Some Approximate Kohn-Sham Molecular Energy Formulas

Density functional calculations have been carried out for twelve 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 Emolecular 37 Vne 2Vnn, in which Vne and Vnn are the nuclear-electronic attraction and nuclear repulsion, reproduces Kohn-Sham energies with an average deviation of less than 0.70. Emolecular alpha.Sigmani epsilonj, where ni and epsilonj are the molecular orbital occupancies and energies, gives an average deviation of 1.6, with alpha determined empirically for each functional combination. The relationship 3Emolecule 1.14 Sigmani epsilonj 2Vnn Vne, an analogue of an exact Hanree-Fock expression, predicts Becke-3 Kohn-Sham molecular energies to within an average 0.23 of the actual values.