TITLE

Computational Error Estimates for Born-Oppenheimer Molecular Dynamics with Nearly Crossing Potential Surfaces

AUTHOR(S)
Bayer, Christian; Hoel, Haåkon; Kadir, Ashraful; Plecháč, Petr; Sandberg, Mattias; Szepessy, Anders
PUB. DATE
July 2015
SOURCE
Applied Mathematics Research eXpress;2015, Vol. 2015 Issue 2, p329
SOURCE TYPE
Academic Journal
DOC. TYPE
Article
ABSTRACT
The difference of the values of observables for the time-independent Schrödinger 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 themaximal 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.
ACCESSION #
110089807

 

Related Articles

Share

Read the Article

Courtesy of THE LIBRARY OF VIRGINIA

Sorry, but this item is not currently available from your library.

Try another library?
Sign out of this library

Other Topics