Subspace method for long time scale molecular dynamics

This article presents the dual foundations of an approach to the long time integration of molecular dynamics equations. This work demonstrates that the long time scale molecular dynamics takes place in a relatively low dimensional subspace spanned by a set of collective eigenmodes and that the molecule remains in this subspace for long spans of time, at least on the order of picoseconds or greater. Both of these points are central to constructing an efficient numerical algorithm for long time scale dynamics. The first point allows for automatic filtering of the high frequency components of the dynamics and thus enables the stable use of very large time steps. The second observation allows for possibly using the same basis set for a long time span. Calculations are presented to substantiate these points. The model molecule consists of a 32 atom chain for which the equilibrium configuration is a helix. The chain interactions are of a two, three, and four body nature, allowing respectively for stretch, bending, and torsional motions. The molecule is intentionally chosen to undergo extreme dynamical changes for a severe test of both assertions 1 and 2 and the resulting algorithm. Moreover, one initial state is chosen very far from thermal equilibrium, with all of the energy of the molecule residing in a single local normal mode of the equilibrium configuration. Another initial condition, with a thermal distribution of kinetic energy, is explored. The methods presented are shown to be capable of handling both diverse initial conditions. The dynamical results permit a detailed analysis of the spectral aspects of the problem and provide further support for the subspace concept and the methodology based on it. Stable subspace dynamic integration for time steps of δt = 100 fs were executed, and the results agree well with the full dynamics (for which the maximum allowable time step using standard molecular dynamics would be δt ≈ 1 fs); the dynamics included torsional barrier crossings.