Modelling charge transport in organic semiconductors with a fragment-orbital based surface hopping method

Charge transport in organic semiconductors is an important current topic of research, but the exact nature of the charge transport remains an unresolved question. Experimental evidence exists to support either of two common models (band-like transport or small polaronic hopping) and various computational simulations suggest that for the standard parameter ranges for organic semiconducting devices, both of these models are likely invalid, with temperatures too high for a band-like transport model and couplings too high relative to the reorganization energy for charge localization to be assumed. There is potential for a non-adiabatic molecular dynamics method that partially separates classical and quantum degrees of freedom, such as surface hopping, to be applied to the problem. This is what I have begun with my fragment-orbital based surface hopping (FOB-SH) method. Based on Tully's famous fewest-switches surface hopping algorithm, FOB-SH simulates a condensed phase organic semiconductor with a classical molecular dynamics approach while solving the Schr\"odinger equation to directly model the behaviour of a single excess electronic charge. The latter is made computationally efficient by using an analytic overlap method to calculate the Hamiltonian off-diagonal elements. In this thesis I discuss in detail the theory behind FOB-SH, along with my first implementation and validation of the method. I present results on two systems, of two and ten `ethylene-like' molecules respectively. In the two-molecule system I calculate charge transfer rates and find that my method qualitatively agrees with standard charge transfer theory in regimes where agreement is expected, though questions are posed in regimes where standard theory becomes invalid. For the ten-molecule system I demonstrate that charge mobilities can be calculated from my simulations. I observe a thermal activation peak for low couplings and a crossover from activated hopping to band-like transport with increasing temperature, qualitatively agreeing with another similar surface hopping method. I show that FOB-SH has great potential to tackle the charge transport in organics problem.