DFTFIT: Potential Generation for Molecular Dynamics Calculations
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DFTFIT 1 Christopher Ostrouchov University of Tennessee Material Science and Engineering Potential Generation for Molecular Dynamics Calculations HTCMC Toronto June 30 th 2016 2:20-2:40
DFTFIT: Potential Generation for Molecular Dynamics Calculations
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 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 Need for Multi-scale Simulations
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
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 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 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 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 Generalized Force Matching Fitting additionally to
forces and stresses allows us to match local properties of the
material
11. 11 Force Matching Success oxides simple metals alloys
liquids *found in Google Scholar search for citations of Ercolessi
force matching paper
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 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 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 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 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 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 MgO Potential Buckingham Potential We have 10 free
variables For Example: + Mg/O Charge Coloumbic Interaction Ignoring
Coloumbic Term
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 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!
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 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 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 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