The graph-like state of matter. Part 8.—LCGI schemes and the statistical analysis of experimental data

Abstract

All additivity schemes can be expressed in terms of an LCGI (linear combination of graphtheoretical invariants) and they are exact in a mathematically almost trivial way. With the aid of the combinatorial method of Möbius inversion, the LCGI formulation tackles efficiently the confirmation (or rejection) of theories from experimental data by exact calculation. Optimisation methods are out of place for this purpose. However, optimisation over a truncated LCGI series does remain the most consistent approach to data reduction and prediction. These conclusions are illustrated by reference to standard molar enthalpy data for alkanes. Our example provides a paradigm for the collection and statistical analysis of molecular data.