Page - 31 - in Charge Transport in DNA - Insights from Simulations

2.5ChargeTransport inDNA G(E) = (E1−H−ΣL−ΣR)−1 (ΣL)lj = −iγLδl1δj1 (2.34) (ΣR)lj = −iγRδlNδjN Then, the instantaneous current can be obtainedwith the integration of the trans- mission functionas I(V)= 2e h ·4γLγR · ∫ ∞ −∞ dE ( f ( E− eV 2 ) − f ( E+ eV 2 )) |G1N(E)|2 (2.35) with f being theFermi–Diracdistribution function. To obtain single values for the instantaneous current, the converged limiting cur- rent at the voltage of 2V,which is independent of the choice of the Fermi level, was considered. With theapplicationof this framework, two further conditions are assumed: • theCT ispurely coherent,meaning thatpossible incoherent scatteringwould bemissed [84] • themotionof electrons is faster than themotionofnuclei. These issues were addressed in Refs. [44, 45], where the methodology was de- scribed in detail. Note that the aim here is not to compute quantitative current– voltage characteristics, forwhichexplicit evaluationofFermienergies andaccount of all states possibly contributing to conductance at the consideredvoltagewould be required. Rather, themaximumcurrent at highvoltage is considered as a con- venientmeasure of the ability of theDNA-basedmolecular system to support co- herent CT. Actually, the CT parameters (electronic coupling (EC) and ionization potential(IP)) are the key quantities determining the rate of CT proceeding with anymechanism. Therefore, the obtained values ofmaximumcurrent can be con- sidered tobe indicative for the efficiencyofCT ingeneral. 31