Analytical Evaluation of Multicenter Integrals of r12−1 with Slater-Type Atomic Orbitals. V. Four-Center Integrals by Fourier-Transform Method

The four‐center integral of $r_{12}^{\text{−1}}$ with Slater‐type atomic orbitals is evaluated analytically. The Fourier‐transform convolution theorem is used to express the integral as an infinite sum in which the internuclear angles appear in spherical harmonics, and the internuclear distances in integrals over spherical Bessel functions and exponential‐type integrals. These “radial” integrals are evaluated as convergent infinite expansions by contour integration techniques. The formulas are valid for general values of the $\mathrm{n,\; l,\; m,\; \zeta }$ parameters of the orbitals and for general nonzero values of the internuclear distance vectors.