Construction and validation of a rigorous surface hopping algorithm for conical crossings

Abstract

This article presents and evaluates a surface hopping algorithm for time-dependent two-level Schr¨odinger systems with conically intersecting eigenvalues. The algorithm implements an asymptotic semigroup for approximating the solution’s Wigner function, that was rigorously defined and derived from the Schr¨odinger equation by two of the authors in previous work. It is applied to two-dimensional isotropic systems, which include linear Jahn-Teller Hamiltonians, and Gaussian initial data. It reproduces energy level populations and expectation values with an accuracy of two to three percent.