Abstract
We analyze the time reversible Born-Oppenheimer molecular dynamics (TRBOMD) scheme, which preserves the time reversibility of the Born-Oppenheimer molecular dynamics even with non-convergent self-consistent field iteration. In the linear response regime, we derive the stability condition as well as the accuracy of TRBOMD for computing physical properties such as the phonon frequency obtained from the molecular dynamic simulation. We connect and compare TRBOMD with the Car-Parrinello molecular dynamics in terms of accuracy and stability. We further discuss the accuracy of TRBOMD beyond the linear response regime for non-equilibrium dynamics of nuclei. Our results are demonstrated through numerical experiments using a simplified one dimensional model for Kohn-Sham density functional theory.
Highlights
Ab initio molecular dynamics (AIMD) [1,2,3,4,5,6] has been greatly developed in the past few decades, so that nowadays, it is able to quantitatively predict the equilibrium and non-equilibrium properties for a vast range of systems
The recently developed time reversible Born-Oppenheimer molecular dynamics (TRBOMD) scheme provides a promising way for reducing the number of self-consistent field (SCF) iterations in molecular dynamics simulation
By introducing auxiliary dynamics to the initial guess of the SCF iteration, TRBOMD preserves the time-reversibility of the NVE dynamics, both at the continuous and at the discrete level, and exhibits improved long time stability over the Born-Oppenheimer molecular dynamics with the same accuracy
Summary
Ab initio molecular dynamics (AIMD) [1,2,3,4,5,6] has been greatly developed in the past few decades, so that nowadays, it is able to quantitatively predict the equilibrium and non-equilibrium properties for a vast range of systems. To reduce the cost of BOMD, in particular, the number of SCF iterations needed per MD time step, a new type of AIMD method, the time reversible Born-Oppenheimer molecular dynamics (TRBOMD). TRBOMD, alternative ideas based on time-reversible predictor-corrector methods [21] and Langevin dynamics [22,23] can relax the requirement on the accuracy of the force for AIMD simulation. We first focus on the linear response regime, i.e., we assume that each atom oscillates around their equilibrium position and the electron density stays around the “true” electron density Under such assumptions, we analyze the accuracy and stability of TRBOMD.
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