Revisiting triplet correlation functions of classical fluids

Wertheim's perturbation theory proposes that the thermodynamic properties of an associating tangential-core chain fluid can be recast in terms of the structural properties of the non-bonded state. In this context, triplet correlation functions (TCFs), in addition to the radial distribution function (RDF), help to explain angular effects and branching in non-linear molecules. Nonetheless, unlike the RDF, computing TCFs via molecular simulation requires building a sophisticated framework to obtain accurate data at minimal computational cost. Furthermore, available simulation data and correlations for simple fluids are either outdated or scarce. In this work, we focus on the classical pure hard-sphere fluid and provide extensive datasets of TCFs for some representative geometries found in alkane isomers. We revisit the general algorithm for computing volume elements in distance histograms and present the open-source Monte Carlo code ENIG3 to efficiently calculate these structural observables for simple fluids (e.g., hard, square-well, and Mie spheres). Finally, contact values are correlated following a semiempirical approach, and we report accurate closed-form expressions readily to be incorporated into Wertheim's solutions.