Comments on the approximate calculation of lattice potential

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 |r|. 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.