Conduction-Electron Exchange and the Local Pseudopotential Form Factors in the Alkali Metals

Abstract

We estimate the size of the error caused by omitting the exchange potential of the conduction electrons from the crystal potential when calculating the local pseudopotential form factors in the alkali metals. This error is determined by relating these approximate form factors to the true energy eigenvalues of the complete Hartree-Fock band-structure Hamiltonian. We then use this relation to deduce the approximate form factors from the measured anisotropy of the band energy at the Fermi surface. These form factors may be compared with the true form factors determined from Fermi-surface measurements. This comparison permits a prediction of the errors expected in present a priori calculations of the form factors due to the approximate treatment of the conduction-electron exchange potential. A numerical calculation is made for sodium, based on the formalism of this paper, which predicts that the errors in $V_{110}$ for this metal are of the order of 15%. The possibility of extending the calculations to other alkali metals is also discussed.