where the operators P + (pr, qs) and P -(p, q) generate symmetrized/antisymmetrized expressions, respectively. Here ρ is the density of the reference determinant, which is diagonal in case of canonical Hartree-Fock molecular orbitals. When contracted with a two-electron operator A = 1 2 pqrs A pqrs p † q † sr, the separable part of two-particle density matrix yields: