Skip to main content
SpringerLink
Log in
Book cover

Density Functional Methods in Chemistry pp 49–60Cite as

Symmetry and Local Potential Methods

  • Chapter

Abstract

The Xα method1 and its offspring are becoming more and more important in quantum chemistry for chemical systems that are too large for accurate configuration interaction (CI) calculations. All self-consistent-field (SCF) methods of quantum chemistry method begin with one or more systems of one-electron equations of the form,

$$\epsilon_i\phi_i(\textbf{r}) = [-\frac{1}{2}\bigtriangledown^2 + V]\phi_i(\textbf{r})\;\;\;(1)$$

.

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

Chapter
USD   29.95
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
eBook
USD   39.99
Price excludes VAT (USA)
  • Available as PDF
  • Read on any device
  • Instant download
  • Own it forever
Softcover Book
USD   54.99
Price excludes VAT (USA)
  • Compact, lightweight edition
  • Dispatched in 3 to 5 business days
  • Free shipping worldwide - see info

Tax calculation will be finalised at checkout

Purchases are for personal use only

Learn about institutional subscriptions

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. J.C. Slater, Quantum Theory of Molecules and Solids, Vol. 4 (McGraw-Hill, New York, 1974).

    Google Scholar 

  2. W. Kohn and L.J. Sham, Phys. Rev. 140, A1133 (1965).

    Article  Google Scholar 

  3. M. Levy, Phys. Rev. A 26, 1200 (1982).

    Article  CAS  Google Scholar 

  4. E.H. Lieb, Int. J. Quantum Chem. 24, 243 (1983).

    Article  CAS  Google Scholar 

  5. H. Englisch and R. Englisch, Physica 121A, 253 (1983).

    CAS  Google Scholar 

  6. D.M. Ceperley and B.J. Alder, Phys. Rev. Lett. 45, 566 (1980).

    Article  CAS  Google Scholar 

  7. B.I. Dunlap, J.W.D. Connolly and J.R. Sabin, J. Chem. Phys. 71, 3396; 4993 (1979).

    Article  CAS  Google Scholar 

  8. J.P. Perdew and A. Zunger, Phys. Rev. B 23, 5048 (1981).

    Article  CAS  Google Scholar 

  9. J.W.D. Connolly, in Modern Theoretical Chemistry, Vol. 7, ed. G.A. Segal (Plenum, New York, 1977) p. 105.

    Google Scholar 

  10. F. Herman and S. Skillman, Atomic Structure Calculations (Prentice-Hall, Englewood Cliffs, 1963).

    Google Scholar 

  11. A.D. Becke, I. J. Quantum Chem. 27, 585 (1985).

    Article  CAS  Google Scholar 

  12. L. Laaksonen, D. Sundholm and P. Pyykkö, Comp. Phys. Rept. 4, 313 (1986).

    Article  CAS  Google Scholar 

  13. D. Heinemann, B. Fricke and D. Kolb, Chem. Phys. Lett. 145, 125 (1988).

    Article  CAS  Google Scholar 

  14. W. Hehre, L. Radom, P.v.R. Schleyer, and J.A. Pople, Ab Initio Molecular Orbital Theory (Wiley-Interscience, New York, 1986).

    Google Scholar 

  15. E.J. Baerends, D.E. Ellis, and P. Ros, Chem. Phys. 2, 41 (1973).

    Article  CAS  Google Scholar 

  16. H. Sambe and R.H. Felton, J. Chem. Phys. 62, 1122 (1975).

    Article  CAS  Google Scholar 

  17. B.I. Dunlap and N. Rösch, in Density Functional Theory for Many-Fermion Systems, S.B. Trickey, editor, Adv. Quantum Chem., to be published.

    Google Scholar 

  18. J.W. Mintmire and B.I. Dunlap, Phys. Rev. A 25, 88 (1982).

    Article  CAS  Google Scholar 

  19. B.I. Dunlap, J. Chem. Phys. 78, 3140 (1983).

    Article  CAS  Google Scholar 

  20. B.I. Dunlap, J. Phys. Chem. 90, 5524 (1986).

    Article  CAS  Google Scholar 

  21. B.I. Dunlap and M. Cook, Int. J. Quantum Chem. 29, 767 (1986).

    Article  CAS  Google Scholar 

  22. B.I. Dunlap, Adv. Chem. Phys. 69, 287 (1987).

    Article  CAS  Google Scholar 

  23. J.W.D. Connolly, H. Siegbahn, U. Gelius, and C. Nordling, J. Chem. Phys. 58, 4265 (1973).

    Article  CAS  Google Scholar 

  24. B.I. Dunlap, P.A. Mills, and D.E. Ramaker, J. Chem. Phys. 75, 300 (1981).

    Article  CAS  Google Scholar 

  25. N.A. Baykara, B.N. McMaster, and D.R. Salahub, Moi. Phys. 52, 891 (1984).

    Article  CAS  Google Scholar 

  26. G.S. Painter, J. Phys. Chem. 90, 5530 (1986).

    Article  CAS  Google Scholar 

  27. B.I. Dunlap, Phys. Rev. A 29, 2902 (1984).

    Article  CAS  Google Scholar 

  28. B.I. Dunlap, Chem. Phys. 125, 89 (1988).

    Article  CAS  Google Scholar 

  29. L. Noodleman, J. Chem. Phys. 74, 5737 (1981).

    Article  CAS  Google Scholar 

  30. L. Noodleman, D.L. Case, and F. Sontum, J. Chim. Phys. Phys-chim. Biol. 86, 743 (1989).

    Google Scholar 

  31. F.W. Kutzler and G.S. Painter, Phys. Rev. Lett. 59, 1285 (1987).

    Article  CAS  Google Scholar 

  32. B.I. Dunlap and N. Rösch, J. Chim. Phys. Phys-chim. Biol. 86, 671 (1989).

    Google Scholar 

  33. N. Rösch, P. Knappe, P. Saudi, A. Görling, and B.I. Dunlap, in The Challenge of d and f Electrons. Theory and Computation, eds. D.R. Salahub and M.C. Zerner, ACS Symposium Series 394 (Washington 1989) p. 180.

    Google Scholar 

  34. B.I. Dunlap, Phys. Rev. A 41, 5691 (1990).

    Article  CAS  Google Scholar 

  35. B.I. Dunlap, Int. J. Quantum Chem. S22, 257 (1988).

    Article  Google Scholar 

  36. B.I. Dunlap and C.T. White, unpublished.

    Google Scholar 

  37. J.C. Slater, J.B. Mann, T.M. Wilson, and J.H. Wood, Phys. Rev., 184, 672 (1969).

    Article  CAS  Google Scholar 

  38. M. Cook and M. Karplus, J. Phys. Chem. 91, 31 (1987).

    Article  CAS  Google Scholar 

  39. B.I. Dunlap, Phys. Rev. A 25, 2847 (1982).

    Article  CAS  Google Scholar 

  40. J.F. Janak, Phys. Rev. B 18, 7165 (1978).

    Article  CAS  Google Scholar 

  41. C.W. Bauschlicher, Jr., and L.G.M. Pettersson, J. Chem. Phys. 87, 2198 (1987).

    Article  CAS  Google Scholar 

Download references

Authors
  1. Brett I. Dunlap
    View author publications

    You can also search for this author in PubMed Google Scholar

Editor information

Editors and Affiliations

  1. Ohio Supercomputer Center, 1224 Kinnear Road, Columbus, OH, 43212, USA

    Jan K. Labanowski

  2. Industry, Science, and Technology Department, Cray Research, Inc., 655 East Lone Oak Drive, Eagan, MN, 55121, USA

    Jan W. Andzelm

Rights and permissions

Reprints and permissions

Copyright information

© 1991 Springer-Verlag New York, Inc.

About this chapter

Cite this chapter

Dunlap, B.I. (1991). Symmetry and Local Potential Methods. In: Labanowski, J.K., Andzelm, J.W. (eds) Density Functional Methods in Chemistry. Springer, New York, NY. https://doi.org/10.1007/978-1-4612-3136-3_4

Download citation

  • DOI: https://doi.org/10.1007/978-1-4612-3136-3_4

  • Publisher Name: Springer, New York, NY

  • Print ISBN: 978-1-4612-7809-2

  • Online ISBN: 978-1-4612-3136-3

  • eBook Packages: Springer Book Archive

Publish with us

Policies and ethics

Search

Navigation