The molecular Hamiltonian (in the position representation) is expressed as ĤM = TR + Ĥel (r, R), where TR =i h2 ∇ 2 R i /2M i is the nuclear kinetic energy operator, Ĥel (r, R) = Tr + Vcoul (r, R) is the electronic Hamiltonian, with the electronic kinetic energy Tr and Coulomb potential Vcoul (R, r) among electrons and nuclei. The electronic adiabatic state |ψ α (R)⟩ is defined as the eigenstate of Ĥel as,