Page - 18 - in Charge Transport in DNA - Insights from Simulations

TheoreticalBackground of freedomand solve the equations ofmotion directlywith the barostat incorpo- rated. In this sense, theParrinello–Rahmanbarostat [60,61] is theequivalent to the Nosé–Hoover thermostat. 2.3 QuantumChemistry MMmethods, like shown in the latter chapter, are only able todescribe the struc- ture and dynamic properties of molecules without accounting for their explicit electronic structure. In contrast, quantum chemistry (QC)methods are designed todescribe the electronic structures ofmolecular systems. Here, a short introduc- tion into the basic concepts of theQCmethods, which are applied in the studies of CT in the later parts of thiswork,will be given. The starting pointwill be the density functional theory (DFT).Having summarized theDFT, the approximative density-functional tight-binding (DFTB) (chapter 2.3.2)method is introduced. The latterwill beused in theCTcalculations. 2.3.1 DensityFunctionalTheory DFT is a quantumchemicalmethod todescribe electronic structures of atomsand molecules. In contrast to thewave functionbasedmethods likeHartree–Fock (HF) and post-HF (e.g. perturbation theory or configuration interaction), DFT is based on thecalculationof theelectrondensity. This approachhas twomainadvantages: • The system is no longer described by 3Ncoordinates of thewave function, butonlyby3 coordinatesoverall. • Theelectrondensity isaphysicalobservablewhereas thewave-function (WF) isnot. Theprobabilityoffindinganelectronatapositionrcanbecomputedbyintegrating over all other electrons in the system. ρ(r1)=N ∫ Ψ∗(r1...rN)Ψ(r1...rN)dr2...drN (2.14) 18