A statistical exchange approximation for localized electrons

An approximate expression for the interelectronic exchange is derived from the free-electron-gas model in a similar way as the ordinary Slater ρ1/3 approximation. This is combined with the exact expression for the self-interaction (same as in the Hartree potential) to an approximation of the full Hartree-Fock exchange. This approximation—called the Hartree-Slater approximation—does not contain any adjustable parameters. A (non-local) potential, to be used in the SCF procedure, is obtained from the energy expression by use of the variational principle. This scheme has been tested in atomic calculations—non-relativistic as well as relativistic—and found to reproduce the HF exchange better than any available local exchange potential. The new exchange approximation is therefore believed to be of general validity and applicable not only to free atoms. Since only exchange is considered in the present work, the applications are limited to cases where screening and other correlation effects are not too important. Possible applications are heavy atoms (as a substitute for relativistic HF), molecules and localized electrons in solids, e.g. d and f electrons in transition elements.