Theoretica chimica acta

, Volume 65, Issue 4, pp 233–242 | Cite as

A principle of linear covariance for quantum mechanics and the electronic structure theory of molecules and other atom clusters

  • Oktay Sinanoğlu
Original Investigations

Abstract

Quantum mechanical equations should look the same in any non-orthonormal or orthonormal basis frame when properly formulated so as to be fully covariant under the largest group indicated. Non-orthonormal frames are crucial especially for the quantum theory of chemistry. Various methods such as valence-bond, localized orbital, molecular orbital, etc. result from a single formulation using the principle of linear covariance which is stated, proved, and exemplified. Molecular quantities with the full inclusion of overlaps are derived with the same ease as without overlaps.

Key words

Linear covariance atom clusters electronic structure theory 

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    Dirac, P. A. M.: Principles of quantum mechanics, 4th Ed., Oxford: University Press 1958Google Scholar
  2. 2.
    Condon, E. U., Shortley, G. H.: The theory of atomic spectra, Cambridge: University Press 1963Google Scholar
  3. 3.
    Slater, J. C.: Quantum theory of atomic structure, Vol. I. New York: McGraw-Hill 1960Google Scholar
  4. 4.
    Sinanoğlu, O.: Rev. Mod. Phys. 35, 517 (1963); Advances in Chem. Phys. VI, 315 (1964); XIV, 237 (1968); Atomic physics, Vol. I pp. 131 ff (New York: Plenum Press 1969)Google Scholar
  5. 6.
    Sinanoğlu, O. Westhaus, P.: Phys. Rev. 183, 56 (1969); cf. also Int. J. Qu. Chem. 3s, 391 (1970)Google Scholar
  6. 7.
    Bashkin, S.: Topics in Current Physics I, 1 (1976)Google Scholar
  7. 8.
    Sinanoğlu, O., Öksüz, I.: Phys. Rev. Letts. 21, 507 (1968); Sinanoğlu, O.: Topics in Current Physics I, 111 (1976)Google Scholar
  8. 9.
    Specialized formalisms were developed as the need arose (notably the work of Löwdin, P. O.: Advs. Chem. Phys. II, 207 (1959) but by-and-large the non-O.N.'ity problem remained a constriction between a fundamental qualitative theory and the calculation methods (cf. O.S. Ref. in 5)Google Scholar
  9. 10.
    Pauling, L.: The nature of the chemical bond, 3rd Ed. Ithaca: Cornell Univ. Press 1960Google Scholar
  10. 11.
    Coulson, C. A.: Valence, 2nd Ed. Oxford: University Press: 1961Google Scholar
  11. 12.
    Hückel, E.: Z. Physik 70, 204 (1931)Google Scholar
  12. 13.
    Feynman, R. P.: Lectures in physics. London: Addison Wesley 1960Google Scholar
  13. 14.
    Sinanoğlu, O.: in Chemical spectroscopy and photochemistry in the vacuum ultraviolet, C. Sandorfy et al. ed. pp. 337–384, Dordrecht: D. Reidel, 1974Google Scholar
  14. 15.
    Lennard-Jones, J. E. Ann. Rev. Phys. Chem. 4, 167 (1953)Google Scholar
  15. 16.
    cf. the review on other works and references: Sinanoğlu, O., Tuan, D. F.: Ann. Rev. Phys. Chem. 15, 251 (1964)Google Scholar
  16. 17.
    Luken, W. L. in press, 1983Google Scholar
  17. 18.
    Wigner, E., Witmer, E. E.: Z. Physik 51, 859 (1928)Google Scholar
  18. 19.
    Walsh, A. D.: J. Chem. Soc. 2260 (1953)Google Scholar
  19. 20.
    Woodward, R. B., Hoffmann, R.: J. Am. Chem. Soc., 87, 395 (1965)Google Scholar
  20. 21.
    Daudel R., Sandorfy, C.: New Haven and London: Semi-empirical wave-mechanical calcns. on polyatomic molecules. Yale Press 1971Google Scholar
  21. 22.
    Sinanoğlu, O., Wiberg, K. B.: Sigma MO theory New Haven and London: Yale Press 1970Google Scholar

Copyright information

© Springer-Verlag 1984

Authors and Affiliations

  • Oktay Sinanoğlu
    • 1
  1. 1.Sterling Chemistry LaboratoryYale UniversityNew HavenUSA

Personalised recommendations