Advertisement

Theoretica Chimica Acta

, Volume 11, Issue 2, pp 135–144 | Cite as

The determination of SCF LCAO solutions for open shell configurations

  • Derek H. Sleeman
Commentationes

Abstract

A series of calculations has been carried out using the McWeeny and Roothaan Open Shell methods for determining LCAO-SCF solutions. The work reported here suggests that in order to obtain convergence to the absolute minimum with the McWeeny method it is often necessary to provide a very good initial approximation and that the rate of convergence could be improved by replacing the Steepest Descent by a more powerful minimization technique. Further the Roothaan method does not converge in all cases considered and it appears that Extrapolation techniques accelerate convergence but do not induce convergence in cases displaying oscillatory behaviour.

Keywords

Iterative Procedure Steep Descent Extrapolation Procedure Slater Type Orbital Diagonalization Method 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Zusammenfassung

LCAO-SCF-Rechnungen an offenen Schalen wurden nach den Methoden von Roothaan und McWeeny durchgeführt. Um bei dem McWeenyschen Verfahren Konvergenz zum absoluten Minimum zu erhalten, ist oft eine schon sehr gute Anfangsnäherung nötig. Die Methode des steilsten Abstiegs ist keineswegs optimal. Extrapolationsmethoden können wohl eine Konvergenz beschleunigen, nicht aber das beim Roothaan-Verfahren manchmal auftretende Oszillieren unterdrücken.

Résumé

On a exécuté des calculs LCAO SCF en couches ouvertes avec les méthodes de Roothaan et de McWeeny. Dans la méthode de McWeeny il est souvent nécessaire d'avoir une bonne approximation initiale, pour obtenir une convergence vers le minimum absolu. La méthode de descente le plus escarpé n'est pas optimale. Les méthodes d'extrapolation peuvent accélérer la convergence en effet, mais ils ne suppriment pas l'oscillation, qui arrive quelquefois dans la méthode de Roothaan.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Roothaan, C. C. J.: Rev. modem Physics32, 179 (1960).CrossRefGoogle Scholar
  2. 2.
    McWeeny, R.: Proc. Roy. Soc. (London) A241, 239 (1957).CrossRefGoogle Scholar
  3. 3.
    Sleeman, D. H.: Univ. of London. Ph. D. Thesis 1965.Google Scholar
  4. 4.
    Löwdin, P. O.: J. chem. Physics18, 365 (1950).CrossRefGoogle Scholar
  5. 5.
    Mulliken, R. S.: J. Chim. physique46, 497 (1949).Google Scholar
  6. 6.
    See Hatree, D. R.: “Numerical Analysis”. Clarendon Press 1958, or any standard Numerical Analysis text.Google Scholar
  7. 7.
    Roothaan, C. C. J., and P. S. Bagus: Methods in Computational Physics, Academic Press,2, 47 (1963).Google Scholar
  8. 8.
    Nesbet, R. K.: Quarterly Progress Reports, Solid State and Molecular Theory Group, M.I.T.18 (1955).Google Scholar
  9. 9.
    Csizmadia, I. G.: Private communication (1964).Google Scholar
  10. 10.
    McWeeny, R.: Physic. Rev.114, 1528 (1959).CrossRefGoogle Scholar
  11. 11.
    Fletcher, R., and M. J. D. Powell: Computer Journal6, 163 (1963).CrossRefGoogle Scholar
  12. 12.
    —, and C. M. Reeves: Computer Journal7, 149 (1964).CrossRefGoogle Scholar
  13. 13.
    Bradbury, W. W., and R. Fletcher: Numerische Mathematik9, 259 (1966).CrossRefGoogle Scholar
  14. 14.
    Rüdenberg, K.: J. chem. Physics19, 1433 (1951).CrossRefGoogle Scholar

Copyright information

© Springer-Verlag 1968

Authors and Affiliations

  • Derek H. Sleeman
    • 1
  1. 1.Electronic Computing LaboratoryThe University of LeedsLeeds 2England

Personalised recommendations