Dynamical MultipleTimestepping Methods for Overcoming the HalfPeriod Time Step Barrier.pdfVIP

Dynamical Multiple-Timestepping Methods for Overcoming the Half-Period Time Step Barrier Siu A. Chin Department of Physics, Texas AM University, College Station, TX 77843, USA Current molecular dynamic simulations of biomolecules using multiple time steps to update the 3 slowingly changing force are hampered by an instability occuring at time step equal to half the period 0 0 of the fastest vibrating mode. This has became a critical barrier preventing the long time simulation 2 of biomolecular dynamics. Attemps to tame this instability by altering the slowly changing force and efforts to damp out this instability by Langevin dynamics do not address the fundamental cause of g this instability. In this work, we trace the instability to the non-analytic character of the underlying u spectrum and show that a correct splitting of the Hamiltonian, which render the spectrum analytic, A restores stability. The resulting Hamiltonian dictates that in additional to updating the momentum due to the slowly changing force, one must also update the position with a modified mass. Thus 3 multiple-timestepping must be done dynamically. 1 ] h I. INTRODUCTION p - The evolution of any dynamical variable W (q , p ) is given by the Poisson bracket, m i i e d ∂W ∂H ∂W ∂H h