Regularized Born-Oppenheimer molecular dynamics

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.

Ab initio molecular dynamics with screened Lorentz forces. I. Calculation and atomic charge interpretation of Berry curvature

“…There has been recent work seeking to address this issue in the context of dynamics equations where the Berry curvature is present. 35 Methods such as surface hopping 36,37 can also be applicable in this framework. However, these concerns are beyond the scope of the present work.…”

The bohmion method in nonadiabatic quantum hydrodynamics

“…The bohmion method [15] overcomes this difficulty by inserting a mollifier K(r − r ), so that the regularized probability density D(r, t) = ´K(r − r )D(r , t) d 3 r is made available. A similar approach was recently applied to regularize conical intersections in adiabatic dynamics with geometric phase effects [40]. The mollifier is typically rotation-invariant and depends on a lengthscale parameter α so that the limit α → 0 returns the original hydrodynamic variable D. For example, α could be the width of a Gaussian convolution.…”

Ab-Initio Molecular Dynamics with Screened Lorentz Forces. Part I. Calculation and Atomic Charge Interpretation of Berry Curvature

“…There has been recent work seeking to address this issue in the context of dynamics equations where the Berry curvature is present. 34 Methods such as surface hopping 35,36 can also be applicable in this framework. However, these concerns are beyond the scope of the present work…”