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.