Wave packet dynamics in the optimal superadiabatic approximation

TL;DR

This paper introduces a new method for predicting wave packet transitions at avoided crossings using superadiabatic approximations, which simplifies computations by relying only on adiabatic energy levels without diabatization.

Contribution

The paper presents an explicit formula and a simple computational method for wave packet dynamics across avoided crossings within the Born-Oppenheimer framework, avoiding diabatization.

Findings

Accurate predictions of wave packet transitions at avoided crossings.

Good agreement with exact calculations in NaI photo-dissociation.

Method requires only adiabatic energy levels near crossings.

Abstract

We explain the concept of superadiabatic approximations and show how in the context of the Born- Oppenheimer approximation they lead to an explicit formula that can be used to predict transitions at avoided crossings. Based on this formula, we present a simple method for computing wave packet dynamics across avoided crossings. Only knowledge of the adiabatic electronic energy levels near the avoided crossing is required for the computation. In particular, this means that no diabatization procedure is necessary, the adiabatic energy levels can be computed on the fly, and they only need to be computed to higher accuracy when an avoided crossing is detected. We test the quality of our method on the paradigmatic example of photo-dissociation of NaI, finding very good agreement with results of exact wave packet calculations.