l -Averaged Exchange Term in the Hartree-Fock Equations

A possible improvement of Slater's simplification of the Hartree–Fock equations was suggested by Harman, Callaway, and Acton wherein an averaged exchange potential was defined for each set of states having a common orbital angular momentum. In the present paper, such an averaging is performed on the Hartree–Fock equations, and the resulting equations are solved self-consistently. Comparisons are made between results obtained from the l-averaged exchange approximation, Slater's average, the free-electron exchange approximation, and the complete Hartree–Fock method. With very little increase in computational difficulty, the l-averaged exchange approximation yields results which are an improvement over Slater's average or the free-electron exchange approximation.