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Density Equation Theory in Chemical Physics

  • Chapter
Book cover Many-Electron Densities and Reduced Density Matrices

Part of the book series: Mathematical and Computational Chemistry ((MACC))

Abstract

Two basic principles in non-relativistic quantum mechanics are the Schrödinger equation (SE),

$$ \widehat{H}(1, \ldots ,N)\Psi (1, \ldots ,N) = E\Psi (1, \ldots ,N), $$
((1.1))

and the pauli principle,

$$ \widehat{P}\Psi (1, \ldots ,N) = {( - )^{P}}\Psi (1, \ldots ,N), $$
((1.2))

[note that the notation 1 ≡ (r 1,σ1) is used here and in the following]. The SE is a determinative equation of the wave function ψ and the Pauli principle imposes an anti-symmetric constraint on ψ The wave function depends on all the N electron coordinates of the system, while the Hamiltonian, is the sum of the one- and two-electron operators, \( {\hat v} \) and ŵ, respectively.

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References

  1. K. Husimi, Proc. Phys. Math. Soc. Jap. 22, 264 ( 1940).

    Google Scholar 

  2. P.-O. Löwdin, Phys. Rev. 99, 1474, 1490 (1955).

    Article  Google Scholar 

  3. R. McWeeny, Rev. Mod. Phys. 32, 335 (1960).

    Article  Google Scholar 

  4. E. R. Davidson, Reduced Density Matrices in Quantum Chemistry, Academic, New York (1976).

    Google Scholar 

  5. B. M. Deb (ed.), The Force Concept in Chemistry, Van Nostrand Reinhold, New York (1978).

    Google Scholar 

  6. H. Nakatsuji, J. Am.Chem. Soc. 95, 345, 354, 2084 (1973); 96, 24, 30 (1974).

    Google Scholar 

  7. H. Nakatsuji, Kagaku (Chemistry) 28, 17, 108 (1973).

    Google Scholar 

  8. H. Nakatsuji and T. Koga, in The Force Concept in Chemistry, B. M. Deb (ed.), Van Nostrand Reinhold, New York (1981), p. 137.

    Google Scholar 

  9. H. Hellmann, Einfuhrung in die Quantenchemie, Franz Deuticke, Leipzig (1987), p. 285; R. P. Feynman, Phys. Rev. 56, 340 (1939).

    Google Scholar 

  10. A. J. Coleman, Rev. Mod. Phys. 35, 668 (1963).

    Article  Google Scholar 

  11. R. M. Erdahl, J. Math. Phys. 13, 1608 (1972).

    Article  Google Scholar 

  12. C. Garrod and J. K. Percus, J. Math. Phys. 6, 763 (1964).

    Google Scholar 

  13. C. Garrod and M. Rosina, J. Math. Phys. 10, 1855 (1969).

    Article  Google Scholar 

  14. L. J. Kijewski, Phys. Rev.A 6, 31 (1972); A 9,22 63 (1974).

    Google Scholar 

  15. M. Nakata, H. Nakatsuji, M. Ehara, M. Fukuda, K. Nakata, and K. Fujisawa, to be published.

    Google Scholar 

  16. P. Hohenberg and W. Kohn, Phys. Rev.B 136, 864 (1964).

    Article  Google Scholar 

  17. H. Nakatsuji and R. G. Parr, J. Chem. Phys. 63, 1112 (1975).

    Article  CAS  Google Scholar 

  18. See also: S. T. Epstein and C. M. Rosenthal, J. Chem. Phys. 64, 247 (1976).

    Article  CAS  Google Scholar 

  19. Private communication from Prof. Mel Levy.

    Google Scholar 

  20. R. G. Parr and W. Yang, Density-Functional Theory of Atoms and Molecules, Oxford Univ. Press, Oxford (1989).

    Google Scholar 

  21. H. Nakatsuji, Phys. Rev. A14, 41 (1976).

    Google Scholar 

  22. H. Nakatsuji, Theor. Chem. Ace. 102, 97 (1999).

    Article  CAS  Google Scholar 

  23. H. Nakatsuji, to be published.

    Google Scholar 

  24. L. Pauling and E. B. Wilson, Jr., Introduction to Quantum Mechanics, McGraw-Hill, New York (1935), p. 189.

    Google Scholar 

  25. S. Cho, Sei. Rep. Gumma Univ. 11, 1 (1962).

    Google Scholar 

  26. L. Cohen and C. Frishberg, Phys. Rev.A 13,927 (1976).

    Google Scholar 

  27. D. A. Mazziotti, Phys. Rev.A 57, 4219 (1998).

    Google Scholar 

  28. R. G. Parr, J. Chem. Phys. 40, 3726 (1964).

    Article  CAS  Google Scholar 

  29. S. T. Epstein, Variation Method in Quantum Chemistry, Academic, New York (1974).

    Google Scholar 

  30. H. Nakatsuji, J. Chem. Phys. 67, 1312 (1977).

    Article  CAS  Google Scholar 

  31. C. Valdemoro, in Density Matrices and Density Functionals, R. Erdahl and V. Smith (eds.), Reidel, Dordrecht (1987), p.275.

    Chapter  Google Scholar 

  32. C. Valdemoro, Phys. Rev.A 45, 4462 (1992).

    Google Scholar 

  33. F. Colmenero, C. Perez del Valle, and C. Valdemoro, Phys. Rev.A47, 971 (1993).

    Google Scholar 

  34. F. Colmenero and C. Valdemoro, Phys. Rev.A47, 979 (1993).

    Google Scholar 

  35. F. Colmenero and C. Valdemoro, Int. J. Quant. Chem. 62, 369 (1994).

    Article  Google Scholar 

  36. C. Valdemoro, L. M. Tel, and E. Pérez-Romero, Adv. Quant. Chem. 28, 33 (1997).

    Article  CAS  Google Scholar 

  37. H. Nakatsuji and K. Yasuda, Phys. Rev. Lett. 76, 1039 (1996).

    Article  CAS  Google Scholar 

  38. K. Yasuda and H. Nakatsuji, Phys. Rev.A56,2648 (1997).

    Google Scholar 

  39. M. Nakata, M. Ehara, K. Yasuda, and H. Nakatsuji, J. Chem. Phys., submitted.

    Google Scholar 

  40. A. A. Abrikosov, L. P. Gor’kov, and E. Dzyaloshinskii, Methods of Quantum Field Theory in Statistical Physics, Prentice-Hall, Englewood, Cliffs, NJ (1963).

    Google Scholar 

  41. D. A. Mazziotti, Phys. Rev.A60, 3618 (1999).

    Google Scholar 

  42. H. Nakatsuji and K. Yasuda, unpublished.

    Google Scholar 

  43. J. M. Parks and R. G. Parr, J. Chem. Phys. 28, 335 (1957).

    Article  Google Scholar 

  44. H. Shall, J. Chem. Phys. 30, 1405 (1959).

    Article  Google Scholar 

  45. W. Kutzelnigg, J. Chem. Phys. 40, 3640 (1964).

    Article  CAS  Google Scholar 

  46. R. McWeeny and E. Steiner, Adv. Quant. Chem. 2, 93 (1965).

    Article  CAS  Google Scholar 

  47. E. Kapuy, J. Chem. Phys. 44, 956 (1966).

    Article  CAS  Google Scholar 

  48. A. J. Coleman, Int. J. Quant. Chem. 63, 23 (1997).

    Article  CAS  Google Scholar 

  49. P. R. Surján, Topics in Current Chemistry, 203, 63 (1999).

    Article  Google Scholar 

  50. D. T. Finkbeiner, Jr., Introduction to Matrices and Linear Transformations, W. H. Freeman and Co., San Francisco (1960).

    Google Scholar 

  51. M. Ehara, M. Nakata, H. Kou, K. Yasuda, and H. Nakatsuji, Chem. Phys. Lett. 305, 483 (1999).

    Article  CAS  Google Scholar 

  52. H. Nakatsuji and K. Hirao, J. Chem. Phys. 68, 2053 (1978).

    Article  CAS  Google Scholar 

  53. H. Nakatsuji, Chem. Phys. Lett. 59, 362 (1978).

    Article  CAS  Google Scholar 

  54. H. Nakatsuji, Chem. Phys. Lett. 67, 329 (1978).

    Article  Google Scholar 

  55. H. Nakatsuji, in Computational Chemistry, Reviews of Current Trends, J. Leszczynski (ed.), Vol. 2, World Scientific, Singapore (1996), p. 62.

    Google Scholar 

  56. T. Yonezawa, H. Nakatsuji, T. Kawamura, and H. Kato, Chem. Phys. Lett. 2, 454 (1968).

    Article  CAS  Google Scholar 

  57. H. Nakatsuji, H. Kato, and T. Yonezawa, J. Chem. Phys. 62, 3175 (1969).

    Article  Google Scholar 

  58. D. A. Mazziotti, Chem. Phys. Lett. 289, 419 (1998).

    Article  CAS  Google Scholar 

  59. D. A. Mazziotti, Int. J. Quant. Chem. 70, 557 (1998).

    Article  CAS  Google Scholar 

  60. K. Yasuda, Phys. Rev.A59, 4133 (1999).

    Google Scholar 

  61. C. Valdemoro, Int. J. Quant. Chem. 60, 131 (1996).

    Article  CAS  Google Scholar 

  62. C. Valdemoro, M. P. de Lara-Castells, E. Pérez-Romero, and L. M. Tel, Adv. Quant. Chem. 31, 37 (1999).

    Article  Google Scholar 

  63. R. Kubo, J. Phys. Soc. Jap. 17, 1100 (1962).

    Article  Google Scholar 

  64. W. Kutzelnigg and D. Mukherjee, J. Chem. Phys. 110, 2800 (1999).

    Article  CAS  Google Scholar 

  65. W. Kutzelnigg and D. Mukherjee, Chem. Phys. Lett., in press.

    Google Scholar 

  66. M. Levy, in Density Matrices and Density Functionals, R. Erdahl and V. Smith (eds.), Reidel, Dordrecht (1987), p.479.

    Chapter  Google Scholar 

  67. J. Cioslowski and K. Pernal, J. Chem. Phys. III, 3396 (1999).

    Article  Google Scholar 

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Author information

Authors and Affiliations

  1. Department of Synthetic Chemistry and Biological Chemistry, Graduate School of Engineering, Kyoto University, Kyoto, 606, Japan

    Hiroshi Nakatsuji

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  1. Hiroshi Nakatsuji
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Editor information

Editors and Affiliations

  1. Florida State University, Tallahassee, Florida, USA

    Jerzy Cioslowski

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Nakatsuji, H. (2000). Density Equation Theory in Chemical Physics. In: Cioslowski, J. (eds) Many-Electron Densities and Reduced Density Matrices. Mathematical and Computational Chemistry. Springer, Boston, MA. https://doi.org/10.1007/978-1-4615-4211-7_5

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  • DOI: https://doi.org/10.1007/978-1-4615-4211-7_5

  • Publisher Name: Springer, Boston, MA

  • Print ISBN: 978-1-4613-6890-8

  • Online ISBN: 978-1-4615-4211-7

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