Some approximate Kohn-Sham molecular energy formulas

Density functional calculations have been carried out for 12 molecules by several different Kohn-Sham procedures in order to test the effectiveness of two approximate molecular energy formulas that have been applied earlier in the context of Hartree-Fock theory. The equation E-molecular = 3/7 (V-ne + 2V(nn)), in which V-ne and V-nn are the nuclear-electronic attraction and the nuclear repulsion, reproduces Kohn-Sham energies with an average deviation of less than 0.70%. E-molecular = alpha Sigma n(i)epsilon(i), where n(i) and epsilon(i) are the molecular orbital occupancies and energies, gives an average deviation of 1.6%, with alpha determined empirically for each functional combination. The relationship 3E(molecule) = 1.145 Sigma n(i)epsilon(i) + 2V(nn) + V-ne, an analogue of an exact Hartree-Fock expression, predicts Becke-3 Kohn-Sham molecular energies to within an average 0.20% of the actual values.