Alternative ensemble averages in molecular dynamics simulation of hard spheres

ABSTRACT

We consider application to the hard sphere (HS) model of the mapped-averaging framework for generating alternative ensemble averages for thermodynamic properties. Specifically, we develop and examine new formulas for the pressure, the singlet and pair densities, and the cavity-correlation function inside the HS core; the pressure formula in particular is constructed such that it gives an ensemble average that exactly corrects the second-order virial equation of state. The force plays a central role in mapped-averaging expressions, and we write them in a way that accounts for the impulsive, event-driven nature of the HS dynamics. Comparison between results obtained conventionally versus mapped averaging finds that the latter has some advantage at low density, while both perform equally well (in terms of uncertainties for a given amount of sampling) at higher densities.

GRAPHICAL ABSTRACT

KEYWORDS:

• Hard-sphere fluid
• computer simulations
• event driven molecular dynamics
• mapped averaging
• cavity correlation function

Acknowledgements

A.T. acknowledges the Department of Chemical and Biological Engineering of the University at Buffalo, SUNY for hosting him as Fulbright Visiting Scholar 2018–2019, when the present studies were accomplished.

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Andrij Trokhymchuk  http://orcid.org/0000-0003-2257-0779

Andrew J. Schultz  http://orcid.org/0000-0002-1180-0156

David A. Kofke  http://orcid.org/0000-0002-2530-8816

Additional information

Funding

This work was supported in part by the U.S. National Science Foundation, Grant CHE-1464581.