A fresh look at the computation of spherically averaged electron momentum densities for wave functions built from Gaussian-type functions

Abstract

A new method for deriving the spherical average of the product of the Fourier transforms of two Gaussians is described. The method generates the result in terms of a few spherical Bessel functions leading to expressions that are much more compact than those in the literature. These integrals are required in the computation of spherically averaged electron momentum densities, and rotationally averaged X-ray and high-energy electron scattering crossections. All integrals needed for spherically averaged momentum densities are tabulated for s, p, d, and f-type Gaussians. As an illustration of the method, we apply it to calculate spherically averaged electron momentum densities and their moments for H2O. The calculations are performed at the Hartree-Fock and 2nd- and 4th-order Møller-Plesset perturbation theory levels with the aug-cc-pVDZ and aug-cc-pVTZ basis sets.