Topologically correct quantum nonadiabatic formalism for on-the-fly dynamics

TL;DR

This paper compares two methods for simulating nonadiabatic quantum dynamics, highlighting how the second approach naturally incorporates geometric phases without additional gauge transformations.

Contribution

It introduces a topologically correct formalism for on-the-fly quantum nonadiabatic dynamics that inherently accounts for geometric phases using localized electronic functions.

Findings

The second approach naturally captures geometric phases.

The first approach fails without gauge transformations.

Localized basis functions simplify nonadiabatic dynamics modeling.

Abstract

On-the-fly quantum nonadiabatic dynamics for large systems greatly benefits from the adiabatic representation readily available from the electronic structure programs. However, frequently occurring in this representation conical intersections introduce non-trivial geometric or Berry phases which require a special treatment for adequate modelling of the nuclear dynamics. We analyze two approaches for nonadiabatic dynamics using the time-dependent variational principle and the adiabatic representation. The first approach employs adiabatic electronic functions with global parametric dependence on the nuclear coordinates. The second approach uses adiabatic electronic functions obtained only at the centres of moving localized nuclear basis functions (e.g. frozen-width Gaussians). Unless a gauge transformation is used to enforce single-valued boundary conditions, the first approach fails to capture the geometric phase. In contrast, the second approach accounts for the geometric phase naturally because of the absence of the global nuclear coordinate dependence in the electronic functions.