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Electronic Correlation in Polymers

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Quantum Theory of Polymers as Solids
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Abstract

It is well known that the Hartree-Fock method gives only an approximation to the correct total energy and wave function of a system. Unless heavy atoms are present in the system, which would require a relativistic treatment, the exact energy and wave function can be obtained only by solving the Schrödinger equation of the problem

$$\hat H\Psi = E\Psi$$
(5.1)

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References

  1. K. A. Brueckner, Phys, Rev. 100, 36 (1955);

    Article  CAS  Google Scholar 

  2. J. Goldstone, Proc. R. Soc. London, Ser. A 239, 267 (1957);

    CAS  Google Scholar 

  3. H. Primas, in: Modern Quantum Chemistry (O. Sinanoglu, ed.), Vol. 2, Academic Press, New York (1965);

    Google Scholar 

  4. R. Ahlrichs, Theor. Chim. Acta 35, 59 (1974);

    Article  CAS  Google Scholar 

  5. J. A. Pople, R. Seeger, and R. Krishnan, Int. J. Quantum Chem., Quantum Chem. Symp. 11, 149 (1977).

    Article  CAS  Google Scholar 

  6. C. Moller and M. S. Plesset, Phys. Rev. 46, 618 (1934);

    Article  CAS  Google Scholar 

  7. J. Paldus and J. Ci’lek, Adv. Quant. Chem. 9, 105 (1975);

    Article  CAS  Google Scholar 

  8. E. Kapuy, Z. Csépes, and C. Kozmutza, Int. J. Quantum Chem. 23, 981 (1983);

    Article  CAS  Google Scholar 

  9. J. A. Pople, M. J. Frisch, B. T. Luke, and J. S. Binkley, Int. J. Quantum Chem., Quantum Chem. Symp. 17, 307 (1983).

    CAS  Google Scholar 

  10. J. Čížek, J. Chem. Phys. 45, 4256 (1966);

    Article  Google Scholar 

  11. J. Čížek, Adv. Quantum Chem. 3, 35 (1969);

    Google Scholar 

  12. J. Čížek and J. Paldus, Int. J. Quantum Chem. 5, 359 (1971);

    Article  Google Scholar 

  13. J. Paldus and J. Čížek, Adv. Quantum Chem. 9, 105 (1975).

    Article  CAS  Google Scholar 

  14. G. H. Wannier, Phys. Rev. 52, 191 (1934).

    Article  Google Scholar 

  15. S. Suhai, Quantenmechanische Untersuchungen an quasi-eindimen-sionalen Festkorpern (Quantum Mechanical Investigations of Quasi-One-Dimensional Solids), point 2, p. 39, Habilitation Thesis, University Erlangen-Nürnberg (1983).

    Google Scholar 

  16. E. I. Blount, Solid State Phys. 13, 305 (1962).

    Article  CAS  Google Scholar 

  17. J. Des Cloizeaux, Phys. Rev. 135A, 685, 598 (1964);

    Google Scholar 

  18. M. Kertész and G. Biczo, Phys. Status Solidi B 60, 249 (1973).

    Article  Google Scholar 

  19. W. Förner, Beiträge zur Untersuchung der Elektronenkorrelation in großen Molekülen und Polymeren (Contributions to the Investigation of Electron Correlation in Large Molecules and Polymers), Thesis, University Erlangen-Nürnberg (1985).

    Google Scholar 

  20. S. F. Boys, in: Quantum Theory of Atoms, Molecules and the Solid State ( P.-O. Löwdin, ed.), p. 253, Academic Press, New York-London (1966).

    Google Scholar 

  21. W. Förner, J. Čížek, P. Otto, J. Ladik, and E. O. Steinborn, Chem. Phys. 97, 235 (1985).

    Article  Google Scholar 

  22. For a review see W. Kutzelnigg, in: Methods of Electronic Structure Theory ( H. F. Schaefer III, ed.), p. 129, Plenum Press, New York-London (1977).

    Google Scholar 

  23. S. T. Epstein, in: Perturbation Theory and its Application in Quantum Mechanics ( C. H. Wilcox, ed.), p. 49, Wiley-Interscience, New York-London (1974).

    Google Scholar 

  24. For further details see: J. Ladik, in: Recent Advances in the Quantum Theory of Polymers (J.-M. André, J.-L. Brédas, J. Delhalle, J. Ladik, G. Leroy, and C. Moser, eds.), p. 155, Springer-Verlag, Berlin-New York-Heidelberg (1980).

    Google Scholar 

  25. S. Suhai, Point 3, p. 49 in Reference 5; and Reference 26.

    Google Scholar 

  26. D. Pines, Elementary Excitations in Solids, p. 146, W. A. Benjamin Inc., New York (1964).

    Google Scholar 

  27. F. Beleznay, S. Suhai, and J. Ladik, Int. J. Qunatum Chem. 20, 683 (1981).

    Article  CAS  Google Scholar 

  28. T. Koopmans’, Physica 1, 104 (1933).

    Article  Google Scholar 

  29. Y. Toyozawa, Prog. Theor. Phys. (Kyoto) 12, 422 (1954).

    Article  Google Scholar 

  30. A. B. Kunz, Phys. Rev. B 6, 2427 (1972).

    Article  Google Scholar 

  31. J. T. Devreese, A. B. Kunz, and T. C. Collins, Solid State Commun. 11, 670 (1972).

    Article  Google Scholar 

  32. D. J. Mickish, A. B. Kunz, and T. C. Collins, Phys. Rev. B 9, 446 (1974).

    Article  Google Scholar 

  33. S. T. Pantelides, D. J. Mickish, and A. B. Kunz, Phys. Rev. B 10, 2602 (1974).

    Article  CAS  Google Scholar 

  34. M. Inone, C. K. Manutte, and S. Wang, Phys. Rev. B 2, 539 (1970).

    Article  Google Scholar 

  35. S. Suhai, Phys. Rev. B 27, 3506 (1983).

    Article  CAS  Google Scholar 

  36. J. Ladik, in: Electronic Structure of Polymers and Molecular Crystals ( J.-M. André and J. Ladik, eds.), Plenum Press, New York-London (1975).

    Google Scholar 

  37. S. Suhai and J. Ladik, J. Phys. C 15, 4327 (1982).

    Article  CAS  Google Scholar 

  38. W. J. Hehre, R. F. Stewart, and J. A. Pople, J. Chem. Phys. 51, 2657 (1960);

    Article  Google Scholar 

  39. R. Ditchfield, W. Hehre, and J. A. Pople, J. Chem. Phys. 54, 1724 (1971).

    Google Scholar 

  40. S. Huzinaga, J. Chem. Phys. 51, 2657 (1969).

    Article  Google Scholar 

  41. W. Kotos and C. C. Roothaan, Rev. Mod. Phys. 32, 219 (1960).

    Article  Google Scholar 

  42. W. Kotos and L. Wolniewicz, J. Chem. Phys. 41, 3663 (1964).

    Article  Google Scholar 

  43. L. F. Mattheis, Phys. Rev. 123, 129 (1961);

    Google Scholar 

  44. J. W. Moskowitz, J. Chem. Phys. 38, 677 (1963).

    Article  Google Scholar 

  45. S. Suha1 (unpublished result).

    Google Scholar 

  46. D. H. Liskov, J. M. Mckelvey, C. F. Bender, and H. F. Schaefer III, Phys. Rev. Lett. 32, 933 (1974).

    Article  Google Scholar 

  47. M. Seel, P. Bagus, and J. Ladik, J. Chem. Phys. 77, 3123 (1982).

    Article  CAS  Google Scholar 

  48. C. R. Fincher, JR., C. E. Chen, A. J. Heeger, A. G. Macdiarmid, and J. B. Hastings, Phys. Rev. Lett. 48, 100 (1982).

    Article  CAS  Google Scholar 

  49. S. Suhai, J. Chem. Phys. 73, 3843 (1980).

    Article  CAS  Google Scholar 

  50. A. Karpfen and R. Holler, Solid State Commun. 37, 179 (1981).

    Article  CAS  Google Scholar 

  51. J. L. Brédas, R. R. Chance, R. Silbey, and G. P. Durand, J. Chem. Phys. 75, 255 (1981).

    Article  Google Scholar 

  52. S. Sulla’, Chem. Phys. Lett. 96, 619 (1983) (effect of correlation); unpublished results (interaction among PA chains).

    Google Scholar 

  53. W. J. Hehre, R. F. Stewart, and J. A. Pople, J. Chem. Phys. 51, 2657 (1969).

    Article  CAS  Google Scholar 

  54. R. Ditchfield, J. W. Hehre, and J. A. Pople, J. Chem. Phys. 54, 726 (1971).

    Google Scholar 

  55. J. Brinkley, R. A. Whiteside, P. C. Hariharan, R. Seeger, and J. A. Pople, Gaussian 76 program, QCPE 368.

    Google Scholar 

  56. S. Suhai (unpublished).

    Google Scholar 

  57. P. S. Bagus, J. Pacansky, and W. Wahlgren, J. Chem. Phys. 67, 619 (1977).

    Article  Google Scholar 

  58. See, for instance, B. Hudson and B. Kohler, Annu. Rev. Phys. Chem. 25, 437 (1974).

    Article  Google Scholar 

  59. S. Etemat, A. J. Heeger, L. Lanchlan, T.-C. Chung, and G. Macdiarmid, Mol. Cryst. Liq. Cryst. 77, 431 (1981).

    Google Scholar 

  60. J. Ladik, in: Electronic Structure of Polymers and Molecular Crystals ( J.-M. André and J. Ladik, eds.), p. 23, Plenum Press, New York-London (1975).

    Google Scholar 

  61. S. Suhai, Int. J. Quantum Chem., Quantum Biol. Symp. 11, 223 (1984).

    Google Scholar 

  62. For references on the geometry of DNA B see Chapter 2.

    Google Scholar 

  63. S. Suhai, Phys. Rev. B 27, 3506 (1982);

    Article  Google Scholar 

  64. S. Suhai, Int. J. Quantum Chem. 23, 1239 (1983).

    Article  CAS  Google Scholar 

  65. See, for instance, I. Tinoco, JR., J. Chem. Phys. 33, 1352 (1960);

    Google Scholar 

  66. I. Tinoco, JR., J. Chem. Phys. 34, 1067 (1961).

    Article  CAS  Google Scholar 

  67. H. Devoe and I. Tinoco, JR., J. Mol. Biol. 4, 500 (1962).

    Article  CAS  Google Scholar 

  68. J. Čížek, W. Forner, and J. Ladik, Theor. Chim. Acta 64, 107 (1983).

    Article  Google Scholar 

  69. J. M. Foster and S. F. Boys, Rev. Mod. Phys. 32, 300 (1969).

    Article  Google Scholar 

  70. C. Edminston and K. Ruedenberg, Rev. Mod. Phys. 34, 457 (1963).

    Article  Google Scholar 

  71. J. Pipek, Int. J. Quant. Chem. 27, 527 (1983).

    Article  Google Scholar 

  72. W. Ferner, J. Ladik, P. Otto, and J. Čížek, Chem. Phys. 97, 251 (1985).

    Article  Google Scholar 

  73. F. Coester and H. Kummel, Nucl. Phys. 7, 477 (1960).

    Google Scholar 

  74. O. Sinanoölu, J. Chem. Phys. 36, 706 (1962);

    Article  Google Scholar 

  75. O. Sinanoölu, Adv. Chem. Phys. 6, 315 (1964).

    Article  Google Scholar 

  76. See the third Reference of 10.

    Google Scholar 

  77. See the first Reference of 10.

    Google Scholar 

  78. C. F. Bender, J. Comput. Phys. 9, 547 (1972).

    Article  Google Scholar 

  79. J. Paldus, M. Takahashi, and R. W. H. Cho, Phys. Rev. B 30, 4267 (1984);

    Article  CAS  Google Scholar 

  80. M. Takahashi, J. Čížek, and J. Paldus, Phys. Rev. A 30, 2193 (1984).

    Article  Google Scholar 

  81. P. W. Anderson, Phys. Rev. 109, 1492 (1958).

    Article  CAS  Google Scholar 

  82. R. S. Day, J. Ladik, and F. Martino, Chem. Phys. Lett. 81, 494 (1981).

    Article  CAS  Google Scholar 

  83. J. Ladik, Int. J. Quantum Chem. 23, 1073 (1983).

    Article  CAS  Google Scholar 

  84. R. S. Day and F. Martino, Chem. Phys. Lett. 84, 86 (1981);

    Article  CAS  Google Scholar 

  85. B. Gazdy, M. Seel, and J. Ladik, Chem. Phys. 86, 41 (1984).

    Article  CAS  Google Scholar 

  86. K. F. Berggren and F. Martino, Phys. Rev. 184, 484 (1969);

    Article  CAS  Google Scholar 

  87. M. Bénard and J. Paldus, J. Chem. Phys. 72, 6546 (1980);

    Article  Google Scholar 

  88. M. Seel, P. S. Bagus, and J. Ladik, J. Chem. Phys. 77, 3123 (1982).

    Article  CAS  Google Scholar 

  89. C.-M. Liegener and J. Ladik, Phys. Lett. 107A, 79 (1985).

    Article  Google Scholar 

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Ladik, J.J. (1988). Electronic Correlation in Polymers. In: Quantum Theory of Polymers as Solids. Springer, Boston, MA. https://doi.org/10.1007/978-1-4684-5233-4_6

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  • DOI: https://doi.org/10.1007/978-1-4684-5233-4_6

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