Non-Adiabatic Dynamics around a Conical Intersection with Surface-Hopping Coupled Coherent States

TL;DR

This paper introduces an extended surface-hopping coupled coherent states method for simulating non-adiabatic nuclear dynamics, capturing quantum interference effects around conical intersections with high accuracy.

Contribution

It develops a novel quantum dynamics simulation technique combining surface hopping with coherent states, improving the modeling of non-adiabatic effects and interference phenomena.

Findings

Successfully applied to a 2D conical intersection model

Captures quantum interference effects absent in classical methods

Provides exact solutions with sufficient trajectories and known potentials

Abstract

An extension of the CCS-method [Chem. Phys. 2004, 304, p. 103-120] for simulating non-adiabatic dynamics with quantum effects of the nuclei is put forward. The time-dependent Schr\"{o}dinger equation for the motion of the nuclei is solved in a moving basis set. The basis set is guided by classical trajectories, which can hop stochastically between different electronic potential energy surfaces. The non-adiabatic transitions are modelled by a modified version of Tully's fewest switches algorithm. The trajectories consist of Gaussians in the phase space of the nuclei (coherent states) combined with amplitudes for an electronic wave function. The time-dependent matrix elements between different coherent states determine the amplitude of each trajectory in the total multistate wave function; the diagonal matrix elements determine the hopping probabilities and gradients. In this way, both intereference effects and non-adiabatic transitions can be described in a very compact fashion, leading to the exact solution if convergence with respect to the number of trajectories is achieved and the potential energy surfaces are known globally. The method is tested on a 2D model for a conical intersection [J. Chem. Phys., 1996, 104, p. 5517], where a nuclear wavepacket encircles the point of degeneracy between two potential energy surfaces and intereferes with itself. These intereference effects are absent in classical trajectory-based molecular dynamics but can be fully incorporated if trajectories are replaced by surface hopping coupled coherent states.