Skip to main content
Log in

A generalized restricted open-shell Fock operator

  • Published:
Theoretica chimica acta Aims and scope Submit manuscript

Abstract

We reexamine the open shell restricted Hartree-Fock theory and develop Fock-like operators that are quite general and easy to implement on a computer. We present a table of ‘vector coupling coefficients’ that define this operator for most of the cases that commonly arise. We compare the form of this operator with that suggested by others, and discuss the orbitals obtained by this procedure with respect to the generalised Brillouin's theorem, and the orbital energies with respect to Koopmans' approximation.

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

Access this article

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

Instant access to the full article PDF.

Similar content being viewed by others

References and notes

  1. Roothaan CCJ (1952) Rev Mod Phys 22:571

    Google Scholar 

  2. Hall GG 1(51) Proc R Soc London A 205:541

    Google Scholar 

  3. Pople JA, Nesbet RK (1954) J Chem Phys 22:571

    Google Scholar 

  4. The popular Gaussian series of programs by Pople JA and his co-workers is, for example, based on the UHF theory for open-shell SCF for Møller-Plesset Perturbation Theory. Binkley JS, Frisch MJ, DeFrees DJ, Raghavachari K, Whitesides HB, Schlegel HB, Fluder EM, Pople JA, Department of Chemistry, Carnegie Mellon University, Pittsburgh, Pa

  5. Löwdin PO (1959) Adv Chem Phys 2:207

    Google Scholar 

  6. Löwdin PO (1966) Quantum theory of atoms, molecules and the solid state. Academic Press, New York London

    Google Scholar 

  7. Kengsfield III, BH, Schug JC (1978) Mol Phys 35:1113

    Google Scholar 

  8. Amos T, Snyder LC (1964) J Chem Phys 41:1773

    Google Scholar 

  9. Amos AT, Hall GG (1961) Proc R Soc London A 263:483

    Google Scholar 

  10. Bacon AD, Zerner MC (1979) Theor Chim Acta 53:21

    Google Scholar 

  11. Binkley JS, Pople JA (1975) Int J Quantum Chem 9:229

    Google Scholar 

  12. Bartlett RJ (1981) Ann Rev Phys Chem 32:359

    Google Scholar 

  13. Sosa C, Schlegel HB: Int J Quantum Chem, in press

  14. Roothaan CCJ (1960) Rev Mod Phys 32:179

    Google Scholar 

  15. see, for example: Pauncz R (1979) Spin eigenfunctions. Plenum Press, New York; or Shavitt I (1977) In: Schaeffer III HF (ed) Methods of electronic structure theory. Plenum Press, New York

    Google Scholar 

  16. Birss FW, Fraga S (1963) J Chem Phys 38:2552

    Google Scholar 

  17. Huzinaga S (1969) J Chem Phys 60:3215;

    Google Scholar 

  18. Huzinaga S (1961) Phys Rev 122:131

    Google Scholar 

  19. Hirao K, Nakatsuji H (1973) J Chem Phys 59:1457

    Google Scholar 

  20. Hirao K (1974) J Chem Phys 60:3215

    Google Scholar 

  21. Silverstone HJ (1977) J Chem Phys 67:4172

    Google Scholar 

  22. Caballol R, Gallifa R, Riera JM, Carbo R (1974) Int J Quantum Chem 8:373;

    Google Scholar 

  23. Carbo R, Domingo LL, Gregori J (1980) Int J Quantum Chem 17:725;

    Google Scholar 

  24. Carbo R, Riera JM (1978) A general SCF theory. Lect Notes Chem, vol 5. Springer, Berlin Heidelberg New York

    Google Scholar 

  25. Morikawa T (1980) J Chem Phys 73:1303

    Google Scholar 

  26. Davidson ER (1973) Chem Phys Lett 21:565;

    Google Scholar 

  27. Jackels CF, Davidson ER (1974) Int J Quantum Chem 8:707

    Google Scholar 

  28. Pople JA, Beveridge DL, Dobosh PA (1967) J Chem Phys 47:2026

    Google Scholar 

  29. Ridley JE, Zerner MC (1973) Theor Chim Acta 32:111

    Google Scholar 

  30. Edwards WD, Weiner B, Zerner MC (1986) J Am Chem Soc 108:2196

    Google Scholar 

  31. Veillard A (1975) In: Diercksen GHF, Sutcliffe BT, Veillard A (eds) Computational techniques in quantum chemistry. NATO Advanced Series C. D. Reidel, Boston

    Google Scholar 

  32. Levy B, Berthier G (1968) Int J Quantum Chem 2:307

    Google Scholar 

  33. Jorgensen P, Simons J (1981) Second quantization-based methods in quantum chemistry. Academic Press, New York

    Google Scholar 

  34. Yaffe LG, Goddard III WA (1976) Phys Rev A 13:1682:see also Bobrowicz FW, Goddard III WA (1977) In: Schaeffer III HF (ed) Methods of electronic structure theory. Plenum Press, New York

    Google Scholar 

  35. Koopmans TA (1933) Physica 1:104

    Google Scholar 

  36. a Not unique. Such situations should be followed by configuration interaction treatment within the active orbital manifoldbIn theD 2h subgroups of the octahedron, thed(τ) orbitals belong to different irreducible representations. Similarly in theC 2v subgroup of the tetrahedron, thed(τ) orbitals belong to different irreducible representations. Only if the orbitals are subgroup basis do the above expressions hold.N= total number of electrons;M= number of open shell orbitals;Op= number of open shell operators;n μ = occupation number for shellμ = N/M; ↑ represents anα electron; ↓ represents aβ electron; ↕ represents a doubly occupied orbital. The last eight cases representd orbitals in an octahedral field

Download references

Author information

Authors and Affiliations

Authors

Additional information

Dedicated to Professor J. Koutecký on the occasion of his 65th birthday

Rights and permissions

Reprints and permissions

About this article

Cite this article

Edwards, W.D., Zerner, M.C. A generalized restricted open-shell Fock operator. Theoret. Chim. Acta 72, 347–361 (1987). https://doi.org/10.1007/BF01192227

Download citation

  • Received:

  • Revised:

  • Accepted:

  • Issue Date:

  • DOI: https://doi.org/10.1007/BF01192227

Key words

Navigation