The electronic coupling in excitation energy transfer (EET) is composed of a Coulomb coupling (which can be approximated as the Fo ¨rster's dipole coupling), a Dexter's exchange coupling, and a term arising from the orbital overlap of the donor and acceptor fragments. We have developed a new scheme to account for the EET coupling by generalizing the fragment charge difference scheme [Voityuk, A. A.; Ro ¨sch, N. J. Chem. Phys. 2002, 117, 5607] for electron-transfer coupling. As a result, the EET coupling can be calculated in a general class of systems irrespective of the molecular symmetry. The short-range coupling, defined as the contribution from Dexter's exchange coupling and the overlap effect, was obtained as the difference of the EET coupling from this new scheme and a precise account of the Coulomb coupling. For a pair of stacked naphthalenes, the short-range coupling is very similar to the triplet-triplet energy-transfer coupling in both magnitudes and the distance dependences. We have observed cases in which the Coulomb coupling decays either faster or slower than the expected dipole-dipole R -3 distance dependence even at distances of 10-20 Å, due higher multipole interaction. For a well-studied series of rigidly linked naphthalene dimers, the role of through-bond interaction was studied with the new computational methods. Similar to previous reports, our results show that the through-bond component contains a Coulomb coupling, and in some cases, contributions from the short-range couplings can be seen.
The nature of charge carriers in conjugated polymers was elucidated through optical spectroscopy following single- and multielectron reduction of 2,7-(9,9-dihexylfluorene) oligomers, F(n), n = 1-10, yielding spectra with the two bands typical of polarons upon single reduction. For short oligomers addition of a second electron gave a single band demonstrating the classic polaron-bipolaron transition. However, for long oligomers double reductions yielded spectra with two bands, better described as two polarons, possibly residing side-by-side in the F(n) chains. The singly reduced anions do not appear to delocalize over the entire length of the longer conjugated systems; instead they are polarons occupying approximately four fluorene repeat units. The polarons of F(3) and F(4) display sharp absorption bands, but for longer oligomers the bands broaden, possibly due to fluctuations of the lengths of these unconfined polarons. DFT calculations with long-range-corrected functionals were fully consistent with the experiments describing polarons in anions, bipolarons in dianions of short oligomers, and side-by-side polarons in dianions of long oligomers, while results from standard functionals were not compatible with the experimental results. The computations found F(10)(2-), for example, to be an open-shell singlet ( ≈ 1), with electrons in two side-by-side orbitals, while dianions of shorter oligomers experienced a gradual transition to bipolarons with states of intermediate character at intermediate lengths. The energies and extinction coefficients of each anionic species were measured by ultraviolet-visible-near-infrared absorption spectroscopy with chemical reduction and pulse radiolysis. Reduction potentials determined from equilibria mirrored oxidation potentials reported by Chi and Wegner. Anions of oligomers four or more units in length contained vestigial neutral (VN) absorption bands that arise from neutral parts of the chain. Energies of the VN bands correspond to those of oligomers shorter by four units.
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