r is the kinetic energy operator for the nuclear and electronic degrees of freedom (DOF), Vc (r, R) describes the coulomb interactions between all DOF (electronic and nuclear) and Ĥel (r, R) = Tr + Vc (r, R) is the electronic part of the molecular Hamiltonian. Directly simulating quantum dynamics by solving time-dependent Schrödinger equation (TDSE) governed by Ĥ is intractable. Instead, mixedquantum classical and semi-classical quantum dynamics approaches offer an efficient but approximate solution to the TDSE. These approaches solve the quantum dynamics in the following two steps.