and of the electronic Hamiltonian Ĥel , i.e., the sum of the electronic kinetic energy and all interactions. Here, the symbols r and R indicate the coordinates of the N el electrons and of the N n nuclei (with masses M ν ), respectively. The Born-Huang (BH) representation of the molecular wavefunction consists in expressing it as the linear combination of eigenstates of the electronic operator Ĥel , whose dependence on R introduces a dependence on the nuclear positions in the eigenvectors, i.e, the adiabatic states {ϕ l (r; R)} l=1,...,Nst , and in the eigenvalues, i.e., the adiabatic potential energy surfaces (PESs) E l (R). The BH expansion reads