We indicate with T (X) the kinetic energy of the particles identified by the coordinates X and with ĤBO (x, X) the sum of the remaining terms, i.e., the kinetic energy of the particles identified by the coordinates x and all the interactions. In the electron-nuclear problem, x = r stands for the electronic positions and X = R for the nuclear positions, and ĤBO (r, R) is usually referred to as Born-Oppenheimer (BO) Hamiltonian, which explains our choice of labelling this term with the subscript "BO". The time-dependent Schrödinger equation (TDSE) with Ĥ(x, X) dictates the evolution of the wavefunction Ψ(x, X,t) as