Regularized Born-Oppenheimer molecular dynamics

TL;DR

This paper introduces a novel semiclassical molecular dynamics scheme that incorporates geometric phase effects and regularizes conical intersections within the Born-Oppenheimer approximation, aligning well with recent nonadiabatic findings.

Contribution

It presents a new closure of the nuclear Born-Oppenheimer equation that captures geometric phase effects and regularizes conical intersections in molecular dynamics.

Findings

Reproduces the topological index behavior of geometric phase.

Regularizes conical intersections in nuclear particle motion.

Aligns with recent exact nonadiabatic studies in Jahn-Teller problems.

Abstract

While the treatment of conical intersections in molecular dynamics generally requires nonadiabatic approaches, the Born-Oppenheimer adiabatic approximation is still adopted as a valid alternative in certain circumstances. In the context of Mead-Truhlar minimal coupling, this paper presents a new closure of the nuclear Born-Oppenheimer equation, thereby leading to a molecular dynamics scheme capturing geometric phase effects. Specifically, a semiclassical closure of the nuclear Ehrenfest dynamics is obtained through a convenient prescription for the nuclear Bohmian trajectories. The conical intersections are suitably regularized in the resulting nuclear particle motion and the associated Lorentz force involves a smoothened Berry curvature identifying a loop-dependent geometric phase. In turn, this geometric phase rapidly reaches the usual topological index as the loop expands away from the original singularity. This feature reproduces the phenomenology appearing in recent exact nonadiabatic studies, as shown explicitly in the Jahn-Teller problem for linear vibronic coupling. Likewise, a newly proposed regularization of the diagonal correction term is also shown to reproduce quite faithfully the energy surface presented in recent nonadiabatic studies.