Electronic-structure studies of solids. I. Fourier representation method for Madelung sums

By use of Fourier-integral representations and lattice orthogonality relations, Madelung sums are cast in a form which explicitly separates contributions due to crystal symmetry from those due to the detailed arrangement of neighboring ions. The usefulness and mathematical soundness of the method are demonstrated by verifying known Madelung constants and by obtaining more accurate values for the electrostatic energies of low-density plasma models. The method is also easily applied to the study of ionic displacements or crystal defects.