Advertisement

Electronic Structure and Excited States of Polymers

  • J. Ladik
Chapter
Part of the NATO Advanced Study Institutes Series book series (ASIC, volume 46)

Abstract

The SCF LCAO Crystal Orbital (Hartree-Fock) method is reviewed in the cases of polymers with simple translational symmetry and with a combined symmetry operation. As example the band structure of the periodic DNA model polycytosine is discussed.

For the treatment of aperiodic (multicomponent) polymers the coherent potential approximation with a k- and energy-dependent self energy is described. As illustrative example calculations for the \( {(SN)_X} - {\left( {\begin{array}{*{20}{c}} {SN} \\ H \\ \end{array} } \right)_X} \) two-component mixed polymer are presented. To investigate the extra levels of a cluster of impurities embedded in a periodic crystal the SCF resolvent method has been developed.

For the calculations of excited states of polymers applications of the ÔÂÔ method are shown. Further the applicability of the more general Green’s function formalism for the investigation of localized excitations in polymers is discussed. Finally to treat partially delocalized excitations in polymers the formalism of the intermediate (charge transfer) exciton theory and its application to polymers is reviewed.

Keywords

Excited State Mixed System Molecular Crystal State Curve Exciton Band 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.
This is a preview of subscription content, log in to check access.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. 1.
    For a review of this method see: F. Martino in Quantum Theory of Polymers, J.-M. André, J. Delhalle and J. Ladik, Eds., D. Reidel Publ. Co., Dordrecht-Boston, p. 169 (1978).Google Scholar
  2. 2.
    J. Ladik and M. Seel, Phys. Rev. B 13, 5338 (1976).CrossRefGoogle Scholar
  3. 3.
    G. Del Re, J. Ladik and G. Biczó, Phys. Rev. 155, 967 (1967);Google Scholar
  4. 3a.
    J.-M. André, L. Gouverneur and G. Leroy, Int. J. Quant. Chem. 1, 427 and 451 (1967);CrossRefGoogle Scholar
  5. 3b.
    R. N. Euwema, D.L. Wilhite and G.T. Surrat, Phys. Rev. B7, 818 (1973).Google Scholar
  6. 4.
    J. Ladik in “Electronic Structure of Polymers and Molecular Crystals”, J.-M. André and J. Ladik, Eds., Plenum Press, New York-London, p. 23 (1975).Google Scholar
  7. 5.
    G. Biczó, unpublished result.Google Scholar
  8. 6.
    For a review of these calculations see: J.-M. André in “Electronic Structure of Polymers and Molecular Crystals”, J.-M. André and J. Ladik, Eds., Plenum Press, New York-London p. 1 (1975);Google Scholar
  9. 6a.
    J.-M. Andre and J. Delhalle in “Quantum Theory of Polymers”, J.-M. André, J. Delhalle and J. Ladik, Eds., D. Reidel Publ. Co., Dordrecht-Boston, p. 1 (1978).Google Scholar
  10. 7.
    For a review see: T.C. Collins in “Electronic Structure of Polymers and Molecular Crystals”, p. 389.Google Scholar
  11. 8.
    For a review see: J. Ladik in “Electronic Structure of Polymers and Molecular Crystals”, p. 663.Google Scholar
  12. 9.
    J. Ladik in “Quantum Theory of Polymers” p. 279.Google Scholar
  13. 10.
    Ch. Merkel in “Elektronische Eigenschaften vom Molekülkristallen” (Electronic Properties of Molecular Crystals) Thesis, Technical University Munich, 1977.Google Scholar
  14. 11.
    See for instance: M. Hamermesh “Group Theory and its Application to Physical Problems”, Adison Wesley Publ., Reading, Mass. p. 80 (1964).Google Scholar
  15. 12.
    S. Suhai, Ch. Merkel and J. Ladik, Phys. Lett. 61A, 487 (1977).Google Scholar
  16. 13.
    B. Mely and A. Pullman, Theor. Chim. Acta (Berl.) 13, 278 (1969).CrossRefGoogle Scholar
  17. 14.
    S. Huzinaga, J. Chem.Phys. 42, 1293 (1965).CrossRefGoogle Scholar
  18. 15.
    S. Arnott, S.D. Dover and A.J. Wonacott, Acta Cryst. B25, 2192 (1969).Google Scholar
  19. 16.
    J. Ladik in “Adv. Quantum Chem.”, P.-O. Löwdin, Ed., Academic Press, New York-London 7, p. 397 (1973).Google Scholar
  20. 16a.
    S. Suhai and J. Ladik, Int. J. Quant. Chem. 7, 547 (1973).CrossRefGoogle Scholar
  21. 17.
    For a review see: S. Suhai in “Quantum Theory of Polymers”, p. 335.Google Scholar
  22. 18.
    C. Lifschitz, E.D. Bergmann and B. Pullman, Tetrahedron Lett. 46, 4583 (1967).CrossRefGoogle Scholar
  23. 19.
    W.J. Hunt and W.A. Goddard III, Chem. Phys. Lett. 3, 414 (1969)CrossRefGoogle Scholar
  24. 19a.
    H.P. Kelly, Adv. Chem. Phys. 14, 129 (1969).CrossRefGoogle Scholar
  25. 20.
    M. Seel, “Theoretische Untersuchungen zur Aperiodizität und zum Korrelationsproblem in Polymeren und Molekülkristallen” (Theoretical Investigations of Aperiodicity and Correlation in Polymers and Molecular Crystals) Thesis, University Erlangen-Nürnberg 1978.Google Scholar
  26. 21.
    See for instance: W.L. McCubbin in “Quantum Theory of Polymers” p. 185 (1978).Google Scholar
  27. 22.
    A.J. Elliot, J.A. Krumhansl, P.L. Leath, Rev. Mod. Phys. 46, 465 (1974).CrossRefGoogle Scholar
  28. 23.
    P. Soven, Phys. Rev. 156, 809 (1967)Google Scholar
  29. 23a.
    S. Kirkpatrick, B. Velický, H. Ehrenreich, Phys. Rev. B1, 3250 (1970).Google Scholar
  30. 24.
    See for instance: J. Callaway, Quantum Theory of the Solid State, Academic Press, New York-London, p. 517 (1974).Google Scholar
  31. 25.
    M. Seel, T.C. Collins, F. Martino, D.K. Rai and J. Ladik, Phys. Rev. B (submitted).Google Scholar
  32. 26.
    For recent review papers see: H.P. Geserich and L. Pintschovius, Adv. Solid State Phys. 16, 65 (1976)Google Scholar
  33. 26a.
    G.B. Street and R.L. Greene, IBM J. Res. Develop. 21, 99 (1977).CrossRefGoogle Scholar
  34. 27.
    H. Kamimura, A.J. Grant, F. Levy, A.D. Yoffe, C.D. Pitt, Solid State Comm. 17, 49 (1975)CrossRefGoogle Scholar
  35. 27a.
    D.E. Parry, J.M. Thomas, J. Phys. C3, L45 (1975)Google Scholar
  36. 27b.
    A. Zunger, J. Chem. Phys. 63, 4854 (1975)CrossRefGoogle Scholar
  37. 27c.
    S. Suhai, M. Kertész, J. Phys. C9, L347 (1976);Google Scholar
  38. 27d.
    N.T. Rajan and L.M. Falicov, Phys. Rev. B12, 1240 (1975).Google Scholar
  39. 28.
    C. Merkel and J. Ladik, Phys. Lett. 56A, 395 (1976)Google Scholar
  40. 28a.
    M. Kertész, J. Koller, A. Ažman and S. Suhai, Phys. Lett. 55A, 107 (1975).Google Scholar
  41. 29.
    W.E. Rudge and P.M. Grant, Phys. Rev. Lett. 35, 1799 (1975)CrossRefGoogle Scholar
  42. 29a.
    W.Y. Ching, J.G. Harrison and C.C. Lin, Phys. Rev. B15, 5975 (1977)Google Scholar
  43. 29b.
    I.P. Batra, S. Ciraci and W.E. Rudge, Phys. Rev. B15, 5858 (1977).Google Scholar
  44. 30.
    S. Suhai and J. Ladik, Solid State Comm. 22, 227 (1977).CrossRefGoogle Scholar
  45. 31.
    B. Györffy and S. Faulkner (personal communication).Google Scholar
  46. 32.
    W.D. Gill, W. Bludan, R.H. Geiss, P.M. Grant, R.L. Greene, J.J. Mayerle and G.B. Street, Phys. Rev. Lett. 38, 1305 (1977).CrossRefGoogle Scholar
  47. 33.
    S. Suhai (unpublished results).Google Scholar
  48. 34.
    J. Delhalle, Bull. Soc. Chim. Belg. 84, 135 (1975).CrossRefGoogle Scholar
  49. 35.
    See for instance: G. Rickayzen, “Theory of Superconductivity”, Interscience-Wiley, New York-London (1965).Google Scholar
  50. 36.
    J. Ladik, unpublished result.Google Scholar
  51. 37.
    G.F. Koster and J.C. Slater, Phys. Rev. 96, 1208 (1954)CrossRefGoogle Scholar
  52. 37a.
    M. Kertész and G. Biczó, in “Proceedings on Computers in Chemical Research and Education”, J. Hadži, Ed., Ljubljana, p. 4195 (1973).Google Scholar
  53. 38.
    A. van der Avoird, S.P. Liebmann and J.M. Fassaert, Phys. Rev. B10, 1230 (1974).Google Scholar
  54. 39.
    J. Ladik, Phys. Rev. B17, 1663 (1978).Google Scholar
  55. 40.
    See the paper of R.J. Buenker and S.D. Peyerimhoff in this volume.Google Scholar
  56. 41.
    J. Avery, J. Packer, J. Ladik and G. Biczó, J. Mol. Spectr. 29, 194 (1969); A. Bierman and J. Ladik (unpublished result).CrossRefGoogle Scholar
  57. 42.
    For a detailed description of this formalism and for its connection with the general Green’s function theory see [7], T.C. Collins in “Quantum Theory of Polymers”, p. 75 and the paper of T.C. Collins in this volume.Google Scholar
  58. 43.
    L.B. Clark, G.G. Peschel and I. Tinoco Jr., J. Phys. Chem. 69, 3615 (1965).CrossRefGoogle Scholar
  59. 44.
    See the papers of T.C. Collins, of J. Linderberg and Y. Öhrn and of W. v. Niessen in this volume.Google Scholar
  60. 45.
    See for instance: J.D. Thouless, “The Quantum Mechanics of Many Body Systems”, Academic Press, New York-London (1961);Google Scholar
  61. 45a.
    A.L. Fetter and J.D. Walecka, “Quantum Theory of Many Particle Systems”, McGraw-Hill, New York (1971).Google Scholar
  62. 46.
    J. Paldus and J. Čižek, J. Chem. Phys. 60, 149 (1974).CrossRefGoogle Scholar
  63. 47.
    R.G. Parr, “The Quantum Theory of Molecular Electronic Systems”, Benjamin, New York (1963).Google Scholar
  64. 48.
    J. Paldus, J. Čižek, M. Saute and A. Laforque, Phys. Rev. A17, 805 (1978).Google Scholar
  65. 49.
    J. Čižek, J. Chem. Phys. 45, 4256 (1966);CrossRefGoogle Scholar
  66. 49a.
    ibid 14, 35 (1969)Google Scholar
  67. 49b.
    J. Čižek and J. Paldus, Intern. J. Quant. Chem. 5, 359 (1971);CrossRefGoogle Scholar
  68. 49c.
    J. Paldus, J. Čižek and I. Shavitt, Phys. Rev. A5, 50 (1972);Google Scholar
  69. 49d.
    J. Paldus and J. Čižek, Adv. Quant. Chem. 9, 105 (1975).CrossRefGoogle Scholar
  70. 50.
    J. Čižek and S. Suhai (to be published).Google Scholar
  71. 51.
    See for instance: E.I. Blount, Solid State Phys. 13, 305 (1963)CrossRefGoogle Scholar
  72. 51a.
    J. Des Cloizeaux, Phys. Rev. 135, A698 (1964).CrossRefGoogle Scholar
  73. 52.
    Y. Takeuti, Progress of Theor. Phys. 18, 421 (1957)CrossRefGoogle Scholar
  74. 53.
    M, Kertész, Phys. stat. soli. (b) 62, K75 (1974).CrossRefGoogle Scholar
  75. 54.
    M. Kertész, Kémiai Közlemények 46, 393 (1976) (in Hungarian).Google Scholar
  76. 55.
    J. Ladik and G. Biczó, Acta Chim. Acad. Sci. Hung. 67, 297 (1971).Google Scholar
  77. 56.
    S. Arnott, S.D. Dover and A.J. Wonacott, Acta Cryst. B25, 2192 (1969).Google Scholar
  78. 57.
    J.N. Murrell “The Theory of Electronic Spectra of Organic Molecules”, Methuen Co., London (1963).Google Scholar

Copyright information

© D. Reidel Publishing Company, Dordrecht, Holland 1978

Authors and Affiliations

  • J. Ladik
    • 1
    • 2
  1. 1.Lehrstuhl für Theoretische Chemie der Friedrich-AlexanderUniversität Erlangen-Nürnberg852 ErlangenGermany
  2. 2.Laboratory of the National Foundation for Cancer ResearchUniversity Erlangen-NürnbergGermany

Personalised recommendations

Cite chapter

Buy options