Molecular integrals over spherical Laguerre Gaussian-type functions

Abstract

Fieck’s formulation of molecular integrals over the spherical Laguerre Gaussian-type functions, L(l+1/2)n(αr2) exp(−αr2)rlYlm(θ,φ) [where L(s)n(x) is the Sonine (or the generalized Laguerre) polynomial and Ylm(θ,φ) is the complex spherical harmonic], has been generalized to include four types of operators: Ynlm(r), Ŷnlm(∇), Ŷnlm(∇)(1/r), and Ŷnlm(∇12)(1/r12), where Ynlm(r) is the homogeneous solid harmonic and Ŷnlm(∇) its operator. These operators represent such various kinds of molecular properties as the energy (i.e., the overlap, the kinetic energy, the nuclear attraction, and the electron repulsion), the electric multipole moments and transitions, the electric field and gradient, the quasirelativistic interactions (e.g., the mass velocity, the spin–orbit, and the spin–spin), etc. Attention has been paid on the aspects of numerical computation of their molecular integrals so that the integral formulas are suitable for computation in the scheme of ‘‘shell structure’’ and over the contracted Gaussian-type functions.