Chemical combinatorics. Part 3.—Stereochemical invariance law and the statistical mechanics of flexible molecules

Abstract

The replacement of three-dimensional molecular models by one-dimensional molecular graphs is a simplifying feature of many physical and chemical theories, particularly for mixtures. For this to be a sound procedure in statistical mechanics, one requires an explicit invariance law relating symmetry properties of molecules in three-, two- and one-dimensional states. This law is here derived. Although it is simple, it reveals a surprising property of Euclidian spaces and their subspaces. The law articulates the statistical mechanical treatment of systems of molecules which are flexible by virtue of bond rotation, in a manner complementary to the treatment of fluids with interparticle forces by the theory of irreducible cluster graphs. The law can be generalised to rigid bond systems, but with some loss of generality. It completes the rigorous analysis of the statistical basis of gelation, which is important for the understanding of living systems.