Numerical examination of the extended phase-space volume-preserving integrator by the Nosé-Hoover molecular dynamics equations.

This article illustrates practical applications to molecular dynamics simulations of the recently developed numerical integrators [Phys Rev E 2006, 73, 026703] for ordinary differential equations. This method consists of extending any set of ordinary differential equations in order to define a time invariant function, and then use the techniques of divergence-free solvable decomposition and symmetric composition to obtain volume-preserving integrators in the extended phase space. Here, we have developed the technique by constructing multiple extended-variable formalism in order to enhance the handling in actual simulation, and by constituting higher order integrators to obtain further accuracies. Using these integrators, we perform constant temperature molecular dynamics simulations of liquid water, liquid argon and peptide in liquid water droplet. The temperature control is obtained through an extended version of the Nosé-Hoover equations. Analyzing the effects of the simulation conditions including time step length, initial values, boundary conditions, and equation parameters, we investigate local accuracy, global accuracy, computational cost, and sensitivity along with the sampling validity. According to the results of these simulations, we show that the volume-preserving integrators developed by the current method are more effective than traditional integrators that lack the volume-preserving property.