Page - 12 - in Charge Transport in DNA - Insights from Simulations

TheoreticalBackground dependmainlyontheiratomistic structure,whichcanbedescribedwith forcefield basedmethodsverywell. To describe the atomistic structure, MM methods condense the electronic struc- ture with the nuclei and therefore depict the atoms in a classical manner. The correspondingenergyof suchaclassical systemisdue to thebondedand thenon- bonded interactions between the atoms. Atoms connected with each other with covalentbonds formcertainanglesanddihedrals,whichareassignedpotential en- ergy terms that contribute to the total energy. Atoms that are not bound to each other directly interact in terms of theCoulomb interaction and the van-der-Waals forces. The energy is calculated from all these different bonded and non-bonded interactions. Equation2.1 shows the total energyof anMMsystem. E = 1 2 ∑bonds kb(rb−r0b)2+ 1 2 ∑angles kθa(θa−θ0a)2 + 1 2 ∑dihedrals Vn [1+cos(nωn−ω0)] (2.1) + N−1 ∑ i N ∑ j=i+1 [ 4 ij [ ( σij rij )12−(σij rij )6 ] + qiqj 4π 0rij ] Someparametersneedtobedeterminedinadvancetocalculate the totalenergyfor themolecule. For all different bond types such asC-CorC=C,which are present in themolecule, a force constant kb and an equilibriumbond length r0b has to be supplied. Thesameis truefor theforceconstants (ka)andequilibriumvalues(θ0a)of alldifferent angles. Three setsofparameters arenecessary, themultiplicity (n), the correspondingenergy (Vn) and thephase shifts (ω0n) for thedescriptionofdihedral angles. Thenon-bonded interactionsare theelectrostaticCoulombinteractionof theatom- centered charges and a combination of the van-der-Waals interactions with the Pauli repulsion. Fortheformer, thechargesqiof theatomsareobtainedwithafitof theelectrostaticpotentialof thewholemoleculeobtainedfromQCcalculations.[50] The latter canbedescribedefficientlyandwith sufficient accuracyby theLennard- Jones(LJ)potential. Here, theparameters ijandσijdescribethedepthandlocation of the LJ potential. All these parameters are fitted toQM calculations or experi- 12