On the Electronic Constitution of Crystals; LiF and LiH

Abstract

A self-consistent solution of the Hartree-Fock system of equations for the ionic crystals LiF and LiH is attempted using approximation methods previously employed in metals. In part $A$ the boundary equations which the periodic functions must satisfy in the case of a facecentered cubic lattice are examined from the group theoretical standpoint. In part $B$ the Hartree system of equations is solved using ion core fields which include the ${\mathrm{}\left(1s\right)\mathrm{}}^2$ electrons in both Li and F, so that eight electrons are given periodic functions in LiF and two in LiH. These solutions, which are regarded as preliminary ones, involve the use of the "$s$ sphere approximation." The final results in both cases show that the Hartree approximation allows considerable charge to be in the vicinity of the metal ion so that the classical ion model is appreciably incorrect in that the valence electrons are not localized in a definite region about the electronegative atoms. The extent to which this affects the Born-Madelung lattice energy computations is discussed from the viewpoint of a complete solution.