Computational error estimates for Born-Oppenheimer molecular dynamics with nearly crossing potential surfaces
2015 (English)In: Applied Mathematics Research eXpress, ISSN 1687-1200, E-ISSN 1687-1197, no 2, 329-417 p.Article in journal (Refereed) Published
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 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.
Place, publisher, year, edition, pages
Oxford University Press, 2015. no 2, 329-417 p.
HIGH-ORDER CORRECTIONS, NUMERICAL-ANALYSIS, QUANTUM, PROPAGATION, ERGODICITY, OPERATORS, APPROXIMATION, SYSTEMS
IdentifiersURN: urn:nbn:se:kth:diva-156031DOI: 10.1093/amrx/abv007ISI: 000366820400007ScopusID: 2-s2.0-84941214775OAI: oai:DiVA.org:kth-156031DiVA: diva2:764166
Updated from Manuscript to Article. QC 20151012. QC 201601212014-11-182014-11-182016-01-21Bibliographically approved