Canonical mean-field molecular dynamics derived from quantum mechanics

Xin Huang, Petr Plechac, Mattias Sandberg, Anders Szepessy

Research output: Contribution to journalArticlepeer-review


Canonical quantum correlation observables can be approximated by classical molecular dynamics. In the case of low temperature  the ab initio molecular dynamics potential energy is based on the ground state electron eigenvalue problem and the accuracy has been proven to be [[EQUATION]] provided the first electron eigenvalue gap is sufficiently large compared to the given temperature and [[EQUATION]] is the ratio of nuclei and electron masses. For higher temperature eigenvalues corresponding to excited electron states are required to obtain  [[EQUATION]] accuracy and the derivations assume that all electron eigenvalues are separated, which for instance excludes conical intersections. This work studies a mean-field molecular dynamics approximation where the mean-field Hamiltonian for the nuclei is the partial trace [[EQUATION]] with respect to the electron degrees of freedom and [[EQUATION]] is the Weyl symbol corresponding to a quantum many body Hamiltonian [[EQUATION]] . It is proved that the mean-field molecular dynamics approximates canonical quantum correlation observables with accuracy [[EQUATION]] , for correlation time [[EQUATION]] where [[EQUATION]] is related to the variance of mean value approximation [[EQUATION]] . Furthermore, the proof derives a precise asymptotic representation of the Weyl symbol of the Gibbs density operator using a path integral formulation. Numerical experiments on a model problem with one nuclei and two electron states show that the mean-field dynamics  has similar or better accuracy than standard molecular dynamics based on the ground state electron eigenvalue.
Original languageEnglish (US)
JournalESAIM: Mathematical Modelling and Numerical Analysis
StatePublished - Sep 23 2022
Externally publishedYes

Bibliographical note

KAUST Repository Item: Exported on 2022-09-27
Acknowledged KAUST grant number(s): OSR-2019-CRG8-4033.3
Acknowledgements: This research was supported by Swedish Research Council grant 2019-03725 and KAUST grant OSR-2019-CRG8-4033.3. The work of P.P. was supported in part by the U.S. Army Research Office Grant W911NF-19-1-0243.
This publication acknowledges KAUST support, but has no KAUST affiliated authors.


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