Crystal Shape Dependence of Exciton States in Molecular Crystals

Abstract

The transition‐dipole—transition‐dipole interaction model has been analyzed quantitatively, in application to the prediction of fine structure of spectroscopic transitions in molecular crystals, in the range where the particle size is much greater than the lattice parameter but is much less than the wavelength of the exciting radiation. A definite effect of sample shape on apparent multiplicity of a band is predicted. It is shown that the Hamiltonians for Davydov splitting and for shape splitting are separable. The ``shape Hamiltonian'' does not affect inactive states neither can it contain contributions from interactions shorter in range than r<sup>—3</sup>. Splitting energies and relative intensities of components have been calculated as functions of a parameter which measures the axial ratio of crystallite particles. The calculations have been carried out for cubic crystals, in which cases they are relatively simple because the results are independent of the sample orientation relative to the crystallographic axes. The symmetry of a dipole lattice is higher than that of the actual crystal; some of the effects of this ``supersymmetry'' on the spectrum predicted in this approximation have been examined. Several comparisons with experiment (primarily in the infrared region) have been made. The model predicts qualitative features of spectra correctly and where the transition is strong, reasonable quantitative results have been obtained. In most cases, when the transition is weak, the dominance of other effects, such as higher multipole interactions, repulsive forces or crystal defects, is indicated.