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Infrared absorption of positively charged polarons in conjugated polymer chains and π-stacked aggregates is investigated theoretically, employing a Holstein-based Hamiltonian which treats electronic coupling, electron-vibrational coupling, and disorder on equal footing. The spectra evaluated from the Hamiltonian expressed in a one- and two-particle basis set are essentially exact, insofar as the main, aromatic-quinoidal vibrational mode is treated fully nonadiabatically. Diagonal and off-diagonal ("paracrystalline") disorder are resolved along the polymer axis (x) and the aggregate stacking axis (y). Disorder along the polymer axis selectively attenuates the x-polarized spectrum, which is dominated by the polaron peak P1. Disorder along the stacking axis selectively attenuates the y-polarized spectrum, which is dominated by the lower-energy charge-transfer peak, DP1. Calculated spectra are in excellent agreement with the measured induced-absorption and charge-modulation spectra, reproducing the peak positions and relative peak intensities within a line shape rich in vibronic structure. Our nonadiabatic approach predicts the existence of a weak, x-polarized peak P0, slightly blueshifted from DP1. The peak is intrinsic to single polymer chains and appears in a region of the spectrum where narrow infrared active vibrational modes have been observed in nonaggregated conjugated polymers. The polaron responsible for P0 is composed mainly of two-particle wave functions and cannot be accounted for in the more conventional adiabatic treatments.
Pochas et al. (Mon,) studied this question.