where j is the index of the j th charged particle (including all electrons and nuclei), with the corresponding mass, m j , and canonical momentum, pj = -ih∇ j . We denote electronic coordinate with r, and nuclear coordinate with R, and use xj ∈ {r j , R j } to represent either the electron or nucleus, with x being the coordinate operator for all charged particles. Further, T = TR + Tr is the kinetic energy operator for all charged particles, where TR and Tr represent the kinetic energy operator for nuclei and for electrons, respectively. Further, V (x) is the potential operator that describes the Coulombic interactions among the electrons and nuclei. The electronic Hamiltonian is often defined as