Unified treatment of integer and noninteger n multicenter multielectron molecular integrals using complete orthonormal sets of ψ α-ETOs

Abstract

Using complete orthonormal sets of ψ α exponential-type orbitals (ψ α -ETOs) where α=1,0,−1,… the general formulas are derived for the expansion of noninteger n ∗ Slater-type orbitals (NISTOs) in terms of integer n Slater-type orbitals (ISTO's) at a displaced center. For the expansion of one- and two-center electron charge density with NISTOs the analytical expressions in terms of ISTOs at a new origin are also obtained. 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. The final results are expressed in terms of both the one-center multielectron basic integrals over ISTOs, and the expansion coefficients of the electron charge density with NISTOs. The relationships obtained are valid for the integer and noninteger principal quantum numbers, screening constants and arbitrary location of ISTOs and NISTOs.