Rydberg states

Clemens Woywod

Theoretical Chemistry (CTCC), Department of Chemistry, University of Tromsø, N-9037 Tromsø,Norway

The description of Rydberg states by the complete active space self-consistent field (CASSCF) elec-tronic structure method is known to be a tricky business. In particular two problems are frequentlyencountered: (1) The simultaneous presence of valence and Rydberg excited states in the same energyregion can potentially lead to artificial valence-Rydberg mixing in the electronic wave functions. (2)Rydberg states have a tendency to be difficult to converge. A successful wave function optimizationrequires a good starting guess and a well defined active orbital space. On the energy surface spannedby the configuration interaction (CI) and molecular orbital (MO) parameters, a Rydberg state oftencorresponds to a pronounced, but highly localized minimum. Therefore, in many cases the Rydbergorbitals will be undesirably eliminated from the active space during the CASSCF iterations. Onlyif the initial wave function represents a sufficiently good approximation of the target state and if thecorrect Rydberg functions are included in the active space will the designated solution be obtained.The questions are now how to provide an accurate starting wave function and how to derive the infor-mation for a selection of the active orbitals. A newly developed systematic approach for a consistentdescription of both valence and Rydberg excited states within the CASSCF electronic structure modelis presented. By employing multiconfigurational second- and third-order perturbation theory methodsbased on CASSCF reference wave functions, the procedure is verified by comparison with spectro-scopic results for the example molecules pyrazine [1], pyridine and butadiene. Particular attention ispaid the to the relevance of valence excitations for the description of Rydberg states.

References[1] Woywod, C. and Papp, A. and Halasz, G. J. and Vibok, A. Theor. Chem. Acc. 125, 521 (2010).

ESCMQC11 - Posters

P25

Participants

Participants at ESCMQC '11

Ludwik Adamowicz

[email protected]

Department of chemistry andbiochemistry, University of Arizona

Ali Alavi

[email protected]

University of Cambridge, Department ofChemistry

Michiko Atsumi

[email protected]

Uppsala University

Paul Ayers

[email protected]

McMaster University, Department ofChemistry & Chemical Biology

Robert Berger

[email protected]

TU Darmstadt

Alessandro Biancardi

[email protected]

Università di Pisa, Dipartimento diChimica e Chimica Industriale

Alex Borgoo

[email protected]

Durham University

Yannick Carissan

[email protected]

Université Paul Cézanne

Benoît Champagne

[email protected]

FUNDP, UCPTS - LCT

Lan Cheng

[email protected]

Physical chemistry department,University of Mainz

Sonia Coriani

[email protected]

Kemisk Institut, Aarhus University

Daniel Crawford

United [email protected]

Virginia Tech

Ulf Ekström

[email protected]

CTCC, Department of chemistry,University of Oslo

Francesco Evangelista

[email protected]

Institut für Physikalische Chemie,Johannes Gutenberg-Universität Mainz

Heike Fliegl

[email protected]

University of Helsinki, Department ofChemistry, Laboratory for Instruction inSwedish

Luca Frediani

[email protected]

CTCC, University of Tromsø

Jürgen Gauss

[email protected]

Institut für Physikalische Chemie,Universität Mainz

Paola Gori-Giorgi

[email protected]

Vrije Universiteit, Amsterdam,Department of Theoretical Chemistry

Andreas Görling

[email protected]

University of Erlangen Nuremberg

Christof Haettig

[email protected]

Ruhr-University Bochum, TheoreticalChemistry Department

Matthias Hanauer

[email protected]

Institute for Physical Chemistry,University of Mainz

Michael Hanrath

[email protected]

Institute for Theoretical Chemistry,University of Cologne

Trygve Helgaker

[email protected]

CTCC, University of Oslo

So Hirata

[email protected]

University of Illinois at Urbana-Champaign


Ida-Marie Høyvik

[email protected]

Aarhus University, Department ofChemistry

Christoph Jacob

[email protected]

Karlsruhe Institute of Technology (KIT)

Thomas-Christian Jagau

[email protected]

Institut für Physikalische Chemie,Johannes Gutenberg-Universität Mainz

Branislav Jansik

[email protected]

Theoretical chemistry, AarhusUniversity

Michal Jaszunski

[email protected]

Institute of Organic Chemistry, PolishAcademy of Sciences

Stig Rune Jensen

[email protected]

University of Tromsø, CTCC

Hans Jørgen Aagaard Jensen

[email protected]

Department of Physics and Chemistry,University of Southern Denmark

Dan Jonsson

[email protected]


Jonas Juselius

[email protected]

University of Tromsø, HPC/IT-department

Janus Juul Eriksen

[email protected]

Center for Computational MolecularSciences, Department of Chemistry, H.C. Ørsted Institute, University of

Mihály Kállay

[email protected]

Department of Physical Chemistry andMaterials Science, Budapest Universityof Technology and Economics

Magorzata Kauch

[email protected]

University of Warsaw, Department ofChemistry

Hanna Kjær

[email protected]

Department of Chemistry, University ofCopenhagen

Thomas Kjærgaard

[email protected]


Stefan Knecht

[email protected]

Institut for Fysik og Kemi, SyddanskUniversitet, Odense

Peter Knowles

[email protected]

Cardiff University

Jacob Kongsted

[email protected]

University of Southern Denmark

Tatiana Korona

[email protected]

University of Warsaw, Faculty ofChemistry

Kasper Kristensen

[email protected]

Aarhus University

Yuki Kurashige

[email protected]

Institute for Molecular Science

Simen Kvaal

[email protected]

Centre of Mathematics for Applications,University of Oslo

Andreas Köhn

[email protected]

Institut fuer Physikalische Chemie,Johannes Gutenberg-UniversitaetMainz

Kai Kaarvann Lange

[email protected]


Jussi Lehtola

[email protected]

University of Helsinki


Roland Lindh

[email protected]

Dept Physical and Analytic Chemistry,Quantum Chemistry, UppsalaUniversity

Sergio Losilla

[email protected]

University of Helsinki, Department ofChemistry

Maicon Lourenço

[email protected]

Federal University of Minas Gerais,Minas Gerais State

Fred Manby

[email protected]

University of Bristol

Benedetta Mennucci

[email protected]

Dept. Chemistry, University of Pisa

Patrick Merlot

[email protected]

CTCC. University of Oslo

Leonie Anna Mück

[email protected]

Johannes Gutenberg-Universität,Institut für Physikalische Chemie

Carsten Müller

[email protected]

Freie Universität Berlin

Frank Neese

[email protected]

University of Bonn

Christian Ochsenfeld

[email protected]

University of Munich (LMU), D-81377Munich

Jógvan Magnus Olsen

[email protected]

University of Southern Denmark,Department of Physics and Chemistry

Taku Onishi

[email protected]

Mie University, Department ofChemistry for Materials

Magdalena Pecul-Kudelska

[email protected]

University of Warsaw, Faculty ofChemistry

Thomas Bondo Pedersen

[email protected]

CTCC, Department of Chemistry,University of Oslo

Ravindran Ponniah

[email protected]

Department of Chemistry, University ofOslo

Cristina Puzzarini

[email protected]

Dipartimento di Chimica G. Ciamician,University of Bologna

Simen Sommerfelt Reine

[email protected]


Johannes Rekkedal

[email protected]


Michal Repisky

[email protected]


Antonio Rizzo

[email protected]

IPCF/CNR

Kenneth Ruud

[email protected]

University of Tromsø, Department ofChemistry, CTCC

Kai Ruusuvuori

[email protected]

University of Helsinki

Vladimir Rybkin

[email protected]


Trond Saue

[email protected]

Université de Toulouse/CNRS,Laboratoire de Chimie et PhysiqueQuantiques


Stephan P. A. Sauer

[email protected]

Department of Chemistry, University ofCopenhagen

Werner Schwalbach

[email protected]

Johannes Gutenberg-UniversitätMainz, Institut für PhysikalischeChemie

Toru Shiozaki

[email protected]

Universitaet Stuttgart

Arnfinn Hykkerud Steindal

[email protected]


Stella Stopkowicz

[email protected]

Institut für Physikalische Chemie,Johannes Gutenberg-UniversitätMainz, Jakob-Welder-Weg 11, D-55128

Alexandrina Stoyanova

[email protected]

Laboratoire de Chimie Quantique,Institut de Chimie, CNRS/Université deStrasbourg

Dage Sundholm

[email protected]

Department of Chemistry, University ofHelsinki

Andrew Teale

[email protected]

University of Oslo, CTCC

Erik Tellgren

[email protected]

CTCC, Department of Chemistry,University of Oslo

David Tew

[email protected]

Centre for computational chemistry,University of Bristol

David Tozer

[email protected]

Durham University

Denis Usvyat

[email protected]

Institute of Physical and TheoreticalChemistry, University of Regensburg

Edward Valeev

[email protected]

Virginia Tech

Joop van Lenthe

The [email protected]

Theoretical Chemistry Group, UtrechtUniversity

Joost VandeVondele

[email protected]

University of Zurich

Clemens Woywod

[email protected]

CTCC, Chemistry Department,University of Tromsø

Takeshi Yanai

[email protected]

Institute for Molecular Science

Documents

Please download program