Comparison of a Hartree-Fock Like and Statistical Exchange Potentials for Metallic Sodium

Abstract

First-principles OPW energy-band calculations have been made for metallic sodium in two different types of exchange approximations. First a k -dependent core-conduction exchange potential has been derived from the Hartree-Fock equations with the use of the available core and conduction electron wave functions, and combined with the conduction-conduction exchange potential of ρ 1/3 type. Then the Knight shift parameter P F =- av is found to be 0.362 a.u. (80% of the experimental value). The Fermi surface is also in reasonable agreement with experiment. Second the statistical exchange of Slater with a scale factor α (the X α method) has been examined, varying α from 1 to 0.9, 0.81, 0.74, and to 2/3. The best result has been obtained with α=0.81. At this α, the Fermi surface is in good agreement with experiment, but the value of P F is like those of the earlier calculations based on the Prokofjew potential.