Page - 34 - in Charge Transport in DNA - Insights from Simulations

TheoreticalBackground Computing theReorganizationEnergy The RE of CT processes ofmolecules in an aqueous solvent ismainly influenced by the outer-sphere RE introduced through the solvent. In chapter 6 this param- eter will be investigated in detail. Therefore, the method used to compute this parameter is introducedhere. The previously developedMD-based schemewill be used to calculate the outer- sphereRE (λs) forCT inDNA[93]. The general idea is to calculate theREof a charge transfer process froma state α, where the charge is localized on one molecule, to a state β, where the charge is localizedon theothermolecule,where the environmenthas tobe reorientated. λs= 〈Eα(r)〉β−〈Eα(r)〉α (2.37) With the index of E denoting the Hamiltonian used to calculate the energy of the system, and the index of the parenthesis denoting the Hamiltonian used to create the ensemble. This allows the estimation of the outer-sphereREusingMD simulations. 〈Eα(r)〉α is themeanpotential energyof the simulationbeing in stateα, calculated with theappropriateHamiltonian for this state. On theotherhand, 〈Eα(r)〉β is the meanpotential energyof theensemble, createdwith theHamiltonianβ, calculated with theHamiltonian for stateα. 2.6.2 Non-adiabaticPropagationSchemes Mean-Field (Ehrenfest)Theory Thefirstmethodused in thiswork is based on themean-field (Ehrenfest) [94, 95] approach. Here, the energy of the system is an average over all adiabatic states weighted by their populations. All these states interactwith a commonpotential inducedbytheclassicalenvironment. Ontheotherhand, theclassicalenvironment interacts with the combination of these adiabatic states of the quantum system. Thisway, a single potential-energy landscape is constructed. The propagation of 34