Band Structure and Cohesive Energy of Potassium Chloride

Abstract

The band structure of crystalline KCl has been calculated in an LCAO (linear combination of atomic orbitals) approximation. Interactions between free-ion Hartree-Fock functions are calculated directly from molecular-type integrals without reducing exchange interactions to an exchange potential. The structure of the filled bands of KCl is obtained by solving secular equations on a cubic mesh of points in $k$ space. The valence band is found to be quite narrow, about 1.5 ev wide, but the band-structure results do not explain the observed x-ray emission data for KCl. The band structure is recalculated in less detail as a function of interionic distance. Numerical quantities for the band-structure calculation are used also to calculate the cohesive energy of KCl at its normal interionic distance by L\"owdin's method. Inclusion of the second-neighbor interactions here is found to raise L\"owdin's equivalent of the repulsive energy from 18.9 kilocalories per mole to 26.2 kilocalories per mole and thus to raise the total cohesive energy above the experimentally-determined value, in line with expectation.