Ergodicity and Convergence of Fluctuations in Parrinello-Rahman Molecular Dynamics
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Ergodicity and Convergence of Fluctuations in Parrineklo-Rahman Molecular Dynamics 1 2 M. LI ' , W. L. JOHNSON' AND W. A. GODDARD 1112 'W. M. Keck Laboratory, 138-78, California Institute of Technology, Pasadena, California 91125 2 Molecular & Materials Simulation Center, Beckman Institute, 139-74, California Institute of Technology, Pasadena, California 91125
ABSTRACT Distortion and rotation of a molecular dynamics cell used in Parrinello-Rahman molecular dynamics are found to lead to slow convergence, or nonconvergence of fluctuations from thermodynamic averages. The variations are shown to be related to nonconservation of the total angular momentum and translational symmetry variance of the dynamics. A modified equation of motion is presented which eliminates these variations. It is shown that the ergodicity is achieved in the MD ensemble generated by the new equations of motion. However, the rate of convergence is strongly affected by the choice of the MD cell mass W. Simulation results show that not all values of W can be used to give a desired convergence of fluctuations from thermodynamic averages in finite simulations. The fastest convergence is achieved by using the optimal cell mass. INTRODUCTION In most molecular dynamics (MD) methods, volumes and shapes of systems being simulated are held fixed, so the ensembles these MD trajectories generate are either microcanonical or canonical. Although many thermodynamic properties can be studied using these methods, it is desirable to have different ensemble MD methods, for instance, the constant pressure and temperature (NPT) ensemble one, so the comparison of experimental results, which are often performed under the same situation, with the theoretical ones can be facilitated. Rahman-Parrinello molecular dynamics (RP MD) is one of the methods that can generate either constant pressure (or stress) and constant temperature, or constant pressure (or stress) and enthalpy MD ensembles. This is done by treating the shape and volume as well as the orientation of the MD cell as dynamic variables in an extended system [1]. Therefore, the RP MD axe suited to investigations of problems such as structural phase transitions, mechanical behavior of solids and more importantly, determination of heat capacities, elastic constants and compressibilities from fluctuations of relevant thermodynamic functions. The RP MD has been used to study mechanical stabilities of crystals [2], Martensite phase transitions [3], crystal structures at high pressures [4] and elastic properties of solids [5]. However, it has been found that a stable MD cell, or a supposedly equilibrium structure used in RP MD simulations, changes its shape as the simulation proceeds and eventually, reaches a structure of totally different symmetry [1]. This occurs even at the zero temperature where thermal fluctuations are completely absent. Moreover, the MD cell used has also been observed to rotate during simulations in molecular crystals [6] as well as in a simple nearest neighbor Lennard-Jones (LJ) solid [7]. A
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