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

Abstract

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.

Temperature–Energy-space Sampling Molecular Dynamics: Deterministic, Iteration-free, and Single-replica Method utilizing Continuous Temperature System

“…[52] for a general case. The extended space formalism [40,41] defines an extended ODE on an extended space Ω ≡ Ω × R bẏ…”

Numerical Integration Techniques Based on a Geometric View and Application to Molecular Dynamics Simulations

“…The first point is the multiple extended-variable formalism developed by Queyroy et al (Queyroy et al, 2009 v → e (nζ/Q)t v by Φ [4] t n the NH equation. This situation can be avoided by the multiple extended-variable formalism, where v 1 , ...., v M are used instead of v (practically M = n).…”

Symmetric, explicit numerical integrator for molecular dynamics equations of motion with a generalized friction

“…(t), in the original ODE (10a) is not perturbed at all by attaching (10b). The multiple extended-variable formalism, where v 2 R l is generally considered, is useful to enhance the handling in actual simulation [29].…”

“…in order to satisfy the symmetric property h = h . A number of speci…c values of the parameters, viz., stage s and coe¢ cients f i ; i g, are known [29,37]. The simplest secondorder integrator is a generalization of the Verlet method, de…ned by…”

“…Since the target of the current method is in the general form (1), it presents a uni…ed integration scheme for the three kind of EOMs described above. For the NH EOM, since g has a simple structure such that g (x; K(v); ) = g NH ( ), its e¢ cient integrators have been developed [26][27][28][29]. But this is a special case.…”