Page - 17 - in Charge Transport in DNA - Insights from Simulations

2.2MolecularDynamicsSimulation Now, the equations ofmotion have to be calculated for an extended systemwith 3N+1degreesof freedom r¨i= Fi mi −s · r˙i (2.11) where the second term can be seen as a kind of a “friction” originating from the heat bath. Then, the extra equationofmotion for theheat bath takes the following form: s˙= 1 Q (T−Ttarget) (2.12) Thestrengthof coupling isdeterminedbythe introducedparameterQ, the“mass” of theheatbath. Toget amore intuitiveparameter for the coupling, a timeparam- eterτ is introduced. Q= τ2 ·Ttarget 4π2 (2.13) The period of oscillation of the kinetic energy between the system and the heat bath is specifiedby thisparameterτ. The thermostat is incorporated into the equations ofmotiondirectly in theNosé– Hoover approach. Therefore, it is an integral part of the integrator and not only an a posteriori correction. It can be shown that the ensemble generated by the Nosé–Hoover thermostat is a correct canonical ensemble. PressureCoupling Chemical experiments are normally conductedunder conditions of constant pres- sure. AnNPTensemble isused todescribe such conditions inMDsimulations. In contrast to the thermostatswhere thevelocities are subject to scaling, thebarostats scale thevolumeof the simulationbox. This canbedoneequivalently to themeth- ods described in the previous part. The Berendsen barostat scales the volume of thebox inadirect fashionandthusshares thesamedrawbackswith theBerendsen thermostat. Again, amore sophisticatedway is to introduce an additional degree 17