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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/rc in elliptic coordinates and by subsequent use of ξ/ξc→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 An (p), and Bm (pt) appearing in overlap integrals between Slater-type orbitals. In addition the generalized exponential function En(p) = ∫ 1∞ x−nexp(−px)dx=A−n(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.
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Bosanao et al. (1972) studied this question.
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