Excited and Ionized States of Polymers

  • János J. Ladik


It is well known that in the HF theory of a closed-shell atom or of a finite molecule, the singlet excitation energy from a filled level i to an unfilled level a is given by the expression
$$^1\Delta {E_{i \to a}} = \varepsilon _a^{HF} - \varepsilon _i^{HF} - {J_{ia}} + 2{K_{ia}}$$
where ε a HF and ε i HF are, respectively, the corresponding HF one-electron energies while J ia and K ia denote the Coulomb and exchange integrals between orbitals ψ i and ψ a respectively. It can easily be shown that if we have a very long chain, J ia and K ia tend to zero (see, e.g., Ladik(1)) as the number of unit cells, N, approaches infinity:
$$\underset{N\to \infty }{\mathop{\lim }}\, {{J}_{ia}}=\underset{N\to \infty }{\mathop{\lim }}\, {{K}_{ia}}=\underset{N\to \infty }{\mathop{\lim }}\, \frac{\ln N}{N}\to 0$$
In this way we are left with too large an excitation energy, because equation (8.1) for an infinite system reduces to the HF gap (which is too large anyway).


Ionization Potential Photoionization Cross Section Exciton Band Wannier Function Frenkel Exciton 
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  1. 1.
    J. Ladik, in: Excited States in Quantum Chemistry ( C. A. Nicolaides and D. R. Beck, eds.), p. 495, D. Reidel Publ. Co., Dordrecht-Boston-New York (1979).Google Scholar
  2. 2.
    R. S. Knox, Theory of Excitons, Academic Press, New York (1963).Google Scholar
  3. 3.
    Y. Takeuti, Prog. Theor. Phys. (Kyoto) 18, 421 (1957);CrossRefGoogle Scholar
  4. Y. Takeuti, Prog. Theor. Phys. (Kyoto), Suppl. 12, 75 (1959).CrossRefGoogle Scholar
  5. 4.
    S. Suhai, Phys. Rev. B 29, 4570 (1984);CrossRefGoogle Scholar
  6. S. Suhai, Quantum Mechanical Investigations on QuasiOne-Dimensional Solids, Habilitation Thesis, Erlangen (1983) (in German).Google Scholar
  7. 5.
    A. L. Fetter and J. D. Valecka, Quantum Theory of Many-Particle Systems, McGraw-Hill Book Co., New York (1971).Google Scholar
  8. 6.
    C.-M. Liegener and J. Ladik, Chem. Phys. 106, 339 (1986).CrossRefGoogle Scholar
  9. 7.
    S. Suhai, Int. J. Quantum Chem. 11, 223 (1984).CrossRefGoogle Scholar
  10. 8.
    S. Suhai, in: Quantum Chemistry of Polymers; Solid State Aspects ( J. Ladik and J.-M. André, eds.), p. 101, D. Reidel Publ. Co., Dordrecht-Boston-Lancaster (1984).Google Scholar
  11. 9.
    S. Suhai, J. Mol. Struct. 123, 97 (1985).Google Scholar
  12. 10.
    J. Hermanson and J. C. Phillips, Phys. Rev. 150, 652 (1960).CrossRefGoogle Scholar
  13. 11.
    J. Hermanson, Phys. Rev. 150, 660 (1966).CrossRefGoogle Scholar
  14. 12.
    D. Pines, Elementary Excitations in Solids, p. 146, Benjamin, New York (1984).Google Scholar
  15. 13.
    D. Bloor, D. J. Ando, F. H. Preston, and G. C. Stevens, Chem. Phys. 24, 1407 (1974)Google Scholar
  16. D. Bloor, F. H. Preston, and D. J. Ando, Chem. Phys. Lett. 38, 33 (1976);CrossRefGoogle Scholar
  17. D. Bloor and F. H. Preston, Phys. Status Solidi A 37, 427, 607 (1976).Google Scholar
  18. 14.
    S. Suhai, Phys. Rev. B 27, 3506 (1983).CrossRefGoogle Scholar
  19. 15.
    Z. Igbal, R. R. Chance, and R. H. Baughman, J. Chem. Phys. 67, 3616 (1977).CrossRefGoogle Scholar
  20. 16.
    K. J. Less and E. G. Wilson, J. Phys. C 6, 3110 (1973).CrossRefGoogle Scholar
  21. 17.
    S. Suhai, Int. J. Quantum Chem. 11, 223 (1984).CrossRefGoogle Scholar
  22. 18.
    S. Arnott, S. Doyen, and A. J. Wonacott, Acta Crystallogr., Sect. B 28, 2198 (1969).Google Scholar
  23. 19.
    R. Ditchfield, J. W. Hehre, and A. J. Pople, J. Chem. Phys. 54, 726 (1971).Google Scholar
  24. 20.
    H. Devoe, Ann. N.Y. Acad. Sci. 158, 298 (1969);CrossRefGoogle Scholar
  25. I. Tinoco, Jr., J. Am. Chem. Soc. 82, 4785 (1960); 83, 5047 (1969);CrossRefGoogle Scholar
  26. W. Rhodes, J. Am. Chem. Soc. 83, 3609 (1961);CrossRefGoogle Scholar
  27. H. Devoe and I. Tinoco, Jr., J. Mol. Biol. 4, 51881 (1968);Google Scholar
  28. J. Koutecky and J. Paldus, Theor. Chim. Acta 1, 268 (1963);CrossRefGoogle Scholar
  29. T. A. Hoffmann and J. Ladik, J. Theor. Biol. 6, 26 (1964);CrossRefGoogle Scholar
  30. J. Ladik and K. Sundaram, J. Mol. Spectrosc. 29, 146 (1969);CrossRefGoogle Scholar
  31. A. Pullman and B. Pullman, Adv. Quantum Chem. 4, 287 (1970);Google Scholar
  32. V. I. Danilov, V. T. Pechenaga, and N. V. Zheltorsky, Int. J. Quantum Chem. 17, 307 (1980).CrossRefGoogle Scholar
  33. 21.
    J. P. Ballini, P. Vigny, and H. Daniels, Biophys. Chem. 18, 61 (1983); the first four references of Reference 20.Google Scholar
  34. 22.
    E. Clementi, J.-M. André, M.-CL. André, D. Klint, and D. Hahn, Acta Phys. Hung. Acad. Sci. 27, 493 (1969);CrossRefGoogle Scholar
  35. B. Mely and A. Pullman, Theor. Chim. Acta (Berlin) 13, 278 (1969);CrossRefGoogle Scholar
  36. E. Clementi, J. Mehl, and W. V. Niessen, J. Chem. Phys. 54, 508 (1971).CrossRefGoogle Scholar
  37. 23.
    S. Suhai, C. Merkel, and J. Ladik, Phys. Lett. 61A, 487 (1977);CrossRefGoogle Scholar
  38. J. Ladik and S. Suhai, Int. J. Quantum Chem. QBS7, 181 (1980).Google Scholar
  39. 24.
    S. Suhai, J. Mol. Struct. 123, 97 (1985).Google Scholar
  40. 25.
    J. F. Yan, G. Vanderkooi, and H. Scheraga, J. Chem. Phys. 49, 2713 (1968).CrossRefGoogle Scholar
  41. 26.
    J. S. Binkley, R. A. Whiteside, P. C. Hariharan, R. Seeger, and J. A. Pople, QCPE, Bloomington, Indiana, Program No. 368.Google Scholar
  42. 27.
    S. Suhai, J. Chem. Phys. 73, 3843 (1980).CrossRefGoogle Scholar
  43. 28.
    I. Tinoco, Jr., A. Halpera, and W. T. Simpson, in: Polyamino Acids, Polypeptides and Proteins ( M. A. Stahmann, ed.), p. 147, University of Wisconsin, Madison (1962).Google Scholar
  44. 29.
    W. C. Johnson, Jr. and I. Tinoco, Jr., J. Am. Chem. Soc. 94, 4389 (1972).CrossRefGoogle Scholar
  45. 30.
    S. Onari, J. Phys. Soc. Jpn. 29, 528 (1970).CrossRefGoogle Scholar
  46. 31.
    T. Koopmans, Physica 1, 104 (1933).CrossRefGoogle Scholar
  47. 32.
    S. Suhai, Phys. Rev. B 27, 3506 (1983).CrossRefGoogle Scholar
  48. 33.
    A. A. Murashovi, E. A. Silinsh, and H. Bässler, Chem. Phys. Lett. 93, 1481 (1982).Google Scholar
  49. 34.
    C.-M. Liegener, J. Phys. C 18, 6011 (1985).CrossRefGoogle Scholar
  50. 35.
    D. J. Thouless, The Quantum Mechanics of Many-Body Systems, 2nd Edition, Academic Press, New York-London (1972);Google Scholar
  51. L. S. Cederbaum and W. Domcke, Adv. Chem. Phys. 36, 205 (1977).CrossRefGoogle Scholar
  52. 36.
    J. Delhalle and J.-M. André, in: Quantum Chemistry of Polymers; Solid State Aspects (J. Ladik and J.-M. André, eds.), D. Reidel Pub1. Co., p. 23, Dordrecht-BostonLancaster (1984).Google Scholar
  53. 37.
    J. L. Brédas, J.-M. André, and J. Delhalle, Chem. Phys. 45, 109 (1980).CrossRefGoogle Scholar
  54. 38.
    U. Gelius, in: Electron Spectroscopy ( D. A. Shirley, ed.), p. 311, North-Holland Publishing Company, Amsterdam (1972).Google Scholar
  55. 39.
    J. Delhalle and S. Delhalle, Int. J. Quantum. Chem. 11, 349 (1977).CrossRefGoogle Scholar
  56. 40.
    S. Kavash and J. M. Schultz, J. Polym. Sci. A 28, 243 (1970);Google Scholar
  57. G. Avitebile, R. Napolitano, B. Pirozzi, K. D. Rouse, M. W. Thomas, and B. T. M. Willis, J. Polym. Sci., Polym. Lett. Ed. 13, 351 (1975).CrossRefGoogle Scholar
  58. 41.
    M. H. Wool, M. Barber, I. H. Hillier, and J. M. Thomas, J. Chem. Phys. 56, 1788 (1972).CrossRefGoogle Scholar
  59. 42.
    J. Delhalle, J.-M. André, S. Delhalle, J. J. Pireaux, R. Caudano, and J. J. Verbist, J. Chem. Phys. 60, 595 (1974).CrossRefGoogle Scholar
  60. 43.
    J. Delhalle, S. Delhalle, and J.-M. Andre, Chem. Phys. Lett. 34, 430 (1975).CrossRefGoogle Scholar
  61. 44.
    J. L. Bredas, J.-M. André, and J. Delhalle, Chem. Phys. 45, 109 (1980).CrossRefGoogle Scholar
  62. 45.
    J. Dehalle, Chem. Phys. 5, 306 (1974).CrossRefGoogle Scholar
  63. 46.
    J. J. Pireaux, J. Riga, R. Caudano, J. J. Verbist, J.-M. André, J. Delhalle, and S. Delhalle, J. Electron Spectrosc. 5, 53 (1974);Google Scholar
  64. J. Delhalle, S. Delhalle, J.-M. André, J. J. Pireaux, J. Riga, R. Caudano, and J. J. Verbist, J. Electron Spectrosc. 12, 293 (1977).CrossRefGoogle Scholar
  65. 47.
    J. Delhalle, 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.), Lecture Notes in Physics 113, p. 255, Springer-Verlag, Berlin—New York—Heidelberg (1980).Google Scholar
  66. 48.
    J. J. Pireaux, J. Riga, R. Caudano, and J. J. Verbist, in: Photon, Electron and Ion Probes of Polymer Structure and Properties (D. W. Dwight, T. C. Fabish, and H. R. Thomas, eds.), ACS Symp. Series, 162, p. 169, Washington D. C. (1981).Google Scholar
  67. 49.
    J. Delhalle, R. Montigny, C. Demanet, and J.-M. Andre, Theor. Chim. Acta 50, 343 (1979).CrossRefGoogle Scholar

Copyright information

© Plenum Press, New York 1988

Authors and Affiliations

  • János J. Ladik
    • 1
  1. 1.University of Erlangen-NurembergErlangen-WaterlooFederal Republic of Germany

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