Skip to main content
U.S. flag

An official website of the United States government

Official websites use .gov
A .gov website belongs to an official government organization in the United States.

Secure .gov websites use HTTPS
A lock ( ) or https:// means you’ve safely connected to the .gov website. Share sensitive information only on official, secure websites.

Ergodic Convergence Times For Molecular Liquids



Raymond D. Mountain


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 initial value of the energy metric to decay to 1% of the initial value is a useful indication that adequate sampling has been realized. The energy metric based ergodic convergence times for the molecular liquids water, methanol, and carbon dioxide plus mixtures of water and methanol are reported. The convergence time 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 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.
International Journal of Thermophysics


energy metric, water, methanol, carbon dioxide, liquid state, acetonitrile


Mountain, R. (2010), Ergodic Convergence Times For Molecular Liquids, International Journal of Thermophysics (Accessed July 20, 2024)


If you have any questions about this publication or are having problems accessing it, please contact

Created January 22, 2010, Updated February 19, 2017