Ewald-type formulas for Gaussian-basis Bloch states in one-dimensionally periodic systems.

Expressions for integrals involving general Gaussian (s, p, d, [ellipsis (horizontal)]) basis Bloch functions are presented. Applying the Poisson transformation and the Ewald-type partitioning scheme, all lattice sums appearing in these expressions lead to fast convergence in both direct and Fourier spaces. Numerical results produced for selected test cases show that a limited number of terms in the lattice sums are necessary to get convergence in the two spaces.