Correlation of the Molecular Cross-Sectional Area of Organic Monofunctional Compounds with Topological Descriptors

The molecular cross-sectional area (σ) has proved to be an interesting molecular measure not only in the field of adsorption phenomena on solids but also in biochemistry, physiology, or surfactant chemistry. The existing methods to estimate the cross-sectional areas are either not readily applicable or can only be applied to a limited number of compounds. The aim of this work was to describe a method, as general as possible, quick and easy to perform. To that end, the molecular cross-sectional areas were correlated with topological indices. The Emmett–Brunauer formula was used to calculate the reference cross-sectional areas (σEB) of 431 compounds. The correlations of the Wiener (W), hyper-Wiener (WW), Balaban (J), and Randić (χ) indices with σEB were compared for n-alkanes as well as branched and cyclic alkanes. Only the Wiener and hyper-Wiener indices correlated well with σEB, with the data being best fitted by power law regression curves. The lower degeneracy of the hyper-Wiener index did not translate into any significant gain of performance when correlated with σEB. Following the parsimony principle, the less complex Wiener index was thus selected to correlate with the σEB of compounds representing 31 other monofunctional and structural families. The integration of all the compound families into a single curve allowed a quick rough estimation of the cross-sectional areas. The specific reference equations σEB = qWp were determined for the 34 selected families, allowing the fast and reliable calculation of the cross-sectional area of any monofunctional compound.