Practical phase-space electronic Hamiltonians for ab initio dynamics

Author:

Tao Zhen1ORCID,Qiu Tian1ORCID,Bhati Mansi1ORCID,Bian Xuezhi1ORCID,Duston Titouan1ORCID,Rawlinson Jonathan2ORCID,Littlejohn Robert G.3ORCID,Subotnik Joseph E.1ORCID

Affiliation:

1. Department of Chemistry, University of Pennsylvania 1 , Philadelphia, Pennsylvania 19104, USA

2. Department of Mathematics, University of Manchester 2 , Manchester M13 9PL, United Kingdom

3. Department of Physics, University of California 3 , Berkeley, California 94720, USA

Abstract

Modern electronic structure theory is built around the Born–Oppenheimer approximation and the construction of an electronic Hamiltonian Ĥel(X) that depends on the nuclear position X (and not the nuclear momentum P). In this article, using the well-known theory of electron translation (Γ′) and rotational (Γ″) factors to couple electronic transitions to nuclear motion, we construct a practical phase-space electronic Hamiltonian that depends on both nuclear position and momentum, ĤPS(X,P). While classical Born–Oppenheimer dynamics that run along the eigensurfaces of the operator Ĥel(X) can recover many nuclear properties correctly, we present some evidence that motion along the eigensurfaces of ĤPS(X,P) can better capture both nuclear and electronic properties (including the elusive electronic momentum studied by Nafie). Moreover, only the latter (as opposed to the former) conserves the total linear and angular momentum in general.

Funder

Division of Chemistry

Publisher

AIP Publishing

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