describes a system of interacting electrons and nuclei, whose positions are collectively indicated as q and x, respectively. The nuclear kinetic energy operator is expressed in Cartesian coordinates and contains a sum over the 3N n nuclear degrees of freedom, each labeled with the index ν, with spatial derivatives ∂ ν with respect to nuclear positions; M ν are the nuclear masses. The electronic Hamiltonian Ĥel (q, x) is the sum of the electronic kinetic energy and of all interactions. The time evolution of the electron-nuclear system is dictated by the molecular time-dependent Schrödinger equation (TDSE)