l-Averaged Exchange Term in the Hartree-Fock Equations

Abstract

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.