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Numerical Methods for 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});
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PrimeFaces.cw("AccordionPanel","widget_formSmash_responsibleOrgs",{id:"formSmash:responsibleOrgs",widgetVar:"widget_formSmash_responsibleOrgs",multiple:true}); 2016 (English)Doctoral thesis, comprehensive summary (Other academic)
##### Abstract [en]

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

Stockholm: KTH Royal Institute of Technology, 2016.
##### Series

TRITA-MAT-A, 2016:09
##### Keyword [en]

Numerical Methods, Molecular Dynamics, Nearly Crossing Potential Surfaces, Error Estimation, Adaptive Algorithm
##### National Category

Computational Mathematics
##### Research subject

Applied and Computational Mathematics
##### Identifiers

URN: urn:nbn:se:kth:diva-195098ISBN: 978-91-7729-157-2 (print)OAI: oai:DiVA.org:kth-195098DiVA: diva2:1044055
##### Public defence

2016-12-09, D2, Lindstedtsvägen 5, Stockholm, 10:00 (English)
##### Opponent

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt453",{id:"formSmash:j_idt453",widgetVar:"widget_formSmash_j_idt453",multiple:true});
##### Supervisors

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#####

PrimeFaces.cw("AccordionPanel","widget_formSmash_j_idt465",{id:"formSmash:j_idt465",widgetVar:"widget_formSmash_j_idt465",multiple:true});
##### Funder

Swedish e‐Science Research Center
##### Note

##### List of papers

This thesis consists of four papers that concern error estimates for the Born-Oppenheimer molecular dynamics, and adaptive algorithms for the Car-Parrinello and Ehrenfest molecular dynamics.

In Paper I, we study error estimates for the Born-Oppenheimer molecular dynamics with nearly crossing potential surfaces. The paper first proves an error estimate showing that the difference of the values of observables for the time-independent Schrödinger equation, with matrix valued potentials, and the values of observables for the ab initio Born-Oppenheimer molecular dynamics of the ground state depends on the probability to be in the excited states and the nuclei/electron mass ratio. Then we present a numerical method to determine the probability to be in the excited states, based on the Ehrenfest molecular dynamics, and stability analysis of a perturbed eigenvalue problem.

In Paper II, we present an approach, motivated by the so called Landau-Zener probability estimation, to systematically choose the artificial electron mass parameters appearing in the Car-Parrinello and Ehrenfest molecular dynamics methods to approximate the Born-Oppenheimer molecular dynamics solutions.

In Paper III, we extend the work presented in Paper II for a set of more general problems with more than two electron states. A main conclusion of Paper III is that it is necessary to resolve the near avoided conical intersections between all electron eigenvalue gaps, including gaps between the occupied states.

In Paper IV, we numerically compare, using simple model problems, the Ehrenfest molecular dynamics using the adaptive mass algorithm proposed in Paper II and III and the Born-Oppenheimer molecular dynamics based on the so called purification of the density matrix method concluding that the Born-Oppenheimer molecular dynamics based on purification of density matrix method performed better in terms of computational efficiency.

QC 20161102

Available from: 2016-11-02 Created: 2016-11-01 Last updated: 2016-11-07Bibliographically approved1. Computational error estimates for Born-Oppenheimer molecular dynamics with nearly crossing potential surfaces$(function(){PrimeFaces.cw("OverlayPanel","overlay764166",{id:"formSmash:j_idt503:0:j_idt508",widgetVar:"overlay764166",target:"formSmash:j_idt503:0:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

2. An Adaptive Mass Algorithm for Car-Parrinello and Ehrenfest ab initio molecular dynamics$(function(){PrimeFaces.cw("OverlayPanel","overlay764172",{id:"formSmash:j_idt503:1:j_idt508",widgetVar:"overlay764172",target:"formSmash:j_idt503:1:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

3. An Adaptive Mass Algorithm for Ehrenfest and Car-Parrinello ab initio Molecular Dynamics: dynamics with several electronic states$(function(){PrimeFaces.cw("OverlayPanel","overlay1044045",{id:"formSmash:j_idt503:2:j_idt508",widgetVar:"overlay1044045",target:"formSmash:j_idt503:2:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

4. A numerical comparison between Ehrenfest dynamics and purification of the density matrix method for Born-Oppenheimer dynamics$(function(){PrimeFaces.cw("OverlayPanel","overlay1044047",{id:"formSmash:j_idt503:3:j_idt508",widgetVar:"overlay1044047",target:"formSmash:j_idt503:3:partsLink",showEvent:"mousedown",hideEvent:"mousedown",showEffect:"blind",hideEffect:"fade",appendToBody:true});});

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