A Robust and Automated Approach for the Calculation of Absolute Entropy from the Two-Phase Thermodynamic Model with Gaussian Memory Function

Abstract

The two-phase thermodynamic (2PT) model provides an efficient route for calculating the absolute entropy values from a typical trajectory of molecular dynamic simulations. The method calculates the entropy based on the vibrational density of state (DOS), which is considered to be the superposition of contributions from a gas-like and a solid-like component. A fluidicity parameter is used to determine the fraction of the gas-like component, which is considered as a hard-sphere gas. The DOS of the hard-sphere gas was estimated using a delta memory function. Recently Desjarlais suggested to use a Gaussian memory function for better description of the gas-like DOS, in particular in the high-frequency region. However, a systematic but tedious approach involving the evaluation of moments of the DOS was required for evaluating the fluidicity. In this work, we propose a new approach to determine the fluidicity which can be easily implemented in a computer code. We validated this new approach by calculating the entropy of Lennard–Jones fluids in the gas, liquid, solid, and supercritical regions. It is found that the entropy determined from using the Gaussian memory function for the gas-like component (denoted as 2PT-GMF) is always lower than that determined from that using delta memory function (denoted as 2PT-δMF). Furthermore, 2PT-GMF is more accurate (with an absolute average relative error of 1% compared to the results from MBWR EOS) than 2PT-δMF (AARD = 2%) in the liquid and supercritical regions, whereas their performances are comparable in other regions (AARD = 1%).