  A mixture of solvent particles with short-range, directional interactions and
solute particles with short-range, isotropic interactions that can bond
multiple times is of fundamental interest in understanding liquids and
colloidal mixtures. Because of multi-body correlations predicting the structure
and thermodynamics of such systems remains a challenge. Earlier Marshall and
Chapman developed a theory wherein association effects due to interactions
multiply the partition function for clustering of particles in a reference
hard-sphere system. The multi-body effects are incorporated in the clustering
process, which in their work was obtained in the absence of the bulk medium.
The bulk solvent effects were then modeled approximately within a second order
perturbation approach. However, their approach is inadequate at high densities
and for large association strengths. Based on the idea that the clustering of
solvent in a defined coordination volume around the solute is related to
occupancy statistics in that defined coordination volume, we develop an
approach to incorporate the complete information about hard-sphere clustering
in a bulk solvent at the density of interest. The occupancy probabilities are
obtained from enhanced sampling simulations but we also develop a concise
parametric form to model these probabilities using the quasichemical theory of
solutions. We show that incorporating the complete reference information
results in an approach that can predict the bonding state and thermodynamics of
the colloidal solute for a wide range of system conditions.
