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Interatomic Poten-als in LAMMPS
Aidan P. Thompson Sandia Na1onal Laboratories
2nd LAMMPS Users Workshop August 2011, Albuquerque, New Mexico
Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company,for the United States Department of Energy’s National Nuclear Security Administration under contract DE-AC04-94AL85000."
Recently Added Poten-als • COMB poten-al (Genera-on 2)
Tzu-‐Ray Shan (U Florida), talk on Tues PM metal and semiconductors and their oxides
• Embedded ion method poten-als (EIM) Xiaowang Zhou (Sandia), ionic compounds combo of Li, Na, K, Rb, Cs, F, Cl, Br, and I
• C++ version of ReaxFF Me1n Aktulga (LBNL), talk on Wed PM can be faster than Fortran version by 2-‐3x
• Electron force field (eFF) Andres Jaramillo (Caltech), explicit electron dynamics in extreme condi1ons
Recently Added Poten-als • AIREBO poten-al bug fixes
Marcel Fallet & Steve Stuart (Clemson), one more bug-‐fix, upgrade is imminent
• Mishin ADP poten-al Chris Weinberger (Sandia) & Chandra Veer Singh (Cornell) angular-‐dependent EAM for metals and alloys
• Dreiding poten-al Tod Pascal (Caltech) hydrogen bonding for solvated bio-‐molecules
• New Peridynamics poten-als Mike Parks & Stuart Silling (Sandia), talk on Wed PM fracture at the meso and con1nuum scales
Upcoming Poten-als • Core/shell poten-al
Mike Chandross (Sandia), zero-‐order model for polariza1on, uranium and other nuclear fuel materials
• COMB poten-al (Genera-on 3) Tzu-‐Ray Shan (U Florida), more materials with polariza1on effects
• MGPT poten-al from John Moriarty & Jaime Marian (LLNL), tantalum and other transi1on metals
• BOP poten-al Xiaowang Zhou and Don Ward (Sandia) High-‐accuracy poten1al for semiconductors
LAMMPS Poten-al benchmarks
Compute Cost of Interatomic Poten-als Growing Exponen-ally
Drivers • Cycles are cheap • Availability of quantum calcula1ons (N < 100) • Qualita1ve accuracy no longer enough
h`p://lammps.sandia.gov/bench.html#poten1als
Compute cost of LAMMPS poten1als versus publica1on date
CHARMm
EAMStillinger-Weber
Tersoff
AIREBO
MEAM
ReaxFF
ReaxFF/C
eFF
COMB
EIM
GAP(Estim.)
1980 1990 2000 2010Year Published
10-6
10-5
10-4
10-3
10-2
Cost
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c/at
om-ti
mes
tep]
Challenges with Complex Poten-als
• How to Implement in LAMMPS? – Rewrite code from scratch (REBO) – Integrate exis1ng serial code (ReaxFF) – Access via general API (KIM)
• How to Validate LAMMPS Version? • How to Handle New Versions?
How to Fit Poten-als to New Materials?
• Automated fieng procedures exist for certain classes of materials and poten1als (EAM)
• More commonly, good fits can be obtained only by gurus (Baskes, van Duin)
• Combina1on of nonlinear op1miza1on and physical intui1on • Increasing interest in automated machine-‐learning
approaches – Splines – Gene1c programs – Mul1-‐objec1ve op1miza1on – Neural networks – Series expansions
GAP Approach for Interatomic Poten-als
Diamond: Force errors for GAP fi`ed to DFT. Adding higher-‐order GAP coefficients systema1cally increases accuracy Bartok et al., PRL 104 136403 (2010)
GAP: A systema-c, informa-cs approach • Based on QM and mathema1cs rather than
empiricism. • Local density around each atom expanded in
4D hyperspherical harmonics, analogous to Fourier series
• Atomic configura1ons described by bispectrum of lowest-‐order coefficients in series
• Preserves universal physical symmetries: invariance w.r.t. rota1on, transla1on, permuta1on
• Gaussian process (GP) regression used to interpolate energy of QM configura1ons
• 100-‐1000x more expensive than MEAM • Far cheaper than QM, linear scaling • Can trade performance and accuracy
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0 50 100 150 200 250 300Pzz
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0
1000
2000
3000
4000
5000
6000
Tem
per
ature
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]
Dr09 a-axisBa09i a-axisDFTDFT Melt LineEOS Benedict et al.
GAP Poten-al for Beryllium
Beryllium
Working with GAP developers, fieng directly to forces and energies from high-‐temperature DFT MD simula1ons of small systems (from Mike Desjarlais, 1640)
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GAP Forces versus DFT Forces for Liquid Be at 5,000 K, 250 atoms
0 50 100 150 200 250 300Pxx
[GPa]
0
1000
2000
3000
4000
5000
6000
Tem
per
atu
re [
K]
Dr09 a-axisBa09i a-axisDFTDFT Melt LineEOS Benedict et al.
• Ini1al fit to: − ambient HCP − high-‐pressure BCC and liquid
• Accurately reproduced that data • Problems with:
− ambient elas1c constants − high-‐pressure HCP
• Need to refit with more data
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