The Cuboidal Lattices and their Lattice Sums

Abstract

Lattice sums of cuboidal lattices, which connect the face-centered with the mean-centered and the body-centered cubic lattices through parameter dependent lattice vectors, are evaluated by decomposing them into two separate lattice sums related to a scaled cubic lattice and a scaled Madelung constant. Using theta functions we were able to derive fast converging series in terms of Bessel functions. Analytical continuations of these lattice sums are discussed in detail.