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A variational coupled cluster theory for closed shells using a propagator modification procedure

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Abstract

A general partial summation method for including arbitrary classes of diagrams to all orders in the coupled cluster based size consistent energy functional for closed shell states is developed. Since the various reduced density matrices which appear in the energy functional are essentially the time-independent analogues of the corresponding many body Green functions, it is possible to derive Dyson-like equations for these quantities. By expanding the associated “proper” self energy parts in terms of the T-amplitudes, one can carry out partial summations in the reduced density matrices and thus in energy. At a higher level, higher order terms in a “proper” self energy can also be generated by renormalizing the internal propagators in it, and considering only the “irreducible” self-energy terms.

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References

  1. Coester, F.: Nucl. Phys. 7, 421 (1958); Coester, F. and Kümmel, H.: Nucl. Phys. 17, 477 (1960)

    Google Scholar 

  2. Čižek, J.: J. Chem. Phys. 45, 4256 (1966); Čižek, J.: Adv. Chem. Phys. 14, 35 (1969); Paldus, J., Čižek, J., Shavitt, I.: Phys. Rev. A5, 50 (1972); Čižek, J., Paldus, J.: Phys. Scripta. 21, 251 (1980)

    Google Scholar 

  3. Nakatsuji, H., Hirao, K.: J. Chem. Phys. 68, 2053, 4279 (1978); Nakatsuji, H.: Chem. Phys. Lett. 59, 362 (1978); Paldus, J., Čižek, J., Shavitt, I.: Phys. Rev. A5, 50 (1972); Harris, F. E.: Int. J. Quantum Chem. S11, 403 (1977)

    Google Scholar 

  4. Primas, H.: Modern Quantum Chemistry. Sinanoğlu, O. (ed.) Vol. II, p. 45. New York: Academic Press, 1965

    Google Scholar 

  5. Pople, J. A., Binkley, J. S., Seeger, R.: Int. J. Quantum Chem. S10, 1 (1976)

    Google Scholar 

  6. Pople, J. A., Krishnan, R., Schlegel, H. B., Binkley, J. S.: Int. J. Quantum Chem. 14, 545 (1978); Taylor, P. R., Bacskey, G. B., Hurley, A. C., Hush, N. S.: J. Chem. Phys. 41, 1976 (1971); Bartlett, R. J., Purvis, G. D.: Int. J. Quantum Chem. 14, 561 (1978); Bartlett, R. J.: Ann. Rev. Phys. Chem. 32, 359 (1981); Koch, S., Kutzelnigg, W.: Theoret. Chem. Acta (Berl.) 59, 387 (1981); Chilles, R. A., Dykstra, C.: J. Chem. Phys. 74, 4544 (1981)

    Google Scholar 

  7. Bartlett, R. J., Purvis, G. D.: Ann. NY Acad. Sci. 367, 62 (1981); Bartlett, R. J., Purvis, G. D.: Phys. Scr. 21, 255 (1980)

    Google Scholar 

  8. Kutzelnigg, W.: Modern Theoretical Chemistry. Schaefer, H. F. (ed.) Vol. III, p. 129. New York: Plenum Press, 1977

    Google Scholar 

  9. Van Vleck, J. H.: Phys. Rev. 33, 467 (1929); Jordahl, O. M.: Phys. Rev. 45, 87 (1934); Kemble, E. C.: Fundamental Principles of Quantum Mechanics. New York: McGraw-Hill 1937

    Google Scholar 

  10. Pal, S., Durga Prasad, M., Mukherjee, D.: Theoret. Chim. Acta (Berl.) 62, 523 (1983); Pal, S., Durga Prasad, M., Mukherjee, D.: Pramana, 18, 261 (1982)

    Google Scholar 

  11. Reitz, H., Kutzelnigg, W.: Chem. Phys. Lett. 66, 111 (1979); Kutzelnigg, W.: J. Chem. Phys. 77, 3081 (1982); Koch, S., Kutzelnigg, W.: J. Chem. Phys. 79, 4315 (1983); Kutzelnigg, W.: J. Chem. Phys. 80, 822 (1984)

    Google Scholar 

  12. Pal, S., Durga Prasad, M., Mukherjee, D.: Theoret. Chim. Acta (Berl.), 66, 311 (1984)

    Google Scholar 

  13. Three Approaches to Electron Correlation in Atoms. Sinanoğlu, O., Bruckner, K. (eds.) p. 203. New Haven: Yale Univ. Press 1970

    Google Scholar 

  14. Emery, V. J.: Nucl. Phys. 6, 385 (1958); Bell, J. S., Squires, E. J.: Adv. Phys. 10, 21 (1962); Schaeffer, K., Schutte, G.: Nucl. Phys. A183, 1 (1972)

    Google Scholar 

  15. Noziers, P.: Theory of Interacting Fermi Systems. New York: Benjamin 1964; Linderberg, J., Öhrn, Y.: Propagators in Quantum Chemistry. New York: Acad. Press 1973; Cederbaum, L. S., Domcke, W.: Adv. Chem. Phys. 36, 205 (1977)

    Google Scholar 

  16. Jones, R. W., Mohling, F., Beeker, R. L.: Nucl. Phys. A 220, 45 (1974); Brandow, B. H.: Phys. Rev. 152, 863 (1966)

    Google Scholar 

  17. Durga Prasad, M., Pal, S., Mukherjee, D.: J. Chem. Soc. Faraday II, 78, 1743 (1982)

    Google Scholar 

  18. Fetter, A. L., Walecka, J. D.: Quantum Theory of Many Particle Systems. New York: McGraw-Hill 1971

    Google Scholar 

  19. Mukherjee, D., Bhattacharyya, D.: Mol. Phys. 34, 773 (1977); Mukherjee, D., Bhattacharyya, D.: Pramana, 13, 535 (1979); Ghosh, S., Bhattacharyya, S., Mukherjee, D.: Chem. Phys. 72, 161 (1982)

    Google Scholar 

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Authors and Affiliations

  1. Theoretical Chemistry Group, Physical Chemistry Division, National Chemical Laboratory, 411008, Pune, India

    Sourav Pal

  2. Theory Group, Department of Physical Chemistry, Indian Association for the Cultivation of Science, 700032, Calcutta, India

    M. Durga Prasad & Debashis Mukherjee

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  1. Sourav Pal
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  2. M. Durga Prasad
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  3. Debashis Mukherjee
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Pal, S., Durga Prasad, M. & Mukherjee, D. A variational coupled cluster theory for closed shells using a propagator modification procedure. Theoret. Chim. Acta 68, 125–138 (1985). https://doi.org/10.1007/BF00527528

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