1. 1. DFTFIT 1 Christopher Ostrouchov University of Tennessee Material Science and Engineering Potential Generation for Molecular Dynamics Calculations HTCMC Toronto June 30th 2016 2:20-2:40
2. 2. 2 About Me I Python and develop computational tools for Material Science costrouc I strongly believe in reproducible research and the use of open databases for results pyqe python interface to Quantum Espresso lammps-python high performance interactive parallel LAMMPS sessions dftfit framework for potential development and quantification
3. 3. 3 Need for Multi-scale Simulations
4. 4. 4 Classical Molecular Dynamics But how do we get the potential? *more complex potentials include many-body terms Given potential Calculate forces Apply Newton's second law
5. 5. 5 Motivation Buckingham potential + 3-body angular potential
6. 6. 6 Empirical Formulation of Potentials Fitting Experimental Data cohesive energy lattice constant bulk modulus sublimation energy vacancy formation energies elastic constants DFT could only simulate small atom clusters prior to the mid-90s An MD simulation for each set of potential parameters is expensive Limited to specific materials where experimental data is present
7. 7. 7 Empirical Formulation of Potentials a major problem in deriving such potentials for oxides is the lack of experimental data Gets migration energies within 0.1-0.3 eV for elements! Ionic Metallic We are only fitting to energies!
8. 8. 8 Ab Initio Potential Generation With the increase in compute capabilities we can easily compute the energies, forces, and stresses of configurations of atoms from DFT calculations.
9. 9. 9 Force Matching Method 1996 Force Matching Algorithm Ercolessi, Furio, and James B. Adams. "Interatomic potentials from first-principles calculations: the force- matching method." EPL (Europhysics Letters) 26.8 (1994): 583. this first study shows that the force-matching method is a very effective tool to obtain realistic classical potentials with a high degree of transferability
10. 10. 10 Generalized Force Matching Fitting additionally to forces and stresses allows us to match local properties of the material
11. 11. 11 Force Matching Success oxides simple metals alloys liquids *found in Google Scholar search for citations of Ercolessi force matching paper
12. 12. 12 A Need For Software? Currently only one open-source package available for Force-Matching Limited set of potentials. Does not interface with DFT and MD software. Complicated to use (requires recompiling code for each run) DFTFIT Can use any potential found in integrated MD packages (LAMMPS) Directly uses DFT output from integrated DFT packages (QE, VASP) Provides easy ways for users to quantify performance of potentials Implemented in Python Will have a GUI for users
13. 13. 13 DFTFIT Optimization Function number of system configurations number of atoms in each configuration tensor with 3D dimensions [x, y, z] results from molecular dynamics simulation results from DFT simulation MD parameters weights to assign respectively for force, stress, energy force, stress, and energy respectively note: relative energies minimize
14. 14. 14 Software Implementation Molecular Dynamics Package Calculate Forces, Stresses, Energy for given parameters Optimization algorithm updates parameters to minimize Available on Github! github.com/costrouc/dftfit Evaluate Choose initial parameters (preferably close to solution) START Optimization algorithm achieves convergence condition END Good luck with that! scipy.optimize or NLopt
15. 15. 15 Quantifying Fitness of Potential We must compare with experimental data and DFT to verify the quality of a potential Equilibrium Properties Lattice Constant Bulk Modulus Elastic Tensor Implemented Partially Implemented Additional properties can be easily added Non-Equilibrium Properties Defect Formation Energies Defect Migration Energies Melting Point Phonon Dispersion
16. 16. 16 Test System - MgO Simple cubic oxide (Rock Salt) Nuclear Applications Long term storage Used in Light Water Reactors B. P. Uberuaga, R. Smith, A. R. Cleave, G. Henkelman, R. W. Grimes, A. F. Voter, and K. E. Sickafus, Phys Rev. B 71, 2005, Dynamical simulations of radiation damage and defect mobility in MgO Mg - OMotivation Heavily studied in Simulation & Experiment
17. 17. 17 Generating MgO DFT Data MgO - (2 x 2 x 2) 9.26 per edge 64 atoms perturb atoms of relaxed cell 29 configurations x 64 atoms = 1856 forces 29 configurations = 29 stress tensors 29 configurations = 29 energies = 406 relative energies Mg, O 29 static calculations Simulations done with relax unitcell strain relaxed cell
18. 18. 18 MgO Potential Buckingham Potential We have 10 free variables For Example: + Mg/O Charge Coloumbic Interaction Ignoring Coloumbic Term
19. 19. 19 MgO Potentials in Literature Matsui (1989) (partial charges) Lewis and Catlow (1985) Ball and Grimes (2005) Ball and Grimes (2005) (partial charges) Available MgO Buckingham Potentials [1] Masanori Matsui, J. Chem. Phys. 91, 489 (1989), Molecular dynamics study of the structural and thermodynamic properties of MgO crystal with quantum correction [2] G. V. Lewis and C. R. A. Catlow, J. Phys. C: Solid State Phys. 18 1149, (1985), Potential models for ionic oxides [3] Graeme Henkelman, Blas P. Uberuaga, Duncan J. Harris, John H. Harding, and Neil L. Allan, Phys. Rev. B 72, 115437, 2005, MgO addimer diffusion on MgO(100): A comparison of ab initio and empirical models Can we improve upon on these potentials?
20. 20. 20 Potential Improvement a0 [A] B0 [GPa] Ev f [eV] Ev m [eV] C11 [GPa] C12 [GPa] C44 [GPa] DFT [VASP] 4.228 156.80 4.57* 2.38 308 100 153 Lewis Catlow 4.199 193.25 2.843* 1.72 333 113 130 Results 4.221 188.17 4.219* 1.81 300 114 120 Experiment 4.211 156-160 N/A 2.0-2.7 291 91 139 *Using conventional MD method for defect formation energy Overall improvement of the potential!
21. 21. 21 Difficulties Weighting parameters Optimization algorithm
22. 22. 22 Choosing Weighting Parameters the weights chosen determine how the objective function optimizes. my experience and references have shown Forces are most important Brommer, Peter, et al. "Classical interaction potentials for diverse materials from ab initio data: a review of potfit." Modelling and Simulation in Materials Science and Engineering 23.7 (2015): 074002.
23. 23. 23 Optimization Algorithm Global vs. Local Optimization Local BOBYQA [nlopt] Powell [scipy, nlopt] Global Simulated Annealing Genetic Algorithms Stochastic Gradient Decent global optimization will require parallelization
24. 24. 24 Conclusion Working code for creating MD potentials Interfaces with LAMMPS, Quantum Espresso, and VASP Tools for quantifying performance of potentials Shown DFTFIT can improve potentials for MgO Goal is to make potential generation easier
25. 25. 25 Thank You! References [1] B. P. Uberuaga, R. Smith, A. R. Cleave, G. Henkelman, R. W. Grimes, A. F. Voter, and K. E. Sickafus, Phys Rev. B 71, 2005, Dynamical simulations of radiation damage and defect mobility in MgO [2] Masanori Matsui, J. Chem. Phys. 91, 489 (1989), Molecular dynamics study of the structural and thermodynamic properties of MgO crystal with quantum correction [3] G. V. Lewis and C. R. A. Catlow, J. Phys. C: Solid State Phys. 18 1149, (1985), Potential models for ionic oxides [4] Graeme Henkelman, Blas P. Uberuaga, Duncan J. Harris, John H. Harding, and Neil L. Allan, Phys. Rev. B 72, 115437, 2005, MgO addimer diffusion on MgO(100): A comparison of ab initio and empirical models [5] - F. Ercolessi and J. B. Adams Europhys. Lett. 26 583, 1994 Interatomic Potentials from First-Principles Calculations: The Force-Matching Method [6] - Sergei Izvekov, Michele Parrinello, Christian J. Burnham and Gregory A. Voth, J. Chem. Phys. 120, 10896, 2004, Effective force fields for condensed phase systems from ab initio molecular dynamics simulation: A new method for force-matching [7] - Eric Jones, Travis Oliphant, Pearu Peterson and others., SciPy: Open source scientific tools for Python, www.scipy.org, 2001 MgO applications MgO potentials Force matching origin Beautiful force matching paper Least Square Solver Charge Density for LiNbO3 calculated with Quantum Espresso Acknowledgements UTK Compute Cluster Newton NERSC Super Computer Hopper NICS Super Computer Darter All images and figures created by Chris Ostrouchov