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Title: Shadow energy functionals and potentials in Born–Oppenheimer molecular dynamics

Abstract

In Born–Oppenheimer molecular dynamics (BOMD) simulations based on the density functional theory (DFT), the potential energy and the interatomic forces are calculated from an electronic ground state density that is determined by an iterative self-consistent field optimization procedure, which, in practice, never is fully converged. The calculated energies and forces are, therefore, only approximate, which may lead to an unphysical energy drift and instabilities. Here, we discuss an alternative shadow BOMD approach that is based on backward error analysis. Instead of calculating approximate solutions for an underlying exact regular Born–Oppenheimer potential, we do the opposite. Instead, we calculate the exact electron density, energies, and forces, but for an underlying approximate shadow Born–Oppenheimer potential energy surface. In this way, the calculated forces are conservative with respect to the approximate shadow potential and generate accurate molecular trajectories with long-term energy stabilities. We show how such shadow Born–Oppenheimer potentials can be constructed at different levels of accuracy as a function of the integration time step, δt, from the constrained minimization of a sequence of systematically improvable, but approximate, shadow energy density functionals. For each energy functional, there is a corresponding ground state Born–Oppenheimer potential. These pairs of shadow energy functionals and potentials aremore » higher-level generalizations of the original “zeroth-level” shadow energy functionals and potentials used in extended Lagrangian BOMD [Niklasson, Eur. Phys. J. B 94, 164 (2021)]. The proposed shadow energy functionals and potentials are useful only within this extended dynamical framework, where also the electronic degrees of freedom are propagated as dynamical field variables together with the atomic positions and velocities. The theory is quite general and can be applied to MD simulations using approximate DFT, Hartree–Fock, or semi-empirical methods, as well as to coarse-grained flexible charge models.« less

Authors:
ORCiD logo [1];  [1]
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  1. Theoretical Division, Los Alamos National Laboratory, Los Alamos, New Mexico 87545, USA
Publication Date:
Sponsoring Org.:
USDOE
OSTI Identifier:
1970645
Grant/Contract Number:  
LANLE8AN
Resource Type:
Publisher's Accepted Manuscript
Journal Name:
Journal of Chemical Physics
Additional Journal Information:
Journal Name: Journal of Chemical Physics Journal Volume: 158 Journal Issue: 15; Journal ID: ISSN 0021-9606
Publisher:
American Institute of Physics
Country of Publication:
United States
Language:
English

Citation Formats

Niklasson, Anders M. N., and Negre, Christian F. A. Shadow energy functionals and potentials in Born–Oppenheimer molecular dynamics. United States: N. p., 2023. Web. doi:10.1063/5.0146431.
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Niklasson, Anders M. N., & Negre, Christian F. A. Shadow energy functionals and potentials in Born–Oppenheimer molecular dynamics. United States. https://doi.org/10.1063/5.0146431
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Niklasson, Anders M. N., and Negre, Christian F. A. Fri . "Shadow energy functionals and potentials in Born–Oppenheimer molecular dynamics". United States. https://doi.org/10.1063/5.0146431.
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@article{osti_1970645,
title = {Shadow energy functionals and potentials in Born–Oppenheimer molecular dynamics},
author = {Niklasson, Anders M. N. and Negre, Christian F. A.},
abstractNote = {In Born–Oppenheimer molecular dynamics (BOMD) simulations based on the density functional theory (DFT), the potential energy and the interatomic forces are calculated from an electronic ground state density that is determined by an iterative self-consistent field optimization procedure, which, in practice, never is fully converged. The calculated energies and forces are, therefore, only approximate, which may lead to an unphysical energy drift and instabilities. Here, we discuss an alternative shadow BOMD approach that is based on backward error analysis. Instead of calculating approximate solutions for an underlying exact regular Born–Oppenheimer potential, we do the opposite. Instead, we calculate the exact electron density, energies, and forces, but for an underlying approximate shadow Born–Oppenheimer potential energy surface. In this way, the calculated forces are conservative with respect to the approximate shadow potential and generate accurate molecular trajectories with long-term energy stabilities. We show how such shadow Born–Oppenheimer potentials can be constructed at different levels of accuracy as a function of the integration time step, δt, from the constrained minimization of a sequence of systematically improvable, but approximate, shadow energy density functionals. For each energy functional, there is a corresponding ground state Born–Oppenheimer potential. These pairs of shadow energy functionals and potentials are higher-level generalizations of the original “zeroth-level” shadow energy functionals and potentials used in extended Lagrangian BOMD [Niklasson, Eur. Phys. J. B 94, 164 (2021)]. The proposed shadow energy functionals and potentials are useful only within this extended dynamical framework, where also the electronic degrees of freedom are propagated as dynamical field variables together with the atomic positions and velocities. The theory is quite general and can be applied to MD simulations using approximate DFT, Hartree–Fock, or semi-empirical methods, as well as to coarse-grained flexible charge models.},
doi = {10.1063/5.0146431},
journal = {Journal of Chemical Physics},
number = 15,
volume = 158,
place = {United States},
year = {Fri Apr 21 00:00:00 EDT 2023},
month = {Fri Apr 21 00:00:00 EDT 2023}
}
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