Mixed algorithm for modeling of charge transfer in DNA on long time intervals

Charge transfer in DNA is simulated by a discrete Holstein model “quantum particle + classical site chain + interaction”. Thermostat temperature is taken into account as stochastic force, which acts on classical sites (Langevin equation). Thus dynamics of charge migration along the chain is described by ODE system with stochastic right-hand side. To integrate the system numerically, algorithms of order 1 or 2 are usually applied. We developed “mixed” algorithm having 4th order of accuracy for fast “quantum” variables (note that in quantum subsystem the condition “sum of probabilities of charge being on site is time-constant” must be held), and 2nd order for slow classical variables, which are affecting by stochastic force. The algorithm allows us to calculate trajectories on longer time intervals as compared to standard algorithms. Model calculations of polaron disruption in homogeneous chain caused by temperature fluctuations are given as an example.