Fourier transform of spherical Laguerre Gaussian functions and its application in molecular integrals

The Fourier transform of the spherical Laguerre Gaussian‐type function (LGTF), L ${}_{\text{n}}^{\text{l}\text{+½}}$ (αr²)r^lY_lm( r̂ )e, was derived. Applying the Fourier transform convolution theorem, the basic two‐center integrals over the general two‐electron irregular solid harmonic operator, Y_LM( r̂ ₁₂)/r (which becomes Coulomb repulsion, spin–other‐orbit interaction or spin–spin interaction when L=0, 1, or 2, respectively) as well as the overlap were evaluated analytically. These basic integral results generate the two‐electron integrals of the Coulomb type, hybrid type, and exchange type as well as that of three‐ and four‐center. The formulas obtained, which are general for electronic wave functions of unrestricted quantum numbers n, l, and m, are expressed explicitly in terms of nuclear spherical LGTFs of internuclear geometrical variables. ©1999 John Wiley & Sons, Inc. Int J Quant Chem 73: 265–273, 1999