Self-consistent-field-Ξamethod: Parametrization ofain the modified Hartree-Fock-Slater method for atoms

The Ξa method, in which the self-interaction integrals are explicitly calculated, and the remaining portion of the charge density ρ^', is scaled in the same way as in the Xα method, has been applied to atoms from Li to Ar. The total Ξa atomic energy is made equal to the total atomic energy for the Hartree-Fock (HF) limit, to give a set of parameters aHF. The aHF generally increase as Z increases, in contrast to the behavior of αHF in the Xα theory. The plot of aHF against Z reflects the atomic shell structure. Energy results for several small-Z atoms show that the atomic one-electron energy in the Ξa method, compared to those from the Xα method, are much closer to the HF results. Within the Ξa scheme, calculated atomic energies using aHF are compared with those calculated using αₜₐ, the average theoretical α value from the Xα theory.