Theoretica chimica acta

, Volume 52, Issue 1, pp 55–66 | Cite as

Possible artifacts occurring in the calculation of intermolecular energies from delocalized pictures

  • J. P. Malrieu
  • F. Spiegelmann
Original Investigations


The intermolecular energy between two identical subsystems may be calculated from symmetrydelocalized MO's resulting for instance from a preliminary SCF calculation of the supersystem. Then each second-order energy correction mixes intramolecular correlation,R−6 intermolecular dispersion energy, andR−3 components. TheR−3 components disappear through subtle cancellations. The shifted Epstein-Nesbet energy denominators introduce an artificial second-order intermolecularR−1 component, which would be cancelled by off-diagonal third-order terms, as well as a bad asymptotic limit at infinite distances. TheR−1 artifact will also occur in strong symmetrical chemical bonds calculated in the Epstein-Nesbet perturbation scheme from delocalized MO's. These defects will occur in all variational approximate CI techniques which neglect off-diagonal elements between delocalized doubly excited determinants. These artifacts are avoided when using the Moller-Plesset definition of the zeroth order Hamiltonian or when starting from (SCF)localized MO's (even in the Epstein-Nesbet perturbation). The discussion is exemplified on an accurateab initio calculation of the Ar2 molecule.

Key words

Delocalized MOs 


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  1. 1.
    London, F.: Trans. Faraday Soc.33, 8 (1937); Margenau, M.: Rev. Mod. Phys.11, 1 (1939); Hirschfelder, J. O.: Intermolecular forces, Advan. Chem. Phys.12, 3 (1967)Google Scholar
  2. 2.
    Claverie, P.: Intern. J. Quantum Chem.5, 273 (1971); Thesis Univ. P. et M. Curie, Paris (1973)Google Scholar
  3. 3.
    Claverie, P.: Intermolecular interactions: from diatomics to biopolymers, B. Pullman (ed.). New York: John Wiley 1978Google Scholar
  4. 4.
    Murrel, J. N., Shaw, G. J.: Chem. Phys.49, 4731 (1968); Murrel, J. N., Teixeria Dias, J. J. C.: Mol. Phys.19, 521 (1970); Certain, P. R.: J. Chem. Phys.55, 3045 (1971); Daudey, J. P., Claverie, P., Malrieu, J. P.: Intern. J. Quantum Chem.8, 1 (1974); Daudey, J. P., Malrieu, J. P., Rojas, O.: Intern. J. Quantum Chem.8, 17 (1974); Daudey, J. P.: Intern. J. Quantum Chem.8, 29 (1974); Kochanski, E., Gouyet, J. F.: Mol. Phys.29, 693 (1975)Google Scholar
  5. 5.
    Bertoncini, P., Wahl, A. C.: Phys. Rev. Letters25, 991 (1970)Google Scholar
  6. 6.
    Schaeffer III, M. F., McLaughlin, D. R., Harris, F. E., Alder, B. J. Phys. Rev. Letters25, 988 (1970)Google Scholar
  7. 7.
    McLaughlin, D. R., Schaefer III, H. F.: Chem. Phys. Letters12, 244 (1971)Google Scholar
  8. 8.
    Liu, B., McLean, A. D.: J. Chem. Phys.59, 4557 (1973)Google Scholar
  9. 9.
    Matsuoka, O., Clementi, E., Yoshimine, M.: J. Chem. Phys.64, 1351 (1976)Google Scholar
  10. 10.
    Brueckner, K. A., in: The many-body problem. New York: Wiley 1959Google Scholar
  11. 11.
    Claverie, P., Diner, S., Malrieu, J. P.: Intern. J. Quantum Chem.1, 751 (1967)Google Scholar
  12. 12.
    Moller, C., Plesset, M. S.: Phys. Rev.46, 618 (1934)Google Scholar
  13. 13.
    Epstein, P. S.: Phys. Rev.28, 695 (1926)Google Scholar
  14. 14.
    Nesbet, R. K.: Proc. Roy. Soc. A230, 312, 322 (1955)Google Scholar
  15. 15.
    Spiegelmann, F., Malrieu, J. P.: Chem. Phys. Letters57, 214 (1978)Google Scholar
  16. 16.
    Durand, Ph., Barthelat, J. C.: Theoret. Chim. Acta (Berl.)38, 283 (1975); Durand, Ph., Barthelat, J. C., Serafini, A.: Mol. Phys.33, 159 (1977)Google Scholar
  17. 17.
    Parson, J. M., Siska, P. E., Lee, Y. T.: J. Chem. Phys.56, 1511 (1972); Tanaka, Y., Yoshino, K.: J. Chem. Phys.53, 2012 (1970); Leroy, R. J.: J. Chem. Phys.57, 573 (1972); Rae, A. I. M.: J. Chem. Phys.29, 467 (1975)Google Scholar
  18. 18.
    Morokuma, K., Perdersen, C.: J. Chem. Phys.48, 3275 (1968); Clementi, E.: J. Chem. Phys.46, 3851 (1967); Daudey, J. P., Claverie, P., Malrieu, J. P.: Intern. J. Quantum Chem.8, 1 (1974); Daudey, J. P.: Intern. J. Quantum Chem.8, 29 (1974)Google Scholar
  19. 19.
    Gershgorn, Z., Shavitt, I: Intern. J. Quantum Chem.2, 751 (1968)Google Scholar
  20. 20.
    Sinanoğlu, O.: J. Chem. Phys.36, 706, 3198 (1962)Google Scholar
  21. 21.
    Nesbet, R. K.: Advan. Chem. Phys.9, 321 (1965)Google Scholar
  22. 22.
    Langhoff, S. R., Davidson, E. R.: Intern. J. Quantum Chem.8, 61 (1974)Google Scholar
  23. 23.
    Segal, G. A., Wetmore, R. W.: Chem. Phys. Letters32, 556 (1975); Segal, G. A., Wetmore, R. W., Wolf, K.: Chem. Phys.30, 269 (1978)Google Scholar
  24. 24.
    Buenker, R. J., Peyerimhoff, S. D.: Theoret. Chim. Acta (Berl.)35, 33 (1974);39, 217 (1975)Google Scholar

Copyright information

© Springer-Verlag 1979

Authors and Affiliations

  • J. P. Malrieu
    • 1
  • F. Spiegelmann
    • 1
  1. 1.Laboratoire de Physique QuantiqueUniversité Paul SabatierToulouse CedexFrance

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