Analytical Evaluation of Multicenter Integrals of r12− 1 with Slater-Type Atomic Orbitals. I. (1-2)-Type Three-Center Integrals

The three-center integral of r12− 1, with one electron on one center in a Slater-type orbital, the second electron on two centers described by a product of Slater-type orbitals, is evaluated analytically. The result is an infinite sum in which the internuclear angles appear in spherical harmonics and the internuclear distances appear in modified spherical Bessel functions and exponential-type integrals. When one of the internuclear distances goes to zero, the two-center hybrid integral is obtained as a finite sum. The main mathematical techniques used to evaluate the integrals are the Fourier-transform convolution theorem, expansion of a Slater-type orbital on one center about another, coupling properties of spherical harmonics, and contour integration.