Page - 32 - in Charge Transport in DNA - Insights from Simulations

TheoreticalBackground 2.6 ChargeTransfer inDNA In this chapter, a short introduction into the basics of charge transfer and the needed parameters is given. Then, two advanced methods for the propagation of thewave-functionof the excess chargewill be summarized. This represents the rather chemical point of view of a charge transfer process, where the charge re- sides on onemolecule, or part of themolecule, and then is transferred to another molecule. Two of these non-adiabatic methods were implemented in our frame- workandrecentlypublished[72,73]. 2.6.1 BasicsofChargeTransfer The classical way to the CT in complexmolecular systems isMarcus’ theory [71, 85] and its extensions [86–90] Here, a rate of transfer between a donor and an acceptor for the non-adiabatic case can be calculated from several charge transfer parameters. kDA= |VDA|2 h¯ √ π λkBT exp [ −(ΔG 0+λ)2 4λkBT ] (2.36) Theseparameters are: • the electronic coupling (EC) |VDA|2 between thedonorand theacceptor • the reaction free energyΔGof theCTprocess • and the reorganizationenergy (RE)λ All three can be obtained using various computationalmethods. The static elec- tronic couplings can be calculated with highly accurate quantum chemical (QC) methods likeCAS-PT2.Moreefficientmethodshave tobeused tocalculate thedy- namicelectroniccouplings in thecourseofanMDsimulation. Inourapproach, the dynamicECareobtainedusingtheDFTB2method(seesection2.3.2 fordetails)and a fragment orbital approach[91]. ΔG andλ are thermodynamic quantities, so that their computationcanbedonebysamplingof theconfigurationspace, e.g. freeen- ergy calculations. TheRE is the energyneeded to reorient themolecules and their environmenttotheconformationcorrespondingtothefinalstateof theCTreaction. 32