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 = α σ n i ϵ i , where n i and ϵ 1 are the molecular orbital occupancies and energies, gives an average deviation of 1.6%, with α determined empirically for each functional combination. The relationship 3E molecular = 1.145 σ n i ϵ 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.