In this case, E 0 in Eq. (3a) is the Kohn-Sham groundstate energy and the quantities {ψ r } and {ε KS r } are the Kohn-Sham MOs and their energy levels, respectively. The quantities J ia and K ia in Eq. (3a) are Coulomb and exchange integrals, respectively, evaluated using the Kohn-Sham MOs. Equation (3b) is a Brillouin-like condition that is invoked by fiat. Empirical corrections that appear in the matrix elements of Eq. (3a) are discussed below, specifically the parameter c 1 and the function ∆J ia (ε i ).