This form of the hard-sphere potential (r < 2a) is designed to separate a pair of overlapping nanoparticles to contact over the course of a single time step and is functionally equivalent to the Heyes-Melrose algorithm for hard-sphere interactions. The attractive interaction (2a ≤ r ≤ 2a + 2δ) is the Asakura-Oosawa potential for the effective depletion attraction of hard spheres in a sea of noninteracting depletants. The particular functional form is not important, as all short-ranged, isotropic attractions have similar phase behavior when cast in terms of reduced second virial coefficients. We have previously used this model to accurately predict the structure and optical properties across a range of colloidal dispersions and assemblies. Hard-sphere dispersion states (U 0 = 0) were equilibrated for 100τ D before sampling, attractive hard-sphere fluid states (U 0 = 3k B T ) were equilibrated for 1000τ D , and phase-separated states (U 0 = 10k B T ) were equilibrated for 10000τ D .