Page - 37 - in Charge Transport in DNA - Insights from Simulations

2.6ChargeTransfer inDNA can be called hops or switches. The key issue to be solvedhere is to calculate the probabilityof suchahop inevery timestepunder thegivencircumstances. The implementation used in this work is based on the SH algorithm by Persico et al. [104]. This algorithmuses the local diabatization of the adiabatic states of the system. The advantage of this is a stable representation of adiabatic states in regionsof avoidedcrossingor conical intersections. In the implementedsetup, theeigenproblemof theexcess charge is solved inevery time step. From this, thewave-function of the excess charge is given as a combi- nationof the adiabatic states. Then thediabatic states are redefined tobe identical with the ones at the beginning of the time step. The TDSE is then solved for this locallydiabaticbasis topropagate thewave-functionof theexcess charge. Thecru- cial step here is the calculation of the probability to hop from the current state to one of the calculated new states from the populations. The transition to another state is thendeterminedbydrawinga randomnumber. This isanalternativetopropagatingthewave-functionwiththemean-fieldmethod. The rest of the simulationprotocol is identicalwith that in themean-fieldmethod. Here again, the propagatedwave-function can be transferred directly to the clas- sicalMDsimulationby themapping to the atomic charges. The advantage of this setup is that there is no over-delocalization issue like in themean-field approach. However, in thismethodtheCGHamiltonianhas tobediagonalized. All represen- tationsof thequantumsystemconsistof individual states. Therefore it isnecessary to choosea representation inadvance. There is no artificial CTwhen the electronic couplings are very lowor even zero. Andfinally, themicroscopicalreversibility is fulfilled,againincontrast tothemean- fieldapproach,. Unfortunately, also the current implementation of the SH method suffers from some issues, which will be outlined shortly. After a surface hop, the velocities of the classicalMMatoms are not rescaled. This possiblymeans that there is no energyconservation. Another issueare the classically forbidden transitions,which are not treated in our setup. The quantum system is supposed to have enough energyat any time for thehop tooccur. 37