Here, (pq|rs), (pq|r s), ( p q|rs), and ( p q|r s) represent the ERIs, h pq and hpq are the one electron integrals, and V xc pq and Vxc pq are matrix elements of the first functional derivatives of the exchange-correlation functional with respect to electron density, which involve various combinations of two sets of spatial orbitals {χ p } and { χp }. It is noted that c HF is the coefficient for the exact Hartree-Fock exchange for the mean-field (DFT) calculation.