A multi-state trajectory method for non-adiabatic dynamics simulations.

Guohua Tao

doi:10.1063/1.4943006

Abstract

A multi-state trajectory approach is proposed to describe nuclear-electron coupled dynamics in nonadiabatic simulations. In this approach, each electronic state is associated with an individual trajectory, among which electronic transition occurs. The set of these individual trajectories constitutes a multi-state trajectory, and nuclear dynamics is described by one of these individual trajectories as the system is on the corresponding state. The total nuclear-electron coupled dynamics is obtained from the ensemble average of the multi-state trajectories. A variety of benchmark systems such as the spin-boson system have been tested and the results generated using the quasi-classical version of the method show reasonably good agreement with the exact quantum calculations. Featured in a clear multi-state picture, high efficiency, and excellent numerical stability, the proposed method may have advantages in being implemented to realistic complex molecular systems, and it could be straightforwardly applied to general nonadiabatic dynamics involving multiple states.

Highlights

In principle a full quantum description on both electronic and nuclear degrees of freedom (DOFs) in coupled nuclearelectron dynamics, such as the multiconfiguration timedependent Hartree (MCTDH)15 and the multilayer MCTDH method,16 should be able to capture the quantum coherence exactly, and the requirement on the ad hoc hopping scheme may be dismissed
A number of promising trajectory based approaches have been developed, such as the matching-pursuit (MP)/split-operator-Fouriertransform (SOFT) method17 based on the adaptive coherent state expansion of the wavepacket, the multiple spawning approach18,19 featured in the spawning of basis functions due to strong nonadiabatic couplings, and the approximate but less expensive multiconfigurational Ehrenfest (MCE) method20 combining the coupled coherent states and Ehrenfest dynamics
We suggest a multi-state trajectory (MST) method to account for the fact that nuclei follow different dynamics on different states in nonadiabatic systems

Summary

Introduction

In principle a full quantum description on both electronic and nuclear degrees of freedom (DOFs) in coupled nuclearelectron dynamics, such as the multiconfiguration timedependent Hartree (MCTDH) and the multilayer MCTDH method, should be able to capture the quantum coherence exactly, and the requirement on the ad hoc hopping scheme may be dismissed. At variance with the multiple spawning method, a path branching algorithm was suggested to describe quantum wavepacket bifurcation in nonadiabatic dynamics. To account for quantum coherence accurately in a trajectory representation, it is important to treat the electronic and nuclear DOFs at the same dynamical footing. The MeyerMiller (MM) model explains such a philosophical idea perfectly and treats the coupled nuclear-electron dynamics consistently by mapping the electronic DOFs into classical variables. Stock and Thoss demonstrated that the MM Hamiltonian is the exact quantum representation for the

Methods

Results

Conclusion