Electron gas exchange for atoms

Abstract

Current use of electron gas theory for exchange allows calculations of Hartree-Fock (HF) energies through the use of local potentials. A recent proposal of Gopinathan, Whitehead, and Bogdanović to use a realistic pair correlation function $f_{\uparrow \uparrow }(1, 2)$ that incorporates the boundary conditions of Kutzelnigg, Del Re, and Berthier, which consider the finite number of electrons of a given spin, showed much better agreement with atomic HF calculations. This paper explores the use of an improved $f_{\uparrow \uparrow }(1, 2)$ either with the electron cloud form (exponential) or with a modified Wigner form. The total energies obtained from this method are in excellent agreement with HF total energies. The calculated total energies lie above the HF values; we interpret this as an open possibility for the inclusion of refinements such as the inhomogeneity corrections.