Abstract
Since most experimental observations are performed at constant temperature and pressure, the isothermal-isobaric (NPT) ensemble has been widely used in molecular simulations. Nevertheless, the NPT ensemble has only recently been placed on a rigorous foundation. The proper formulation of the NPT ensemble requires a “shell” particle to uniquely identify the volume of the system, thereby avoiding the redundant counting of configurations. Here, we review our recent work in incorporating a shell particle into molecular dynamics simulation algorithms to generate the correct NPT ensemble averages. Unlike previous methods, a piston of unknown mass is no longer needed to control the response time of the volume fluctuations. As the volume of the system is attached to the shell particle, the system itself now sets the time scales for volume and pressure fluctuations. Finally, we discuss a number of tests that ensure the equations of motion sample phase space correctly and consider the response time of the system to pressure changes with and without the shell particle. Overall, the shell particle algorithm is an effective simulation method for studying systems exposed to a constant external pressure and may provide an advantage over other existing constant pressure approaches when developing nonequilibrium molecular dynamics methods.
Highlights
The molecular dynamics (MD) simulation method can be straightforwardly applied to the analysis of an isolated system or a system described by the microcanonical ensemble in which the energy, volume V
While the generation of dynamic information about these systems is of interest, how to modify the equations of motion to describe a system at constant temperature and/or constant pressure is arguably not an obvious task
The agreement between isobars predicted by the new shell molecule molecular dynamics, the shell molecule Monte Carlo algorithm [15] and the equation of state for the Lennard-Jones fluid introduced by Johnson et al [46] is shown in Figure 1 of [17]
Summary
The molecular dynamics (MD) simulation method can be straightforwardly applied to the analysis of an isolated system or a system described by the microcanonical ensemble in which the energy, volume V and particle number N are held fixed. In these new MD algorithms, a shell particle is used to uniquely define the volume of a system exposed to a constant external pressure. Evans and Morriss [19,20] utilized constrained dynamics to develop an N P T MD algorithm In this method, both the instantaneous pressure and kinetic energy are made strict constants of motion, and so, the Andersen piston is not employed. Both the instantaneous pressure and kinetic energy are made strict constants of motion, and so, the Andersen piston is not employed This algorithm does not yield ensemble averages consistent with the N P T partition function (either with or without the shell particle), as the instantaneous pressure fluctuates within the N P T ensemble [15].
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