LAUSR

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 non-radiative 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 the paper we discuss computational issues related to the suitable representation for electronic dynamics and to the different nature 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.