Translational invariance of Coulomb series and symmetric potentials in crystals

Abstract

It is shown that Coulomb series are to be considered within a special mode of summation so as to describe bulk properties of crystals. The translational invariance is then an explicit integral property of Coulomb series that is tantamount to the effect of invariant periodic boundary conditions discussed earlier. Absolute bulk potentials with zero mean value are then substantiated as a unique solution in the general case of triclinic lattices. An invariant treatment of the bulk Coulomb energy follows therefrom. The potential symmetry is verified for simple point-charge lattices and is connected with the centre of gravity of the potential field that is relevant to non-local charges as well.