Symmetry Numbers and Statistical Factors in Self-Assembly and Multivalency

Abstract

Evaluation of statistical factors in self-assembly processes is not a firmly settled question. As a contribution to solve this problem, a critical re-examination of the symmetry number method and generalization of the direct count method are presented. The two approaches, producing the same results, mutually reinforce their role with respect to other discordant methods whose results cannot be independently checked. The direct count method moreover serves as a rationale for the apparently odd results the symmetry number method sometimes provides. The two methods thus turn out to be complementary to each other. Discussion of some exemplary cases points to the importance and subtlety of the role played by the geometrical features of assemblies involving intramolecular bonds.