Theory of the Coupling of Electronic and Vibrational Excitations in Molecular Crystals and Helical Polymers

Abstract

The effect of the internal vibrations of monomers (or molecules) on the electronic absorption spectra of aggregates with either helical or three dimensional translational symmetry is considered using molecular exciton theory. In this treatment the single‐particle excitations (vibronic excitons) are coupled to all those two‐particle manifolds in which vibronic and ground vibrational excitons occupy different lattice sites. This allows for collective coupling among single‐particle levels overlapped by two‐particle continua. The main approximations invoked are (a) the crude Born—Oppenheimer approximation to factorize the wavefunctions of isolated monomers, (b) neglect of electron exchange between monomer wavefunctions (tight binding), and (c) the neglect of any mixing of different electronic states by intermonomer forces. Wave sums of exciton resonance interactions are eliminated in favor of a density of sums function. To test the range of coupling strengths for which the theory is valid calculations are performed for a one‐dimensional polymer model with only nearest‐neighbor interactions and a three‐dimensional crystal model with a simple density function. For intermediate coupling the influence of three‐ and higher‐particle states becomes important and these states are included in the energy calculations by an extended fraction type of technique. Other calculations explore the effect of (a) a change in the vibrational frequency of the monomer after electronic excitation, (b) changes in the energy of the optical $\mathrm{k}\text{=0}$ levels with direction of the exciting radiation, and (c) changes in the transition intensity of the isolated monomer.