Linear prediction of force time series to accelerate molecular dynamics simulations

We have recently proposed a molecular dynamics simulation scheme in which the time-consuming evaluation of non-bonding forces is periodically replaced by linear prediction of the latter from previous values [B. Brutovsky, T. Mülders, G.R. Kneller, J. Chem. Phys. 118 (2003) 6179]. For a simple molecular liquid, consisting of linear molecules with an internal vibrational degree of freedom, the method yields a speedup of up to 7 compared to conventional simulations. The hybrid simulation scheme preserves all essential structural and dynamical quantities. We show here that the linear predictor can be considered as an optimal integrator for finite time steps whose coefficients approach those of a discrete Taylor series if the simulation step tends to zero. The short time dynamics and the structure of the liquid are preserved for much longer periods if linear prediction is used instead of Taylor expansion to predict the non-bonding forces.