  The densities of states are evaluated for very short chain molecules made up
of overlapping monomers, using a model which has previously been shown to
produce helical structure. The results of numerical calculations are presented
for tetramers and pentamers. We show that these models demonstrate behaviors
relevant to the behaviors seen in longer, helix forming chains, particularly,
"magic numbers" of the overlap parameter where the derivatives of the densities
of states change discontinuously, and a region of bimodal energy probability
distributions, reminiscent of a first order phase transition in a bulk system.
