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Title: Density-Matrix Based Extended Lagrangian Born–Oppenheimer Molecular Dynamics

Abstract

Extended Lagrangian Born–Oppenheimer molecular dynamics [ Phys. Rev. Lett. 2008, 100, 123004] is presented for Hartree–Fock theory, where the extended electronic degrees of freedom are represented by a density matrix, including fractional occupation numbers at elevated electronic temperatures. In contrast to regular direct Born–Oppenheimer molecular dynamics simulations, no iterative self-consistent field optimization is required prior to the force evaluations. To sample regions of the potential energy landscape where the gap is small or vanishing, which leads to particular convergence problems in regular direct Born–Oppenheimer molecular dynamics simulations, an adaptive integration scheme for the extended electronic degrees of freedom is presented. The integration scheme is based on a tunable, low-rank approximation of a fourth-order kernel, K, that determines the metric tensor, T ≡ KTK, used in the extended harmonic oscillator of the Lagrangian that generates the dynamics of the electronic degrees of freedom. Here, the formulation and algorithms provide a general guide to implement extended Lagrangian Born–Oppenheimer molecular dynamics for quantum chemistry, density functional theory, and semiempirical methods using a density matrix formalism.

Authors:
ORCiD logo [1]
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  1. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)
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)
OSTI Identifier:
1843167
Report Number(s):
LA-UR-20-22452
Journal ID: ISSN 1549-9618
Grant/Contract Number:  
89233218CNA000001
Resource Type:
Accepted Manuscript
Journal Name:
Journal of Chemical Theory and Computation
Additional Journal Information:
Journal Volume: 16; Journal Issue: 6; Journal ID: ISSN 1549-9618
Publisher:
American Chemical Society
Country of Publication:
United States
Language:
English
Subject:
37 INORGANIC, ORGANIC, PHYSICAL, AND ANALYTICAL CHEMISTRY; Mathematics; Born-Oppenheimer molecular dynamics; First principles electronic structure theory; Hartree-Fock; Density matrix; Extended Lagrangian; Molecular dynamics; Algorithms; Optimization; Approximation; Electrical properties

Citation Formats

Niklasson, Anders Mauritz N. Density-Matrix Based Extended Lagrangian Born–Oppenheimer Molecular Dynamics. United States: N. p., 2020. Web. doi:10.1021/acs.jctc.0c00264.
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Niklasson, Anders Mauritz N. Density-Matrix Based Extended Lagrangian Born–Oppenheimer Molecular Dynamics. United States. https://doi.org/10.1021/acs.jctc.0c00264
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Niklasson, Anders Mauritz N. Mon . "Density-Matrix Based Extended Lagrangian Born–Oppenheimer Molecular Dynamics". United States. https://doi.org/10.1021/acs.jctc.0c00264. https://www.osti.gov/servlets/purl/1843167.
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@article{osti_1843167,
title = {Density-Matrix Based Extended Lagrangian Born–Oppenheimer Molecular Dynamics},
author = {Niklasson, Anders Mauritz N.},
abstractNote = {Extended Lagrangian Born–Oppenheimer molecular dynamics [ Phys. Rev. Lett. 2008, 100, 123004] is presented for Hartree–Fock theory, where the extended electronic degrees of freedom are represented by a density matrix, including fractional occupation numbers at elevated electronic temperatures. In contrast to regular direct Born–Oppenheimer molecular dynamics simulations, no iterative self-consistent field optimization is required prior to the force evaluations. To sample regions of the potential energy landscape where the gap is small or vanishing, which leads to particular convergence problems in regular direct Born–Oppenheimer molecular dynamics simulations, an adaptive integration scheme for the extended electronic degrees of freedom is presented. The integration scheme is based on a tunable, low-rank approximation of a fourth-order kernel, K, that determines the metric tensor, T ≡ KTK, used in the extended harmonic oscillator of the Lagrangian that generates the dynamics of the electronic degrees of freedom. Here, the formulation and algorithms provide a general guide to implement extended Lagrangian Born–Oppenheimer molecular dynamics for quantum chemistry, density functional theory, and semiempirical methods using a density matrix formalism.},
doi = {10.1021/acs.jctc.0c00264},
journal = {Journal of Chemical Theory and Computation},
number = 6,
volume = 16,
place = {United States},
year = {Mon May 04 00:00:00 EDT 2020},
month = {Mon May 04 00:00:00 EDT 2020}
}
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