The Generator Coordinate Method in Molecular Physics

  • P. Van Leuven
  • L. Lathouwers
Part of the NATO Advanced Study Institutes Series book series (volume 57)

Abstract

There are several reasons why a new method for the study of molecular properties might be proposed. According to some authors (Woolley, 1976; Woolley and Sutcliffe, 1977) there are inherent defects in the semiclassical theory resulting from the Born-Oppenheimer approximation. In the traditional method nuclei and electrons are treated unsymmetrically; the nuclei are considered as classical point charges in the initial stage of the theory. A number of concepts such as the energy surface and the molecular shape are introduced, the precise physical meaning and the theoretical consistency of which may be severely criticized. Although the complete adiabatic method yields an exact result in principle, in practice the nature of the convergence of the Born-Huang series and the complexity of the system of coupled differential equations to which it leads, seem to inhibit fruitful applications. Both of these aspects of the traditional molecular theory will be discussed elsewhere in this course.

Keywords

Helium Convolution Librium Peaked 

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References

  1. Brink, D.M. and Weiguny, A., 1968, Nucl. Phys. A120: 59.ADSGoogle Scholar
  2. Broeckhove, J., 1979, private communication.Google Scholar
  3. Caurier, E., 1975, in “Proceedings of the 2nd International Seminar on the GCM for nuclear Bound states and Reactions”, M. Bouten and P. Van Leuven, eds., S.C.K., Mol.Google Scholar
  4. Griffin, J.J. and Wheeler, J.A., 1957, Phys. Rev. 108: 311.ADSMATHCrossRefGoogle Scholar
  5. Hill, D.L. and Wheeler, J.A., 1953, Phys. Rev. 89: 1106.ADSGoogle Scholar
  6. Hurley, A.C., 1967, Int. J. Quant. Chem., 1S: 677.ADSGoogle Scholar
  7. Lathouwers, L., 1975, Ann. Phys. 102: 347.ADSGoogle Scholar
  8. Lathouwers, L., 1976, J. Math. Phys. 17: 1274ADSCrossRefGoogle Scholar
  9. Lathouwers, L. and Lozes, R., 1977, J. Phys. A10: 1465.MathSciNetADSGoogle Scholar
  10. Messiah, A., 1961, Quantum Mechanics, North Holland Publ., Amsterdam.Google Scholar
  11. Shavitt, I., 1962, Methods in Computational Physics 2, Ac. Press, New York.Google Scholar
  12. Thakkar, A.J. and Smith, V.H., Jr., 1976, Phys. Rev. A15: 15.Google Scholar
  13. Vincent, C.M., 1973, Phys. Rev. C8: 929.ADSGoogle Scholar
  14. Wiener, N., 1933, The Fourier Integral and some of its Applications, Cambridge University Press, Cambridge.Google Scholar
  15. Woolley, R.G., 1976, Adv. Phys. 25: 27.ADSCrossRefGoogle Scholar
  16. Woolley, R.G. and Sutcliffe, B.T., 1977, Chem. Phys. Letters, 45: 393.ADSCrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1980

Authors and Affiliations

  • P. Van Leuven
    • 1
  • L. Lathouwers
    • 1
  1. 1.Dienst Teoretische en Wiskundige Natuurkunde, Rijksuniversitair CentrumUniversity of AntwerpBelgium

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