Skip to main content
SpringerLink
Log in

One-range addition theorems for derivatives of Slater-type orbitals

  • Original Paper
  • Published:
Journal of Molecular Modeling Aims and scope Submit manuscript

Abstract

Using addition theorems for STOs introduced by the author with the help of complete orthonormal sets of ψα-ETOs (Guseinov II (2003) J Mol Model 9:190–194), where α=1, 0, −1, −2, ..., a large number of one-range addition theorems for first and second derivatives of STOs are established. These addition theorems are especially useful for computation of multicenter-multielectron integrals over STOs that arise in the Hartree–Fock–Roothaan approximation and also in the Hylleraas function method, which play a significant role for the study of electronic structure and electron–nuclei interaction properties of atoms, molecules, and solids. The relationships obtained are valid for arbitrary quantum numbers, screening constants and location of STOs.

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. Coolidge AS (1932) Phys Rev 42:189–209

    CAS  Google Scholar 

  2. Barnett MP, Coulson CA (1951) Philos Trans R Soc London Ser A 243:221–233

    Google Scholar 

  3. Löwdin PO (1956) Adv Phys 5:96–172

    Google Scholar 

  4. Harris FE, Michels HH (1965) J Chem Phys 43:S165-S174

    CAS  Google Scholar 

  5. Sharma RR (1976) Phys Rev A 13:517–531

    Article  Google Scholar 

  6. Filter E, Steinborn EO (1980) J Math Phys 21:2725–2736

    Article  Google Scholar 

  7. Guseinov II (1980) Phys Rev A 22:369–371

    Article  CAS  Google Scholar 

  8. Rashid MA (1981) J Math Phys 22:271–274

    Article  Google Scholar 

  9. Trivedi HP, Steinborn EO (1982) Phys Rev A 25:113–118

    Article  CAS  Google Scholar 

  10. Yamaguchi T (1983) Phys Rev A 27:646–651

    Article  CAS  Google Scholar 

  11. Guseinov II (1985) Phys Rev A 31:2851–2853

    Article  CAS  PubMed  Google Scholar 

  12. Weniger EJ (1985) J Math Phys 26:276–291

    Article  Google Scholar 

  13. Rico JF, Lopez R, Ramirez G (1988) Int J Quantum Chem 34:121–131

    Google Scholar 

  14. Weniger EJ, Steinborn EO (1989) J Math Phys 30:774–784

    Article  Google Scholar 

  15. Rico JF, Lopez R, Ramirez G (1989) J Chem Phys 91:4204–4212

    Article  Google Scholar 

  16. Jones HW (1992) Int J Quantum Chem 42:779–786

    CAS  Google Scholar 

  17. Bouferguebe A, Renaldi D (1994) Int J Quantum Chem 50:21–33

    Google Scholar 

  18. Fock VA (1935) Z Phys 98:145–152

    Google Scholar 

  19. Fock VA (1958) Kgl Norske Vidensk Forh 31:138–149

    Google Scholar 

  20. Shibuya T, Wulfman CE (1965) Proc R Soc London Ser A 286:376–385

    Google Scholar 

  21. Judd BR (1975) Angular momentum theory for diatomic molecules. Academic Press, New York

  22. Avery J (2002) Hyperspherical harmonics and generalized Sturmians. Kluwer, Dordrecht

  23. Avery J, Shim R (2001) Int J Quantum Chem 83:1–10

    Article  CAS  Google Scholar 

  24. Guseinov II (2002) Int J Quantum Chem 90:114–118

    Article  CAS  Google Scholar 

  25. Bouferguene A, Jones HW (1998) J Chem Phys 109:5718–5729

    Google Scholar 

  26. Kennedy HL, Zhao Y (1999) Int J Quantum Chem 71:1–13

    Article  CAS  Google Scholar 

  27. Barnett MP (2000) Int J Quantum Chem 76:464–472

    CAS  Google Scholar 

  28. Magnasco V, Rapallo A (2000) Int J Quantum Chem 79:91–100

    CAS  Google Scholar 

  29. Rico JF, Fernandez JJ, Ema I, Lopez R, Ramirez G (2001) J Comput Chem 81:16–28

    CAS  Google Scholar 

  30. Harris FE (2002) Int J Quantum Chem 88:701–734

    Article  CAS  Google Scholar 

  31. Safouhi H, Hoggan P (2002) Int J Quantum Chem 90:119–135

    Article  CAS  Google Scholar 

  32. Berli L, Safouhi H (2003) J Phys A: Math Gen 36:11791–11805

    Google Scholar 

  33. Guidotti C, Salvetti O, Durante N, Lamanna UT, Arrighini GP (2003) Int J Quantum Chem 93:59–71

    Article  CAS  Google Scholar 

  34. Barnett MP (2003) Int J Quantum Chem 95:791–805

    Article  CAS  Google Scholar 

  35. Latosinska JN (2003) Int J Quantum Chem 91:284–296

    Article  CAS  Google Scholar 

  36. Guseinov II (2003) J Mol Model 9:190–194

    Article  Google Scholar 

  37. Guseinov II 2004 J Phys A: Math Gen 37 : 957–964

    Google Scholar 

  38. Levine IN (2000) Quantum chemistry, 5th edn. Prentice Hall, Englewood Cliffs, N.J.

Download references

Author information

Authors and Affiliations

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

    Israfil Guseinov

Authors
  1. Israfil Guseinov
    View author publications

    You can also search for this author in PubMed Google Scholar

Corresponding author

Correspondence to Israfil Guseinov.

Rights and permissions

Reprints and permissions

About this article

Cite this article

Guseinov, I. One-range addition theorems for derivatives of Slater-type orbitals. J Mol Model 10, 212–215 (2004). https://doi.org/10.1007/s00894-004-0188-7

Download citation

  • Received:

  • Accepted:

  • Published:

  • Issue Date:

  • DOI: https://doi.org/10.1007/s00894-004-0188-7

Keywords

Search

Navigation