Vibrational effects in the absorption spectrum of polymer rods

A single band of exciton states is considered for a polymer rod consisting of identical monomers whose nuclei are able to vibrate. It is shown that the shift in the average energy of absorbed photons when the monomers are stacked is equal to the shift one would get in the absence of vibrations of the nuclei. The spread of energy of the absorbed photons (defined by the standard deviation) is equal to the corresponding spread induced by vibrations in the monomer. These results are shown to be true both at zero and at finite temperatures. The result for the average energy confirms the suggestion of McLachlan and Ball that the shift of the envelope of the absorption spectrum when the monomers are stacked should be independent of the vibrations of the nuclei, while avoiding some of the approximations on which that suggestion was based.