Ab initio Hartree-Fock calculations of crystalline systems using full-symmetry analysis of basis-set expansions

A technique is presented for carrying out ab initio Hartree-Fock calculations on systems of infinite three-dimensional periodicity. The method represents an adaptation of standard molecular basis-set expansion techniques and fully utilizes translational and point-group symmetry to simplify the calculations. It is shown that the expression for total energy may be written as a sum of pairwise interactions between neutral charge units consisting of a nucleus and a localized compensating electronic charge. The resulting sums are rapidly convergent. The technique is illustrated with sample calculations on face-centered-cubic lattices of hydrogen, lithium, and sodium. Generalization to systems of lower symmetry is discussed.