Computational error estimates for Born-Oppenheimer molecular dynamics with nearly crossing potential surfaces
Abstract
The difference of the values of observables for the time-independent Schroedinger equation, with matrix valued potentials, and the values of observables for ab initio Born-Oppenheimer molecular dynamics, of the ground state, depends on the probability to be in excited states and the electron/nuclei mass ratio. The paper first proves an error estimate (depending on the electron/nuclei mass ratio and the probability to be in excited states) for this difference of microcanonical observables, assuming that molecular dynamics space-time averages converge, with a rate related to the maximal Lyapunov exponent. The error estimate is uniform in the number of particles and the analysis does not assume a uniform lower bound on the spectral gap of the electron operator and consequently the probability to be in excited states can be large. A numerical method to determine the probability to be in excited states is then presented, based on Ehrenfest molecular dynamics and stability analysis of a perturbed eigenvalue problem.
Keywords
Cite
@article{arxiv.1305.3330,
title = {Computational error estimates for Born-Oppenheimer molecular dynamics with nearly crossing potential surfaces},
author = {Christian Bayer and Hakon Hoel and Ashraful Kadir and Petr Plechac and Mattias Sandberg and Anders Szepessy},
journal= {arXiv preprint arXiv:1305.3330},
year = {2015}
}
Comments
54 pages, 18 figures, Addition/Changes to the previous version: The Hamiltonian molecular dynamics is replaced by ergodic stochastic dynamics, the estimate of the error in observables is uniform in the number of particles, the numerical molecular dynamics method to determine the probability to be in excited states is parameter free, and a section on the WKB method for caustics is included