where j is the index of the j th charged particle (including all electrons and nuclei), with the corresponding mass m j and charge z j . In addition, x ≡ {x j } = { R, r} with R and r representing the sets of nuclear and electronic coordinates, respectively, p ≡ {p R , pr } ≡ {p j } is the mechanical momentum operator as well as the canonical momentum operator, such that pj = -iℏ∇ j . Further, T = TR + Tr is the kinetic energy operator, where TR and Tr represent the kinetic energy operator for nuclei and for electrons, respectively, and V (x) is the potential operator that describes the Coulombic interactions among electrons and nuclei. For a more in-depth review of molecular Hamiltonians, see Appendix A.