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

Anew method for deriving the spherical average of the product of the Fourie r transforms of two Gaussians is described. The method generates the result in terms of a few spherical Bessel functions leading to expressions that a re much more compact than those in the literature. These integrals are requ ired in the computation of spherically averaged electron momentum densities , and rotationally averaged X-ray and high-energy electron scattering cross ections. All integrals needed for spherically averaged momentum densities a re tabulated for s, p, d, and f-type Gaussians. As an illustration of the m ethod, we apply it to calculate spherically averaged electron momentum dens ities and their moments for H2O. The calculations are performed at the Hart ree-Fock and 2nd-and 4th-order Moller-Plesset perturbation theory levels wi th the aug-cc-pVDZ and aug-cc-pVTZ basis sets. (C) 2001 John Wiley & Sons, Inc.