Extremely compact formulas for the Fourier transform of a product of two-centre Slater-type orbitals

Abstract

A compact formula for the Fourier transform of a product of Slater-type orbitals on different centres is derived. The integral is reduced to a finite one-dimensional integration over non-oscillatory hypergeometric functions of type 1F2(x; y; z). The formula is valid for all quantum numbers and does not involve the reduced Bessel functions that are usually used to evaluate these integrals. Reduced formulas are calculated for some special directions in the reciprocal space. Also, some useful identities for the Fourier transforms of a product of Slater-type orbitals with correlated sets of parameters are obtained. In order to illustrate simple and efficient use of the presented results, we have applied them to graphene. © 2010 IOP Publishing Ltd.