Page - 16 - in Charge Transport in DNA - Insights from Simulations

TheoreticalBackground from the reference temperature is correctedbetween two time stepsdependingon thepre-set timeconstantτ. dT dt = 1 τ (Ttarget−T) (2.6) Thus,wecancalculate the change in temperature ΔT= Δt τ (Ttarget−T) (2.7) as there is adirect relationbetween the temperatureand thevelocitiesof theparti- cles in the system. 1 2 m 〈 v2 〉 = 3 2 kT (2.8) The temperature in a system is changedby scaling the velocities of all particles in the systemwitha scaling factorλ,which is obtained fromthe relation ΔT= Δt τ (Ttarget−T)=(λ2−1)T (2.9) as λ= √ 1+ Δt τ ( Ttarget T −1 ) (2.10) Thecoupling to theexternalheatbathnowdependsonthechoiceof theparameter τ. With higher values for τ, the temperaturewill converge faster to the reference temperatureTtarget. Unfortunately, the Berendsen thermostat does not yield a correct canonical prob- ability distribution. Amore sophisticated thermostat that rigorously represents a correct canonical ensemble is the widely used Nosé-Hoover thermostat [58, 59]. Here, a heat reservoir is introduced as an integral part of the system with one degreeof freedom s, towhichamassQ is associated. 16