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The Unitary Group and the Electron Correlation Problem

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New Horizons of Quantum Chemistry

Part of the book series: International Academy of Quantum Molecular Science ((QUCH,volume 4))

Abstract

A survey is given of the background and development of the unitary group approach and its graphically-based implementations for electronic structure calculations. The nature of the unitary group and its relationship to the electronic many-body problem are briefly discussed, as well as the reasons, purpose, and methodology of its application to this problem. As much as possible, this discussion is on a mostly intuitive, non-technical level. Finally, recent accomplishments and expected future developments are briefly mentioned.

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References

  1. Paldus, J.: 1976, in “Theoretical Chemistry: Advances and Perspectives,” Vol. 2, edited by H. Eyring and D. G. Henderson Academic Press, New York ), p. 131.

    Google Scholar 

  2. Gelfand, I. M., and Tsetlin, M. L.: 1950, Dokl. Akad. Nauk SSSR 71, p. 825, p. 1017.

    Google Scholar 

  3. Matsen, F. A.: 1974, Int. J. Quantum Chem. Symp. 8, p. 379.

    Article  CAS  Google Scholar 

  4. Jordan, P.: 1935, Z. Phys. 94, p. 531.

    Article  Google Scholar 

  5. Weyl, H.: 1939, “The Classical Groups, Their Invariants and Representations” (Princeton University Press, Princeton, New Jersey).

    Google Scholar 

  6. Biedenharn, L. C.: 1963, J. Math. Phys. 4, p. 436

    Article  Google Scholar 

  7. Baird, G. E., and Beidenharn, L. C.: 1963, J. Math. Phys. 4, p. 1449

    Article  Google Scholar 

  8. Louck, J. D., and Beidenharn, L. C.: 1970, J. Math. Phys. 11, p. 2386.

    Article  Google Scholar 

  9. Moshinsky, M.: 1963, J. Math. Phys. 4, p. 1128.

    Article  Google Scholar 

  10. Paldus, J.: 1974, J. Chem. Phys. 61, p. 5321.

    Article  CAS  Google Scholar 

  11. Moshinsky, M.: 1968, “Group Theory and the Many-Body Problem” ( Gordon and Breach, New York).

    Google Scholar 

  12. Paldus, J.: 1975, Int. J. Quantum Chem. Symp. 9, p. 165.

    Article  CAS  Google Scholar 

  13. Paldus, J.: 1976, Phys. Rev. A 14, p. 1620.

    Article  CAS  Google Scholar 

  14. Paldus, J.: 1977, in “Electrons in Finite and Infinite Structures,” edited by P. Phariseau and L. Scheire ( Plenum, New York ), p. 411.

    Google Scholar 

  15. Paldus, J.: 1979, in “Group Theoretical Methods in Physics,” edited by W. Beiglbock, A. Bohm, and E. Takasugi ( Springer, New York ), p. 51.

    Chapter  Google Scholar 

  16. Wormer, P. E. S., and Paldus, J.: 1979, Int. J. Quantum Chem. 16, p. 1307

    Article  CAS  Google Scholar 

  17. Paldus, J., and Wormer, P. E. S.: 1979, Int. J. Quantum Chem. 16, p. 1321

    Article  CAS  Google Scholar 

  18. Paldus, J., and Wormer, P. E. S.: 1981, Int. J. Quantum Chem. 18, p. 841.

    Google Scholar 

  19. Paldus, J., and Boyle, M. J.: 1980, Phys. Scripta 21, p. 295.

    Article  CAS  Google Scholar 

  20. Paldus, J.: 1981, in “The Unitary Group for the Evaluation of Electronic Energy Matrix Elements” (Lecture Notes in Chemistry 22), edited by J. Hinze ( Springer, Berlin ), p. 1.

    Google Scholar 

  21. Shavitt, I.: 1977, Int. J. Quantum Chem. Symp. 11, p. 131.

    Google Scholar 

  22. Shavitt, I.: 1978, Int. J. Quantum Chem. Symp. 12, p. 5.

    CAS  Google Scholar 

  23. Shavitt, I.: 1979, Chem. Phys. Lett. 63, p. 421.

    Article  CAS  Google Scholar 

  24. Shavitt, I.: 1981, in “The Unitary Group for the Evaluation of Electronic Energy Matrix Elements” (Lecture Notes in Chemistry 22), edited by J. Hinze ( Springer, Berlin ), p. 51.

    Google Scholar 

  25. Brooks, B. R., and Schaefer III, H. F.: 1979, J. Chem. Phys. 70, p. 5092.

    Article  CAS  Google Scholar 

  26. Brooks, B. R., Laidig, W. D., Saxe, P., Handy, N. C., and Schaefer III, H. F.: 1980, Phys. Scripta 21, p. 312.

    Article  CAS  Google Scholar 

  27. Siegbahn, P. E. M.: 1979, J. Chem. Phys. 70, p. 5391.

    Article  CAS  Google Scholar 

  28. Siegbahn, P. E. M.: 1980, J. Chem. Phys. 72, p. 1647.

    Article  CAS  Google Scholar 

  29. Siegbahn, P. E. M.: 1981, in “The Unitary Group for the Evaluation of Electronic Energy Matrix Elements” (Lecture Notes in Chemistry 22), edited by J. Hinze ( Springer, Berlin ), p. 119.

    Google Scholar 

  30. Lischka, H., Shepard, R., Brown, F. B., and Shavitt, I.: 1981, Int. J. Quantum Chem. Symp. 15, p. 91.

    CAS  Google Scholar 

  31. Shavitt, I.: 1977, in “Methods of Electronic Structure Theory” (“Modern Theoretical Chemistry,” Vol. 3), edited by H. F. Schaefer III ( Plenum, New York ), p. 189.

    Google Scholar 

  32. Roos, B. O.: 1972, Chem. Phys. Lett. 15, p. 153.

    Article  Google Scholar 

  33. Roos, B. O., and Siegbahn, P. E. M.: 1977, in “Methods of Electronic Structure Theory” (“Modern Theoretical Chemistry,” Vol. 3), edited by H. F. Schaefer III ( Plenum, New York ), p. 277.

    Google Scholar 

  34. Lucchese, R. R., and Schaefer III, H. F.: 1978, J. Chem. Phys. 68, p. 769.

    Article  CAS  Google Scholar 

  35. Hausman Jr., R. F., Bloom, S. D., and Bender, C. F.: 1975, Chem. Phys. Lett. 32, p. 483

    Article  CAS  Google Scholar 

  36. Hausman Jr., R. F., and Bender, C. F.: 1977, in “Methods of Electronic Structure Theory” (“Modern Theoretical Chemistry,” Vol. 3), Edited by H. F. Schaefer III ( Plenum, New York ), p. 319.

    Google Scholar 

  37. Bender, C. F.: 1979, J. Comput. Phys. 30, p. 324.

    Article  Google Scholar 

  38. Fox, D., Handy, N., Saxe, P., and Schaefer III, H. F.: 1982, 183rd Amer. Chem. Soc. Natl. Mtg., Las Vegas, Nevada.

    Google Scholar 

  39. Gouyet, J.-F., Schranner, R., and Seligman, T. H.: 1975, J. Phys. A 8, p. 285.

    Article  Google Scholar 

  40. Drake, G. W. F., and Schlesinger, M.: 1977, Phys. Rev. A 15, p. 1990

    Article  CAS  Google Scholar 

  41. Schlesinger, M.: 1981, in “The Unitary Group for the Evaluation of Electronic Energy Matrix Elements” (Lecture Notes in Chemistry 22), edited by J. Hinze ( Springer, Berlin ), p. 144.

    Google Scholar 

  42. Shavitt, I., and Paldus, J.: unpublished.

    Google Scholar 

  43. Roos, B. O., Nelin, C., and Agren, H.: 1982, 183rd Amer. Chem. Soc. Natl. Mtg., Las Vegas, Nevada.

    Google Scholar 

  44. Brown, F. B., Shepard, R., Lischka, H., and Shavitt, I.: work in progress.

    Google Scholar 

  45. Brooks, B. R., Laidig, W. D., Saxe, P., and Schaefer III, H. F.: 1980, J. Chem. Phys. 72, p. 3837.

    Article  CAS  Google Scholar 

  46. Shepard, R., and Simons, J.: 1980, Int. J. Quantum Chem. Symp. 14, p. 211

    CAS  Google Scholar 

  47. Shepard, R., Shavitt, I., and Simons, J.: 1982, J. Chem. Phys. 76, p. 543.

    Article  CAS  Google Scholar 

  48. Brooks, B. R., Laidig, W. D., Saxe, P., Goddard, J. D., and Schaefer III, H. F.: 1981, in “The Unitary Group for the Evaluation of Electronic Energy Matrix Elements” (Lecture Notes in Chemistry 22), edited by J. Hinze ( Springer, Berlin ), p. 158.

    Google Scholar 

  49. Brooks, B. R., Laidig, W. D., Saxe, P., Goddard, J. D., Yamaguchi, Y., and Schaefer III, H. F.: 1980, J. Chem. Phys. 72, p. 4652.

    Article  CAS  Google Scholar 

  50. H. Lischka: 1982, 183rd Amer. Chem. Soc. Natl. Mtg., Las Vegas, Nevada.

    Google Scholar 

  51. Born, G., and Shavitt, I.: 1982, J. Chem. Phys. 76, p. 558.

    Article  CAS  Google Scholar 

  52. Paldus, J., and Boyle, M. J.: 1980, Phys. Rev. A 22, p. 2299;

    Article  CAS  Google Scholar 

  53. Boyle, M. J., and Paldus, J.: 1980, Phys. Rev. A 22, p. 2316.

    Article  CAS  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Chemistry, Ohio State University, Columbus, Ohio, 43210, USA

    Isaiah Shavitt

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  1. Isaiah Shavitt
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Editor information

Editors and Affiliations

  1. Department of Quantum Chemistry, Uppsala University, Uppsala, Sweden

    Per-Olov Löwdin

  2. Institut de Biologie Physico-Chimique, Paris, France

    Bernard Pullman

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© 1983 D. Reidel Publishing Company

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Shavitt, I. (1983). The Unitary Group and the Electron Correlation Problem. In: Löwdin, PO., Pullman, B. (eds) New Horizons of Quantum Chemistry. International Academy of Quantum Molecular Science, vol 4. Springer, Dordrecht. https://doi.org/10.1007/978-94-009-7950-5_18

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  • DOI: https://doi.org/10.1007/978-94-009-7950-5_18

  • Publisher Name: Springer, Dordrecht

  • Print ISBN: 978-94-009-7952-9

  • Online ISBN: 978-94-009-7950-5

  • eBook Packages: Springer Book Archive

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