A Robust and Unified Solution for Choosing the Phases of Adiabatic States as a Function of Geometry: Extending Parallel Transport Concepts to the cases of Trivial & Near Trivial Crossings

TL;DR

This paper presents a robust method for smoothly choosing phases of adiabatic states as a function of geometry, extending parallel transport to handle trivial and near-trivial crossings, improving non-adiabatic dynamics simulations.

Contribution

The authors introduce a phase selection algorithm based on minimizing the log of the overlap matrix, extending parallel transport to complex crossing scenarios in electronic states.

Findings

Performs well in extreme crossing situations

Produces smooth non-adiabatic coupling matrices

Applicable to large systems with complex crossings

Abstract

We investigate a simple and robust scheme for choosing the phases of adiabatic electronic states smoothly (as a function of geometry) so as to maximize the performance of ab initio non-adiabatic dynamics methods. Our approach is based upon consideration of the overlap matrix ($\mathbf{U}$) between basis functions at successive points in time and selecting the phases so as to minimize the matrix norm of $\log(\mathbf{U})$. In so doing, one can extend the concept of parallel transport to cases with sharp curve crossings. We demonstrate that this algorithm performs well under extreme situations where dozens of states cross each other either through trivial crossings (where there is zero effective diabatic coupling), or through nontrivial crossings (when there is a nonzero diabatic coupling), or through a combination of both. In all cases, we compute the time-derivative coupling matrix elements (or equivalently non-adiabatic derivative coupling matrix elements) that are as smooth as possible. Our results should be of interest to all who are interested in either non-adiabatic dynamics, or more generally, parallel transport in large systems.