Approach to calculation of long-range Coulomb interaction matrix elements in ion crystals

Expressions for the calculation of matrix elements of the Coulomb interaction of the electron with an infinite crystal lattice in ion crystals have been obtained. In the general case, matrix elements are calculated on the orbitals belonging to ions of different sites. Gaussian-type orbitals are used in the calculations. All expressions are absolutely and rather rapidly converging series in the space of the inverse lattice vectors. At present the value of this interaction being only one-center is estimated by the Madelung constant, in other words, by calculating the electrostatic potential in the lattice site, i.e., in a point.