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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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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