The graph-like state of matter. Part 2.—LCGI schemes for the thermodynamics of alkanes and the theory of inductive inference

Abstract

The theory of graphs, a rapidly developing mathematical discipline, is immensely useful in chemistry. As first appreciated by Cayley (A. Cayley, Collected Mathematical Papers, Cambridge University Press, 1889–97), a molecule becomes a graph, when we regard atoms as points and bonds as lines. Theories based on this notion define a state of matter. Formally, they almost always equate measurable quantities to linear combinations of graph-theoretical invariants (LCGI).

Using quite elementary concepts and terms of graph theory, a single systematic definition of about 50 words, contains as special cases, practically all that is useful in previously proposed additivity scheme for predicting standard thermodynamic data. For example, the bond additivity schemes, the schemes for alkanes by Allen, by Laidler and by Tatevskii are included as individual members of the set of schemes so defined, which constitute a canonical hierarchy of LCGI schemes.

In this way, estimation of standard enthalpies of alkanes can be rationalised, and that of standard entropies substantially improved. This is exemplified with the aid of recent improvements in computer optimisation procedures. The theory of inductive inference, especially as developed by Carnap (R. Carnap, The Continuum of Inductive Methods, University of Chicago Press, 1952), is useful not merely in suggesting methods of economical and systematic construction of inductive schemes, but in assessing the validity of their postulational basis in the light of experimental data. The customary calculation from standard enthalpies of substantial destabilisation energies in the form of “steric corrections” is criticised as being biassed. It is doubted whether quantum theory had so far contributed significantly to results of analyzing enthalpy data on alkanes.