Internal Conversion and Intersystem Crossing with the Exact Factorization

We present a detailed derivation of the generalized coupled-trajectory mixed quantum-classical (G-CT-MQC) algorithm based on the exact-factorization equations. The ultimate goal is to propose an algorithm that can be employed for molecular dynamics simulations of nonradiative phenomena, as the spin-allowed internal conversions and the spin-forbidden intersystem crossings. Internal conversions are nonadiabatic processes driven by the kinetic coupling between electronic states, whereas intersystem crossings are mediated by the spin–orbit coupling. In this paper, we discuss computational issues related to the suitable representation for electronic dynamics and the different natures of kinetic and spin–orbit coupling. Numerical studies on model systems allow us to test the performance of the G-CT-MQC algorithm in different situations.