Symmetry based potential expansion technique for molecules and point charge lattices

Abstract

A systematic method is presented for evaluating the electrostatic potential of point charge systems with inversion symmetry. By considering two simple ‘dumbbell’ structures, concise general potential expressions are deduced for point charge symmetries of the point groups containing the inversion operation. The explicit formulae presented for the most common basic symmetries are used as a basis to write down the potential for more complicated geometries formed by the combination of any number of basic symmetries. The equations are also valid for geometries obtained by certain distortions of the basic symmetry. The method presented here gives the potential at any general space point. The use of expressions in terms of the real spherical harmonics facilitates matrix element calculations, and with the potentials in such a form, symmetry arguments can be directly applied to eliminate many terms which vanish.