Long time scale molecular dynamics subspace integration method applied to anharmonic crystals and glasses

Abstract

A subspace dynamics method is presented to model long time dynamical events. The method involves determining a set of vectors that span the subspace of the long time dynamics. Specifically, the vectors correspond to real and imaginary low frequency normal modes of the condensed phase system. Most importantly, the normal mode derived vectors are only used to define the subspace of low frequency motions, and the actual time dependent dynamics is fully anhannonic. The resultant projected set of Newton's equations is numerically solved for the subspace motions. Displacements along the coordinates outside the subspace are then constrained during the integration of the equations of motion in the reduced dimensional space. The method is different from traditional constraint methods in that it can systematically deduce and remove both local and collective high frequency motions of the condensed phase system with no a priori assumptions. The technique is well suited to removing large numbers of degrees of freedom, while only keeping the very low frequency global motions. The method is applied to highly anhannonic Lennard-Jones crystal and glass systems. Even in these systems with no intramolecular degrees of freedom or obvious separation of time scales, the subspace dynamics provides a speed up of approximately a factor of 5 over traditional molecular dynamics through use of a larger integration time step. In the cases illustrated here a single set of subspace vectors was adequate over the full time interval, although this is not expected to be true for all systems.