ABSTRACT
Equations relating the radiative and nonradiative decay rate constants of singlet excitons in super-radiant aggregates to the relative intensities of the 0-0 and 0-1 peaks in the emission spectrum were derived and tested against experimental data. In many instances, these equations eliminate the need for a time-dependent fluorescence decay measurement. They can also be useful in determining the fluorescence quantum yield.
ABSTRACT
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.
ABSTRACT
The absorption line shapes of a series of linear and star-shaped perylene diimide (PDI) complexes are evaluated theoretically and compared to experiment. The cyclic trimer and tetrahedral complexes are part of the symmetric series, characterized by a single interchromophoric coupling, J(0), between any two PDI chromophores. The measured spectra of all complexes show pronounced vibronic progressions based on the symmetric ring stretching mode at ~1400 cm(-1). The spectral line shapes are accurately reproduced using a Holstein Hamiltonian parametrized with electronic couplings calculated using time-dependent density functional transition charge densities. Although the "head-to-tail" linear complexes display classic J-aggregate behavior, the star-shaped complexes display a unique photophysical response, which is neither J- nor H-like. In the symmetric N-mers (N = 2-4), absorption and emission are polarized along N - 1 directions in contrast to linear complexes where absorption and emission remain polarized along the long molecular axis. In the symmetric complexes the red-shift of the 0-0 peak with increasing |J(0)|, as well as the initial linear rise of the 0-0/1-0 oscillator strength ratio with increasing |J(0)|, are independent of the number of PDI chromophores, N, and are markedly smaller than what is found in the linear series, where the shifts and ratios depend on N. Moreover, whereas the radiative decay rate, γ(r), scales with N and is therefore superradiant in linear complexes, γ(r) scales with N/(N - 1) in the symmetric complexes. Vibronic/vibrational pair states (two-particle states) are found to profoundly affect the absorption line shapes of both linear and symmetric complexes for sufficiently large coupling.
