Page - 36 - in Charge Transport in DNA - Insights from Simulations

TheoreticalBackground Figure2.5: Schematic representation of the behavior of the wave-function in surface hopping simulations. The possible course of two simulations is shown. Reaching the high-coupling region, the two states do not mix like in the mean-field approach. TheSystemmayhopbetween the states and leave the region onone of them (Based onFig.5 in [72]) therefore no polarization of theMMenvironment[100–102]. It is not necessary to choose a representation in advance,without knowing anything about theCTpro- cess. TheCGHamiltonianneedsnot tobediagonalized(as in the followingsurface hoppingmethod)with thismethod,which saves computational time. The propa- gatedwave-function can be transferreddirectly to the classicalMDsimulation by the mapping to the atomic charges. On the downside, the mean-field approach suffers fromtheso-calledmean-fielderror. Themain issuehere is thatall adiabatic states interactwith the samemeanpotential of the environment. This has the ef- fect, that in homogeneousDNAsequences,where the energetic landscape is very shallow, thedelocalizationof the charge is overestimatedexcessively. SurfaceHopping The othermethodof charge transfer computation in thiswork is the surface hop- ping (SH) scheme [103]. In this approach, the TDSE is propagated as well, but the classical system interacts onlywithonepureadiabatic state. Thekeyhere is to choose thisadiabatic state ineverytimestep. Figure2.5showstwopossiblesurface hoppingsimulations,wherehoppingoccurs in thehigh-coupling region. Thefinal states are adiabatic ones, nomixingof adiabatic statesoccurshere. The propagation of the wave-function then takes place on this adiabatic state through time. Transitions between the states may occur in every time step an 36