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Computational error estimates for Born-Oppenheimer molecular dynamics with nearly crossing potential surfacesPrimeFaces.cw("AccordionPanel","widget_formSmash_some",{id:"formSmash:some",widgetVar:"widget_formSmash_some",multiple:true}); PrimeFaces.cw("AccordionPanel","widget_formSmash_all",{id:"formSmash:all",widgetVar:"widget_formSmash_all",multiple:true}); PrimeFaces.cw("SelectBooleanButton","widget_formSmash_j_idt197",{id:"formSmash:j_idt197",widgetVar:"widget_formSmash_j_idt197",onLabel:"Hide others and affiliations",offLabel:"Show others and affiliations"});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2015 (English)In: Applied Mathematics Research eXpress, ISSN 1687-1200, E-ISSN 1687-1197, no 2, 329-417 p.Article in journal (Refereed) Published
##### Abstract [en]

##### Place, publisher, year, edition, pages

Oxford University Press, 2015. no 2, 329-417 p.
##### Keyword [en]

HIGH-ORDER CORRECTIONS, NUMERICAL-ANALYSIS, QUANTUM, PROPAGATION, ERGODICITY, OPERATORS, APPROXIMATION, SYSTEMS
##### National Category

Mathematics
##### Identifiers

URN: urn:nbn:se:kth:diva-156031DOI: 10.1093/amrx/abv007ISI: 000366820400007ScopusID: 2-s2.0-84941214775OAI: oai:DiVA.org:kth-156031DiVA: diva2:764166
#####

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##### Note

##### In thesis

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.

Updated from Manuscript to Article. QC 20151012. QC 20160121

Available from: 2014-11-18 Created: 2014-11-18 Last updated: 2016-01-21Bibliographically approved1. Error Estimation and Adaptive Methods for Molecular Dynamics$(function(){PrimeFaces.cw("OverlayPanel","overlay764200",{id:"formSmash:j_idt731:0:j_idt735",widgetVar:"overlay764200",target:"formSmash:j_idt731:0:parentLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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