On the Potential of Implicit Integration Methods for Molecular Dynamics Simulation

The purpose of this work was to investigate the utility of implicit integration methods for molecular dynamics (MD) simulation. Implicit methods were investigated in an attempt to address the bottleneck associated with short, stability-limited step size lengths available to the explicit methods currently in widespread use. Two implicit methods were compared to the current standard for time integration, the explicit velocity Verlet (VV) integration scheme. The implicit methods were implemented in a methods development version of a popular research grade MD code, which uses a physically based interaction potential for biological molecules. The nonlinear systems of equations arising from the use of implicit methods were solved in a quasi-Newton framework. In addition to quasi-Newton, a Newton-Krylov type method was considered briefly. The primary aspects of comparison were energy conservation and efficiency. The ideal performance of the implicit methods implemented in a coprocessing framework was estimated. These estimates did not indicate a significant gain in performance over the explicit method. Although the energy conservation provided by the implicit methods was adequate, the length of the time steps was limited by convergence in the Newton iterations. Fourier transform analysis indicated that high frequencies present in the velocity and acceleration signals may be limiting the step size lengths and thereby limiting the utility of implicit methods in MD.