Effect of Local Perturbations on the Electronic Structure of Organic Polymers

Abstract

These lectures notes treat the problem of local perturbations on a polymer with special reference to the actualrange of formally strictly localized perturbation. They are divided into six sections:

• 1. The essential terms are defined.

• 2. A physically significant if crude analysis of the effects of a local perturbation is given in terms of a hierarchy of models: a simple semiempirical scheme for localized bonds, a pure charge--transfer scheme, and the case of a fully conjugated polymer

• 3. The last model is more extensively discussed with reference to Friedel oscillations and SCF procedures.

• 4. The general formalism for treating local perturbations in terms of Green’s matrices is briefly presented.

• 5. A comment on dynamical aspects is given, to emphasize the difference between the instantaneous range of a perturbation and the distance to which it can travel.

• 6. Finally, a short bibliographical note is given.

In sections 2 and 3 it is shown that already in fully saturated chains a perturbation acting a single site induces secondary perturbations on the neighboring sites so that the range of the effect is much larger than the range of the cause due to polarization. It is shown how a perturbation can arise by simple juxtoposition of an appropriate donor or acceptor and electronegativity equalization.

The formal introduction of Green functions is important because they provide a formalism especially useful in the case of quasi continuous energy spectra quasi such as those of large polymer chains, and allow to set on clear formal grounds the question of the perturbation range.

The question of time-dependent perturbations is mentioned as the most important coming issue for p.t. applied to polymers.