  We develop a quasi-chemical theory for the study of packing thermodynamics in
dense liquids. The situation of hard-core interactions is addressed by
considering the binding of solvent molecules to a precisely defined `cavity' in
order to assess the probability that the `cavity' is entirely evacuated. The
primitive quasi-chemical approximation corresponds to a extension of the
Poisson distribution used as a default model in an information theory approach.
This primitive quasi-chemical theory is in good qualitative agreement with the
observations for the hard sphere fluid of occupancy distributions that are
central to quasi-chemical theories but begins to be quantitatively erroneous
for the equation of state in the dense liquid regime of $\rho d^3>$0.6. How the
quasi-chemical approach can be iterated to treat correlation effects is
addressed. Consideration of neglected correlation effects leads to a simple
model for the form of those contributions neglected by the primitive
quasi-chemical approximation. These considerations, supported by simulation
observations, identify a `break away' phenomena that requires special
thermodynamic consideration for the zero (0) occupancy case as distinct from
the rest of the distribution. A empirical treatment leads to a one parameter
model occupancy distribution that accurately fits the hard sphere equation of
state and observed distributions.
