Development and quantification of interatomic potentials. Presented at HTCMC 9 in Toronto, Canada June 30th 2016. For further information on DFTFIT see https://github.com/costrouc/dftfit
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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
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
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 Å 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
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
