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 and Near-Trivial 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 (U) between basis functions at successive points in time and selecting the phases so as to minimize the matrix norm of log(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.

Methods to Calculate Electronic Excited-state Dynamics For Molecules on Large Metal Clusters with Many States: Ensuring Fast Overlap Calculations and a Robust Choice of Phase

“…At this juncture, it is important to emphasize that the sign of a given eigenstate (and the sign of any column in the overlap matrix U) is undetermined. Moreover, the logarithm of the matrix U can be very sensitive to these phases of the adiabatic states and changing the signs of a column of the U matrix can lead to wildly different T matrix [25,26]. To that end, if we wish to run dynamics, it is crucial to choose the phases of the states in such a way that the T matrix elements are as smooth as possible, especially when there are many electronic states and many trivial crossings.…”

“…Thus, the second goal of this paper is to implement Ref. [26] to choose adiabatic eigenstates. As will be reviewed below, Ref.…”

“…As will be reviewed below, Ref. [26] extends parallel transport to the case of nearly trivial crossings by choosing the optimal phases of the overlap matrix through a simple optimization process.…”

“…In section 3, we implement the optimization process as suggested in Ref. [26] for dynamically choosing the phases of the overlap matrix. In section 4, we present results for highly-lying excited-state dynamics of a molecule-nanoparticle system and highlight the performance enhancement of our scheme.…”

Efficient update of determinants for many-electron wave function overlaps

“…At these crossings, nonadiabatic couplings are highly peaked and cannot be assumed to change linearly between two time steps unless prohibitively small time steps are used. This problem is an active area of research in the field of nonadiabatic dynamics, and a number of solutions, all based on overlaps, has been proposed [5,6,7,8,9,10].…”