Ergodic Convergence Times for Molecular Liquids

Abstract

A problem common to all molecular dynamics and Monte Carlo simulations used to estimate fluid properties is how to decide when adequate sampling of the phase space of the system has been realized. One procedure for addressing the sampling question is to construct the energy metric for the system. The energy metric provides an indication of when the time-averaged energies of the individual molecules converge to a common value (self-averaging). The time required for the value of the energy metric to decrease to 1% of its initial value is a useful indication that adequate sampling has been realized. The energy metric based ergodic convergence times for the molecular liquids water, acetonitrile, methanol, and carbon dioxide plus mixtures of water and methanol and of water and acetonitrile are reported. The convergence time τ for water is about 100 ps at ambient conditions; for carbon dioxide it is about 300 ps while for methanol it is about 800 ps. The convergence times for water/acetonitrile mixtures are much longer due to the microheterogeneous structure of the mixtures. The ergodic convergence time is an increasing function of the mole fraction of methanol in the mixtures. The convergence times for water along the liquid side of the liquid–vapor coexistence curve are found to decrease strongly as the temperature increases.