Computation of Fourier transform quantities in Hartree–Fock calculations for simple crystals

An efficient method is presented to compute the Fourier transforms of lattice sums over Slater-type orbital products that arise in crystal Hartree–Fock calculations. Introduction of one-dimensional integral representations for the Fourier transforms of the STO 'S enables a separation of the three infinite sums under the (two-dimensional) integral sign. This, in turn, makes it possible to calculate and store quantities associated with the three Fourier transform vector components separately. The orbital transform integrations are then performed numerically. The method is very advantageous when lattice sum transforms are needed for a large number of transform vectors. Formulas and results are presented for simple-cubic crystals when 1s, 2s, and 2p Slater orbitals are involved.