Optical Properties of Molecular Aggregates. I. Classical Model of Electronic Absorption and Refraction
A theoretical classical model is developed to predict the absorption and refraction of an aggregate of monomer units (a molecular aggregate, molecular crystal, or polymer) at any frequency. The monomers are treated as having complex electronic polarizabilities whose frequency dependence is determined by the absorption bands of the isolated monomers. Polarizations in the aggregate induced by incident light are modified by Coulombic interactions between the monomers. No first-order approximation is involved as in exciton theory. The molar extinction coefficient and molar refraction are obtained from normal mode polarizabilities found by solving an eigenvalue problem. The predicted absorption spectra agree (to first order in interaction energy) with exciton theory in the limit of weak coupling, with the hypochromism theory of Tinoco and Rhodes, and (for a classical oscillator model) with exciton theory for strong coupling. The oscillator strength sum rule is obeyed. The predicted spectrum of a pair of dyelike monomers is illustrated for the cases of weak, intermediate, and strong coupling.