Skip to main content
SpringerLink
Log in

Expansion Formulae for Two-center Integer and Noninteger n STO Charge Densities and their Use in Evaluation of Multi-center Integrals

  • Published:
Journal of Mathematical Chemistry Aims and scope Submit manuscript

Using complete orthonormal sets of Ψα-exponential type orbitals (Ψα-ETOs, α =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.

This is a preview of subscription content, log in via an institution to check access.

Access this article

Log in via an institution

Price excludes VAT (USA)
Tax calculation will be finalised during checkout.

Instant access to the full article PDF.

Institutional subscriptions

Similar content being viewed by others

References

  1. Kato T. (1957). Commun. Pure Appl. Math. 10:151

    Article  Google Scholar 

  2. Agmon S. (1982). Lectures on Exponential Decay of Solutions of Second-Order Elliptic Equations: Bounds on Eigenfunctions of N-Body Schrödinger Operators. Princeton University Press, Princeton, NJ

    Google Scholar 

  3. Coolidge A.S. (1932). Phys. Rev. 42:189

    Article  CAS  Google Scholar 

  4. Landshoff R. (1936). Z. Phys. 102:201

    Article  CAS  Google Scholar 

  5. Löwdin P.O. (1947). Ark Mat Fys Astron. A 35:9

    Google Scholar 

  6. Barnett M.P. and Coulson C.A. (1951). Philos. Trans. R Soc London, Ser. A 243:221

    Article  Google Scholar 

  7. Harris F.E. and Michels H.H. (1965). J. Chem. Phys 43:S165

    Article  CAS  Google Scholar 

  8. Harris F.E. and Michels H.H. (1966). J. Chem. Phys. 45:116

    Article  CAS  Google Scholar 

  9. Sharma R.R. (1976). Phys Rev A 13:517

    Article  Google Scholar 

  10. I.I. Guseinov J. Chem. Phys. 65 (1976) 4718, 69 (1978) 4990; Phys. Rev. A 22 (1980) 369, 31 (1985) 2851; Int. J. Quantum Chem. 81 (2001) 126.

  11. Fernandez Rico J., Lopez R., Ema I., Ramirez G. (2005). J. Comput. Chem 26:846

    Article  CAS  Google Scholar 

  12. Bouferguene A. (2005). J. Phys. A: Math Gen. 38:2899

    Article  Google Scholar 

  13. Silverstone H.J. (1967). J. Chem. Phys 47:537

    Article  CAS  Google Scholar 

  14. Silverstone H.J. and Moats R.K. (1977). Phys. Rev. 16:1731

    Article  Google Scholar 

  15. Kay K.G. and Silverstone H.J. (1969). J. Chem. Phys. 51:4287

    Article  CAS  Google Scholar 

  16. Steinborn E.O. and Filter E. (1975). Theor. Chim. Acta 38:247

    Article  CAS  Google Scholar 

  17. Filter E. and Steinborn E.O. (1980). J. Math. Phys 21:2725

    Article  Google Scholar 

  18. Mekelleche S.M. and Baba-Ahmed A. (2000). Theor. Chem. Acc 103:463

    CAS  Google Scholar 

  19. Guseinov I.I. (2002). Int. J. Quantum Chem. 90:114

    Article  CAS  Google Scholar 

  20. Gradshteyn I.S. and Ryzhik I.M. (1980). Tables of Integrals, Sums, Series and Products, 4th ed. Academic Press, New York

    Google Scholar 

  21. Guseinov I.I. (1970). J. Phys. B 3:1399

    Article  Google Scholar 

  22. Guseinov I.I. (1997). J. Mol. Struct (Theochem) 417:117

    Article  CAS  Google Scholar 

  23. Guseinov I.I., Mamedov B.A. (2005). J. Math. Chem 37:353

    Article  CAS  Google Scholar 

  24. Guseinov I.I. and Mamedov B.A. (2002). J. Mol. Model. 8:272

    Article  CAS  Google Scholar 

  25. Guseinov I.I. and Mamedov B.A. (2002). Theor. Chem. Acc. 108:21

    CAS  Google Scholar 

Download references

Author information

Authors and Affiliations

  1. Department of Physics, Faculty of Arts and Sciences, Onsekiz Mart University, Çanakkale, Turkey

    I. I. Guseinov

Authors
  1. I. I. Guseinov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to I. I. Guseinov.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Guseinov, I.I. Expansion Formulae for Two-center Integer and Noninteger n STO Charge Densities and their Use in Evaluation of Multi-center Integrals. J Math Chem 42, 415–422 (2007). https://doi.org/10.1007/s10910-006-9111-z

Download citation

  • Received:

  • Revised:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s10910-006-9111-z

Keywords

Search

Navigation