Computation of molecular integrals over Slater-type orbitals. IX. Calculation of multicenter multielectron molecular integrals with integer and noninteger n Slater orbitals using complete orthonormal sets of exponential functions

Abstract

By the use of complete orthonormal sets of Lambda and Coulomb Sturmian exponential-type functions the two kinds of formulas for the expansion of noninteger n ∗ Slater-type orbitals (NISTOs) in terms of integer n Slater-type orbitals (ISTOs) at a displaced center are derived. The analytical expressions in terms of ISTOs are also obtained for the expansion of one- and two-center electron charge density with NISTOs. The expansion coefficients in these formulas are presented through the two-center noninteger- n ∗ overlap integrals. The general formulas obtained for the electron charge density are utilized for the evaluation of multicenter multielectron molecular integrals over NISTOs appearing in the determination of various multielectron properties for molecules when the Hartree–Fock–Roothaan (HFR) approximation is employed. The final results are expressed in terms of both the expansion coefficients of the electron charge density with NISTOs, and the one-center multielectron basic integrals over ISTOs. The relationships obtained are valid for the arbitrary location, integer and noninteger quantum numbers and screening constants of STOs.