Page - 30 - in Charge Transport in DNA - Insights from Simulations

TheoreticalBackground The transmission function can be calculated using the Greens function with the Fisher–Lee relation,[83] T(E)= |G1N(E)|2 (2.31) G1N(E) is the (1,N) element of the chainGreen’s functionmatrix,whichwas cal- culatedvia thematrixDysonequation, G(E) = (E1−H)−1 (2.32) Within the Landauer–Büttiker framework it is possible to calculate an instanta- neous current. Todo so, someadditional assumptions have to bemade. First, the chainof charge carrying siteshas tobe coupled toanelectrodeoneach side. The transmission then contains two additional terms,which account for this cou- pling. T(E)=4γLγR|G1N(E)|2 (2.33) Thewide-band-approximation is assumedhere,neglectinganyatomic structureof the electrodes. Then, the coupling to the electrodes is described by single values γL and γR as effective coupling terms. Therefore, the molecule is considered to be contacted to a perfect metal with a constant, energy-independent density of states.Notehere that theassumptionofconstantcoupling to theelectrodesmaybe unrealisticwhen stress is exerted upon theDNA–electrode contact, whichmakes the contact loosen, transformor evenbreak. In this case the (1,N) element of the chainGreen’s functionmatrixG1N(E) contains the coupling to the electrodes, 30