Error Estimation and Adaptive Methods for Molecular Dynamics
2014 (English)Licentiate thesis, comprehensive summary (Other academic)
This thesis consists of two 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 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 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. Then we present a numerical method to determine the probability to be in excited states, based on Ehrenfest molecular dynamics, and stability analysis of a perturbed eigenvalue problem. In Paper II, we present an approach, motivated by the Landau-Zener probability estimation, to systematically choose the artificial electron mass parameter appearing in the Car-Parrinello and Ehrenfest molecular dynamics methods to achieve both good accuracy in approximating the Born-Oppenheimer molecular dynamics solution, and high computational efficiency. This makes the Car- Parrinello and Ehrenfest molecular dynamics methods dependent only on the problem data.
Place, publisher, year, edition, pages
Stockholm: KTH Royal Institute of Technology, 2014. , 12 p.
IdentifiersURN: urn:nbn:se:kth:diva-156035ISBN: 978-91-7595-361-8OAI: oai:DiVA.org:kth-156035DiVA: diva2:764200
2014-11-25, Room 3733, Lindstedtsvägen 25, KTH, Stockholm, 10:15 (English)
Rubensson, Emanuel, Docent
Szepessy, Anders, Professor
QC 201411182014-11-182014-11-182014-11-18Bibliographically approved
List of papers