Predicting the structure of fluids with piecewise constant interactions: Comparing the accuracy of five efficient integral equation theories

We use molecular dynamics simulations to test integral equation theory predictions for the structure of fluids of spherical particles with eight different piecewise-constant pair-interaction forms comprising a hard core and a combination of two shoulders and/or wells. Since model pair potentials like these are of interest for discretized or coarse-grained representations of effective interactions in complex fluids (e.g., for computationally intensive inverse optimization problems), we focus here on assessing how accurately their properties can be predicted by analytical or simple numerical closures including Percus-Yevick, hypernetted-chain, and reference hypernetted-chain closures and first-order mean spherical and modified first-order mean spherical approximations. To make quantitative comparisons between the predicted and simulated radial distribution functions, we introduce a cumulative structural error metric. For equilibrium fluid state points of these models, we find that the reference hypernetted-chain closure is the most accurate of the tested approximations as characterized by this metric or related thermodynamic quantities.