Superadiabatic transition histories in quantum molecular dynamics

TL;DR

This paper analyzes the nuclear wave-function dynamics near avoided crossings in molecules, deriving superadiabatic representations and providing explicit formulas for transition probabilities that match numerical results.

Contribution

It introduces a general form of the Schrödinger equation in superadiabatic representations for all n and derives explicit transition formulas.

Findings

Explicit formulas for wave function transitions near avoided crossings.

Superadiabatic representations improve understanding of transition dynamics.

Theoretical results agree with high-precision numerical simulations.

Abstract

We study the dynamics of a molecule's nuclear wave-function near an avoided crossing of two electronic energy levels, for one nuclear degree of freedom. We derive the general form of the Schroedinger equation in the n-th superadiabatic representation for all n, and give some partial results about the asymptotics for large n. Using these results, we obtain closed formulas for the time development of the component of the wave function in an initially unoccupied energy subspace, when a wave packet crosses the transition region. In the optimal superadiabatic representation, which we define, this component builds up monontonically. Finally, we give an explicit formula for the transition wave function away from the crossing, which is in excellent agreement with high precision numerical calculations.