Two-Center Coulomb Integrals between Atomic Orbitals

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Abstract
General analytical formulas are developed for the two-center Coulomb integrals between Slater-type atomic orbitals of arbitrary integral quantum numbers (nlm). The Coulomb integral C is obtained by integrating the Poisson equation ΔC = —4πS, where S is the corresponding overlap integral. The Coulomb integrals are expressed as trilinear forms of powers and certain auxiliary functions Gαβγ, Hαβγ, Jμνλ, which are related to confluent hypergeometric functions and Jacobi polynomials respectively. Stable recurrence procedures for their evaluation are given, and use with an electronic computer program showed the loss in numerical accuracy to be small for all argument values as well as for high quantum numbers.

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