Chapter 6: From Atomic Orbitals to Nano-scale Charge Transport with Mixed Quantum/Classical Non-adiabatic Dynamics: Method, Implementation and Application

An efficient computational method to perform fully atomistic mixed quantum/classical non-adiabatic molecular dynamics in nano-scale organic semiconductors is reviewed and its numerical implementation presented in detail. The methodology is termed fragment orbital-based surface hopping (FOB-SH) and rests on a DFT-parametrized tight-binding representation of the Hamiltonian (updated on-the-fly along the molecular dynamics) as well as an efficient calculation of nuclear gradients to propagate the coupled electron–nuclear dynamics. Common algorithmic extensions to the original surface hopping algorithm, such as the adjustment of the velocities along the non-adiabatic vectors upon successful non-adiabatic transitions and a decoherence correction, allow FOB-SH to reach total energy conservation, detailed balance and internal consistency. Further improvements and optimizations applied to FOB-SH to deal with a high density of electronic states characterizing condensed phase systems are discussed. Trivial crossing detection and a removal of decoherence correction-induced spurious charge transfers are particularly important for accurate dynamics and the convergence of charge carrier mobility and wavefunction delocalization with increasing system size. The application of FOB-SH to the calculation of charge mobilities and transport mechanism across the 2D high-mobility planes of experimentally well-known molecular crystals is presented.