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The electronic structure of the lowest unoccupied orbitals of [6,6]-phenyl-C 61 -butyric acid methyl ester (PCBM) is computed using a combination of classical molecular dynamics simulations (used to determine the morphology) and approximate quantum chemical calculations (used to determine the energy spectrum and localization length). The time-dependent coupling between localized states and the electron-vibration coupling is also computed. The results show that PCBM possesses an unusual distribution of localized and delocalized states, both thermally accessible at room temperature, which cannot be mapped into standard models of transport in disordered media. The coupling between these states is found to be too strong for simple perturbative treatments. At the same time, the local electron-vibration coupling, dominated by high frequency modes, is too weak to allow the formation of localized small polarons, as the zero point energy is above the barrier for electron hopping.

The charge carrier dynamics in organic semiconductors has been traditionally discussed with the models used in inorganic crystalline and amorphous solids but this analogy has severe limitations because of the more complicated role of nuclear motions in organic materials. In this perspective, we discuss how a new approach to the modelling of charge transport is emerging from the alliance between the conventional quantum chemical methods and the methods more traditionally used in soft-matter modelling. After describing the conventional limit cases of charge transport we discuss the problems arising from the comparison of the theory with the experimental and computational results. Several recent applications of numerical methods based on the propagation of the wavefunction or kinetic Monte Carlo methods on soft semiconducting materials are reviewed.

In partially ordered organic semiconductors, the characteristic times of nuclear motion are comparable to those of charge carrier dynamics. It is impossible to describe charge transport using either static disorder models or temperature averaged electronic Hamiltonians. We build a model Hamiltonian which allows the study of charge transport whenever carrier and nuclear dynamics are not easily separable. Performing nanoseconds long molecular dynamics of a columnar mesophase of a discotic liquid crystal and evaluating electronic couplings, we identify realistic parameters of the Hamiltonian. All modes which are coupled to the electron dynamics can be described in the model Hamiltonian by a limited number of Langevin oscillators. This method can be applied to systems with both slow (nanoseconds) and fast (hundreds of femtoseconds) nuclear motions, i.e., with both dynamic and static disorder.