Statistical Approximation for Exchange in Self-Consistent-Field Calculations of the Ground State of Neutral Argon

Comparisons are made of the orbital functions for the ground state of neutral argon obtained by four self-consistent-field methods. Three of these four are the familiar Hartree method, the Hartree-Fock method, and the Hartree-Fock method with Slater's statistical exchange potential. The fourth method is the same as Slater's but uses an exchange potential two-thirds as large as his. The smaller exchange potential was found by Kohn and Sham and by ourselves in a derivation which differs somewhat from Slater's. The orbitals computed from this set of self-consistent-field equations are closer to the Hartree-Fock orbitals than are the Hartree orbitals or the Hartree-Fock-Slater orbitals.