Comparison of several molecular topological indexes with molecular surface area in aqueous solubility estimation

The molecular topological indexes proposed by Wiener (Wiener number), Hosoya (Z-value), and Randic (branching index) were corelated with computed molecular surface areas and aqueous solubilities for the monofunctional aliphatic alcohols, ethers, ketones, aldehydes, carboxylic acids, esters, and hydrocarbons. Comparison of the indexes with molecular surface area indicates that all three indexes (or simple modifications) correlate with molecular surface area and, although computed in different manners, reflect molecular topology. Comparison of the correlations of log solubility with the several indexes leads to the following conclusions: (a) the branching index works well for aliphatic, acyclic monofunctional compounds but not cyclic aliphatic compounds; (b) the square root of the Wiener number correlates less satisfactorily with log solubility than the other indexes but more correctly handles cyclic compounds (when generalized after Hosoya); (c) correlations of log solubility with the log Z-value are satisfactory, but the index is difficult to compute; and (d) the molecular surface are represents the single best parameter with which to correlate and estimate aqueous solubility due to its generality. However, for a restricted series of compounds, the branching index is perhaps the most useful index by virtue of its simplicity.