The effects of torsional degrees of freedom on the excited-state relaxation of conjugated oligomers in solution are explored computationally by coupling an exciton model of the oligomer to a Brownian dynamics model of the solvent. The exciton model assigns one torsional degree of freedom to each unit cell, or site, of the oligomer. A simple molecular mechanical form is used for the ground electronic state. The excitation energy is obtained assuming coherent coupling between sites that is proportional to the cosine of the difference in torsional angles. The solvent is characterized by a single parameter, which is equivalent to setting the rotational diffusion time, t rot , of a single unit cell about the oligomer axis in the absence of any internal forces. The relaxation of long oligomers exhibits a fast component, with a time constant that is about 0.025t rot and a slow component that is about 0.15t rot . As the oligomer length is decreased, the time constant for the slow component decreases such that the biexponential behavior smoothly diminishes below 10 unit cells, nearly disappearing by three unit cells. Comparisons of the exciton model, which includes self-trapping, with molecular mechanics and harmonic oscillator models, which do not include self-trapping, show similar behaviors. The double-exponential behavior therefore appears to be a general consequence of the participation of many torsional degrees of freedom in establishing the excitation energy. Because the time scales are relatively independent of the details of the torsional potential, experimental measurements of relaxation due to planarization report primarily on t rot .

A model is developed for the mobility of a charge carrier along a conjugated polymer dissolved in solution, as measured by time-resolved microwave conductivity. Each unit cell of the polymer is assigned a torsional degree of freedom, with Brownian dynamics used to include the effects of solvent on the torsions. The barrier to torsional motion is substantially enhanced in the vicinity of the charge, leading to self-trapping of the charge onto a planarized region of the polymer chain. Within the adiabatic approximation used here, motion arises when regions of the polymer on either side of the charge fluctuate into planarity and the wavefunction spreads in the corresponding direction. Well-converged estimates for the mobility are obtained for model parameters where the adiabatic approximation holds. For the parameters expected for conjugated polymers, where crossing between electronic surfaces may lead to breakdown in the adiabatic approximation, estimates for the mobility are obtained via extrapolation. Nonadiabatic contributions from hopping between electronic surfaces are therefore ignored. The resulting mobility is inversely proportional to the rotational diffusion time, trot, of a single unit cell about the polymer axis in the absence of intramolecular forces. For trot of 75 ps, the long-chain mobility of poly(para-phenylene vinylene) is estimated to be between 0.09 and 0.4 cm(2)∕Vs. This is in reasonable agreement with experimental values for the polymer, however, the nonadiabatic contribution to the mobility is not considered, nor are effects arising from stretching degrees of freedom or breaks in conjugation.

Light-driven molecular motors may be useful for nanotechnology applications. The possibility of building such a motor based on the tolane framework is explored here. In the ground electronic state of tolane, the barrier to internal rotation is comparable to room temperature thermal energies, k(B)T. The barrier increases substantially in the excited state, causing the molecule to planarize after absorption of a photon. This tendency to planarize may be converted into unidirectional rotational motion by placing chiral substituents on the phenyl rings. A potential advantage of this class of motors is that they may undergo rapid, nanosecond scale rotation. Computational design of appropriate substituents was done using semiempirical quantum chemical methods, SAM1 for the ground electronic state coupled to INDO for the excitation energy. The torsional surfaces of the best candidate were then generated using ab initio DFT methods, which confirm that the molecule should undergo unidirectional rotation upon photoexcitation. The results provide a proof of principle for this class of motors; however, two aspects of the final candidate are nonideal. First, although the design goal was to use steric interactions between substituents to induce the rotation, decomposition of the interaction energy suggests attractive interactions play a role. Solvent interactions may interfere with these attractive interactions. Second, TDDFT calculations suggest that interactions between excited states lower the rotational driving force in the excited state.