Calculation of Excitation Energies in "Tightly-Bound" Solids

An approximate method of computing the energy of a localized excitation in a solid described by the Heitler-London scheme is presented. The overlap of the excited electron with wave functions centered on neighboring atoms is explicitly taken into account through terms of second order. The use of a Schmidt orthogonalization process avoids questions of convergence of the overlap series expansions found in other methods. Some further simplifying assumptions which are of possible use in ionic crystals are subsequently introduced. The formalism is applied to the system Ne: Ar. In this case it is found that the electrostatic excitation energy predicted for the $3p^6{}_{}{}^1{}_{}{}^{}S-3\mathrm{}{p}^{5}4s{}_{}{}^1{}_{}{}^{}P$ transition using the approximation identical to the symmetric orthogonalization method is appreciably smaller than that given by an "exact" application of the present theory. Questions concerning the reliability of some previous calculations are thus raised.