Optical Properties of Large Molecules in the Frenkel Exciton Approximation

Abstract

The Frenkel exciton approximation provides a means for representing the excited states of large, weakly-interacting systems in terms of the properties of their subunits. Frenkel exciton theory is reviewed, together with its application to the optical properties of large molecules and complexes, A general method is presented for calculating the absorption and circular dichroism spectra of large systems within the Frenkel exciton picture. It is shown that for systems consisting of weakly-interacting identical subunits, the rotatory power of a transition is proportional to tr[H F], where H is the interaction Hamiltonian and F is an “optical matrix” constructed from the transition dipole moments and positions of the individual subunits. Similarly it is shown that the absorption maximum is shifted in frequency by an amount which is proportional to tr[H G]/tr[G], where G is also constructed from the subunit transition dipole moments. The general theory is illustrated by a discussion of the optical properties of helical polymers.