New Gradient Correction Scheme for Electronically Nonadiabatic Dynamics Involving Multiple Spin States

It has been recommended that the best representation to use for trajectory surface hopping (TSH) calculations is the fully adiabatic basis in which the Hamiltonian is diagonal. Simulations of intersystem crossing processes with conven-tional TSH methods require an explicit computation of nonadiabatic coupling vectors (NACs) in the molecular-Coulomb-Hamiltonian (MCH) basis, also called the spin- orbit-free basis, in order to compute the gradient in the fully adiabatic basis (also called the diagonal representation). This explicit requirement destroys some of the advantages of the overlap-based algorithms and curvature-driven algorithms that can be used for the most efficient TSH calculations. Therefore, although these algorithms allow one to perform NAC-free simulations for internal conversion processes, one still requires NACs for intersystem crossing. Here, we show that how the NAC requirement is circumvented by a new computation scheme called the time-derivative-matrix scheme.

Automated summary

It is recommended to use the fully adiabatic basis for trajectory surface hopping (TSH) calculations, where the Hamiltonian is diagonal. Traditional TSH methods for simulating intersystem crossing processes require explicit computation of nonadiabatic coupling vectors (NACs) in the molecular-Coulomb-Hamiltonian (MCH) basis, in order to compute the gradient in the fully adiabatic basis. However, this explicit requirement hinders the advantages of overlap-based and curvature-driven algorithms used for efficient TSH calculations. A new computation scheme called the time-derivative-matrix scheme is proposed to circumvent the need for NACs.