where the first term on the right-hand side (RHS) is the nuclear kinetic energy operator expressed in Cartesian coordinates and ĤBO (r, R) is the electronic (or BO) Hamiltonian which contains the electronic kinetic energy and all the interactions. Here, we assigned an index ν to label the N n nuclei, while indicating their individual masses as M ν . The symbols R and r indicate the sets of 3N n and 3N e nuclear and electronic coordinates, respectively. The time evolution of the electron-nuclear system is dictated by the TDSE