Analytical Evaluation of Three-Center Nuclear-Attraction Integrals with Slater-Type Atomic Orbitals

The general three‐center one‐electron nuclear attraction integral with integer n Slater‐type orbitals is evaluated analytically. The formula is derived using Neumann expansion of 1/r_c in elliptic coordinates and by subsequent use of ξ/ξ_c→ξ substitution in order to restore the integration limits in integrals involving ξ. For the expression [ξ²—1]^M/2 binomial expansion is used. The final results is expressed as a multiple summation of terms built from the well‐known auxiliary functions A_n (p), and B_m (pt) appearing in overlap integrals between Slater‐type orbitals. In addition the generalized exponential function $$E_n\mathrm{(p)\; =}{\displaystyle {\int }_1^{\infty }}{x}^{\mathrm{-n}}\exp {\mathrm{(-px)dx=A}}_{\mathrm{-n}}\mathrm{(p)}$$ appear. Numerical results are given for several combinations of orbitals with quantum numbers n=1, 2, 3 and l=0, 1, 2, while the quantum number m was restricted to zero. The results are compared and are in a satisfactory agreement with those of Yoshimine which are based on numerical integration.