Expansion formulae for two-center integer and noninteger n STO charge densities and their use in evaluation of multi-center integrals

Guseinov I. I.

JOURNAL OF MATHEMATICAL CHEMISTRY, vol.42, no.3, pp.415-422, 2007 (SCI-Expanded) identifier identifier

  • Publication Type: Article / Article
  • Volume: 42 Issue: 3
  • Publication Date: 2007
  • Doi Number: 10.1007/s10910-006-9111-z
  • Journal Indexes: Science Citation Index Expanded (SCI-EXPANDED), Scopus
  • Page Numbers: pp.415-422
  • Çanakkale Onsekiz Mart University Affiliated: No


Using complete orthonormal sets of Psi(alpha)-exponential type orbitals (Psi(alpha)-ETOs, alpha =1, 0, -1, -2, ...) introduced by the author, the series expansion formulae are derived for the two-center integer and noninteger n STO (ISTO and NISTO) charge densities in terms of integer n STOs at a third center. The expansion coefficients occurring in these relations are presented through the two-center overlap integrals between STOs with integer and noninteger principal quantum numbers. The general formulae obtained for the STO charge densities are utilized for the evaluation of two-center Coulomb and hybrid integrals of NISTOs appearing in the Hartee-Fock-Roothaan approximation. The final results are expressed in terms of both the overlap integrals and the one-center basic integrals over integer n STOs. It should be noted that the result for the multi-center multielectron integrals with two-center noninteger n STO charge densities presented in this paper were not appeared in our past publications.