  In the development of equations of state for polyatomic molecules,
thermodynamic perturbation theory (TPT) is widely used to calculate the change
in free energy due to chain formation. TPT is a simplification of a more
general and exact multi-density cluster expansion for associating fluids. In
TPT all contributions to the cluster expansion which contain chain - chain
interactions are neglected. That is, all inter-chain interactions are treated
at the reference fluid level. This allows for the summation of the cluster
theory in terms of reference system correlation functions only. While highly
successful, TPT has many handicaps which result from the neglect of chain -
chain interactions. The subject of this document is to move beyond the
limitations of TPT, and included chain - chain contributions to the equation of
state.
