Non-adiabatic transitions in multiple dimensions

TL;DR

This paper introduces a multi-dimensional algorithm for accurately computing non-adiabatic transitions, including wavepacket phase, in systems where the Born-Oppenheimer approximation fails, demonstrated through two-dimensional examples.

Contribution

A novel multi-dimensional algorithm that computes the entire wavepacket, including phase, using only one-level Born-Oppenheimer dynamics and local potential information.

Findings

Excellent agreement with full quantum dynamics in 2D examples

Effective handling of avoided crossings and conical intersections

Computes complete wavepacket, not just transition probabilities

Abstract

We consider non-adiabatic transitions in multiple dimensions, which occur when the Born-Oppenheimer approximation breaks down. We present a general, multi-dimensional algorithm which can be used to accurately and efficiently compute the transmitted wavepacket at an avoided crossing. The algorithm requires only one-level Born-Oppenheimer dynamics and local knowledge of the potential surfaces. Crucially, in contrast to standard methods in the literature, we compute the whole wavepacket, including its phase, rather than simply the transition probability. We demonstrate the excellent agreement with full quantum dynamics for a range of examples in two dimensions. We also demonstrate surprisingly good agreement for a system with a full conical intersection.