Comments on the approximate calculation of lattice potential

Abstract

The potential of a charge distribution due to a lattice of point charges may be evaluated by the classical multipole expansion method. The leading terms in the resultant expressions are just those used in some of our previous calculations [1–3]. In addition, for cases where the leading terms vanish because of the effect of orthogonality of the basis functions upon the Mulliken expansion (this being especially serious in the case of a one-centre charge distribution), we have derived the first nonvanishing term, involving 〈χ_μ|r|χ_ν〉. In other cases it may be necessary to proceed to still higher multipole terms before a non-zero contribution is obtained. The entire procedure is formulated in such a way that it can be easily applied to LCAO-MO calculations for polyatomic ions in ionic lattices.