Title: Mixed quantum–classical approach to model non-adiabatic electron–nuclear dynamics: Detailed balance and improved surface hopping method

Abstract

We develop a density matrix formalism to describe coupled electron–nuclear dynamics. To this end, we introduce an effective Hamiltonian formalism that describes electronic transitions and small (quantum) nuclear fluctuations along a classical trajectory of the nuclei. Using this Hamiltonian, we derive equations of motion for the electronic occupation numbers and for the nuclear coordinates and momenta. We show that, in the limit, when the number of nuclear degrees of freedom coupled to a given electronic transition is sufficiently high (i.e., the strong decoherence limit), the equations of motion for the electronic occupation numbers become Markovian. Furthermore, the transition rates in these (rate) equations are asymmetric with respect to the lower-to-higher energy transitions and vice versa. In thermal equilibrium, such asymmetry corresponds to the detailed balance condition. We also study the equations for the electronic occupations in the non-Markovian regime and develop a surface hopping algorithm based on our formalism. To treat the decoherence effects, we introduce additional “virtual” nuclear wave packets whose interference with the “real” (physical) wave packets leads to the reduction in coupling between the electronic states (i.e., decoherence) as well as to the phase shifts that improve the accuracy of the numerical approach. Remarkably, the same phasemore » shifts lead to the detailed balance condition in the strong decoherence limit.« less

Authors:

Stolyarov, E. V.  ^[1];

• Search DOE PAGES for author "Stolyarov, E. V."
• Search DOE PAGES for ORCID "0000-0001-7531-5953"

White, A. J.  ^[2];

• Search DOE PAGES for author "White, A. J."
• Search DOE PAGES for ORCID "0000-0002-7771-3899"

Mozyrsky, D.  ^[2]

• Search DOE PAGES for author "Mozyrsky, D."
• Search DOE PAGES for ORCID "0000-0001-5305-4617"

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+ Show Author Affiliations

1. National Academy of Sciences of Ukraine (NASU), Kyiv (Ukraine). Institute of Physics
2. Los Alamos National Lab. (LANL), Los Alamos, NM (United States)

Publication Date:

Fri Aug 21 00:00:00 EDT 2020

Research Org.:

Los Alamos National Laboratory (LANL), Los Alamos, NM (United States)

Sponsoring Org.:

USDOE Laboratory Directed Research and Development (LDRD) Program

OSTI Identifier:

1813849

Alternate Identifier(s):

OSTI ID: 1648579

Report Number(s):

LA-UR-20-24033
Journal ID: ISSN 0021-9606; TRN: US2213378

Grant/Contract Number:  

89233218CNA000001; 20200074ER

Resource Type:

Accepted Manuscript

Journal Name:

Journal of Chemical Physics

Additional Journal Information:

Journal Volume: 153; Journal Issue: 7; Journal ID: ISSN 0021-9606

Publisher:

American Institute of Physics (AIP)

Country of Publication:

United States

Language:

English

Subject:

74 ATOMIC AND MOLECULAR PHYSICS; Chemical reactions; Quantum chemical dynamics; Density-matrix; Surface hopping