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Title: Extended Lagrangian Born–Oppenheimer molecular dynamics using a Krylov subspace approximation

Abstract

It is shown how the electronic equations of motion in extended Lagrangian Born–Oppenheimer molecular dynamics simulations can be integrated using low-rank approximations of the inverse Jacobian kernel. This kernel determines the metric tensor in the harmonic oscillator extension of the Lagrangian that drives the evolution of the electronic degrees of freedom. The proposed kernel approximation is derived from a pseudoinverse of a low-rank estimate of the Jacobian, which is expressed in terms of a generalized set of directional derivatives with directions that are given from a Krylov subspace approximation. The approach allows a tunable and adaptive approximation that can take advantage of efficient preconditioning techniques. The proposed kernel approximation for the integration of the electronic equations of motion makes it possible to apply extended Lagrangian first-principles molecular dynamics simulations to a broader range of problems, including reactive chemical systems with numerically sensitive and unsteady charge solutions. This can be achieved without requiring exact full calculations of the inverse Jacobian kernel in each time step or relying on iterative non-linear self-consistent field optimization of the electronic ground state prior to the force evaluations as in regular direct Born–Oppenheimer molecular dynamics. We note the low-rank approximation of the Jacobian is directly relatedmore » to Broyden’s class of quasi-Newton algorithms and Jacobian-free Newton–Krylov methods and provides a complementary formulation for the solution of nonlinear systems of equations.« less

Authors:
ORCiD logo [1]
  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Uppsala Univ. (Sweden)
Publication Date:
Research Org.:
Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
Sponsoring Org.:
USDOE Office of Science (SC), Basic Energy Sciences (BES); USDOE National Nuclear Security Administration (NNSA)
OSTI Identifier:
1630868
Alternate Identifier(s):
OSTI ID: 1604109
Report Number(s):
LA-UR-19-31455
Journal ID: ISSN 0021-9606
Grant/Contract Number:  
89233218CNA000001; FWP LANLE8AN
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Volume: 152; Journal Issue: 10; Conference: 2019 MRS Fall Meeting & Exhibit, Boston, MA (United States), 1-6 Dec 2019; Journal ID: ISSN 0021-9606
Publisher:
American Institute of Physics (AIP)
Country of Publication:
United States
Language:
English
Subject:
97 MATHEMATICS AND COMPUTING; 71 CLASSICAL AND QUANTUM MECHANICS, GENERAL PHYSICS; Mathematics; Molecular dynamics; Krylov subspace approximation; Integration methods; Quantum based molecular dynamics; Non-linear systems of equations; Nonlinear systems; Numerical linear algebra; Optimization problems; Newton-Krylov method; Self consistent field methods; Born-Oppenheimer molecular dynamics; Density-matrix

Citation Formats

Niklasson, Anders Mauritz N. Extended Lagrangian Born–Oppenheimer molecular dynamics using a Krylov subspace approximation. United States: N. p., 2020. Web. https://doi.org/10.1063/1.5143270.
Niklasson, Anders Mauritz N. Extended Lagrangian Born–Oppenheimer molecular dynamics using a Krylov subspace approximation. United States. https://doi.org/10.1063/1.5143270
Niklasson, Anders Mauritz N. Wed . "Extended Lagrangian Born–Oppenheimer molecular dynamics using a Krylov subspace approximation". United States. https://doi.org/10.1063/1.5143270. https://www.osti.gov/servlets/purl/1630868.
@article{osti_1630868,
title = {Extended Lagrangian Born–Oppenheimer molecular dynamics using a Krylov subspace approximation},
author = {Niklasson, Anders Mauritz N.},
abstractNote = {It is shown how the electronic equations of motion in extended Lagrangian Born–Oppenheimer molecular dynamics simulations can be integrated using low-rank approximations of the inverse Jacobian kernel. This kernel determines the metric tensor in the harmonic oscillator extension of the Lagrangian that drives the evolution of the electronic degrees of freedom. The proposed kernel approximation is derived from a pseudoinverse of a low-rank estimate of the Jacobian, which is expressed in terms of a generalized set of directional derivatives with directions that are given from a Krylov subspace approximation. The approach allows a tunable and adaptive approximation that can take advantage of efficient preconditioning techniques. The proposed kernel approximation for the integration of the electronic equations of motion makes it possible to apply extended Lagrangian first-principles molecular dynamics simulations to a broader range of problems, including reactive chemical systems with numerically sensitive and unsteady charge solutions. This can be achieved without requiring exact full calculations of the inverse Jacobian kernel in each time step or relying on iterative non-linear self-consistent field optimization of the electronic ground state prior to the force evaluations as in regular direct Born–Oppenheimer molecular dynamics. We note the low-rank approximation of the Jacobian is directly related to Broyden’s class of quasi-Newton algorithms and Jacobian-free Newton–Krylov methods and provides a complementary formulation for the solution of nonlinear systems of equations.},
doi = {10.1063/1.5143270},
journal = {Journal of Chemical Physics},
number = 10,
volume = 152,
place = {United States},
year = {2020},
month = {3}
}

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