Molecular Vibrations in the Exciton Theory for Molecular Aggregates. III. Polymeric Systems

Abstract

The theory of Part I of this series is developed for aggregates of many molecules. The low-energy exciton states are considered on the basis of perturbation theory. The conditions for applicability of perturbation theory based on E-V wave functions are examined. It is shown that perturbation theory is valid where the intermolecular interaction in the exciton state is strong and/or the vibronic progression in the monomer spectrum is short.

Expressions relating to the vibrational structure in electronio absorption and emission spectra and the vibrational inhibition of intermolecular interaction are derived. A formula connecting the polarization ratios in absorption and fluorescence is given. The formula is shown to be relatively free from uncertainties arising from the use of perturbation theory, and it offers a new method of calculating the theoretical Davydov splitting for a system of rigid molecules from experimental data.

Numerical calculations are made for a linear aggregate, and the results are compared with the observed electronio spectra of the NN'-diethyl-4-cyanine dye polymer.

It is shown that the rigid-lattice model is an adequate representation of the cyanine dye polymer, but not of the anthracene crystal.