Ewald-type formulas for Gaussian-basis studies of one-dimensionally periodic systems

The history of computations at Namur and elsewhere on the electronic structures of stereoregular polymers is briefly reviewed to place the work reported here in the context of related efforts. Our earlier publications described methods for the formal inclusion of Ewald-type convergence acceleration in band-structure computations based on Gaussian-type orbitals, and that work is here extended to include a discussion of the calculation of total energies. It is noted that the continuous nature of the electronic density leads to different functional forms than are encountered for point-charge lattice sums. Examples are provided to document the correctness and convergence properties of the formulation.