Generalized topological indices. Modeling gas-phase rate coefficients of atmospheric relevance

We develop the idea that the use of ad hoc molecular descriptors in QSAR/QSPR studies is not an optimal solution. Instead, we propose to optimize these descriptors for the specific properties under study. In the case of topological indices (TIs) we propose the use of the generalized topological indices (GTIs), which account for several of the classical TIs in one single graph invariant. GTIs represent points in a six-dimensional space of topological parameters, which can be optimized for describing a specific property. The situation shows some resemblance with the geometry optimization procedures used to minimize molecular energy. Here we study the reaction rate coefficients for the gas-phase radical reactions between alkanes and cycloalkanes with OH, Cl, and NO3 radicals. These reaction rate coefficients were studied recently by using some "classical" TIs, such as Balaban and Randić indices. Despite the fact that the Randić index produces acceptable QSPR models for some of these reactions, the models developed are still far from being optimal. Using the GTI approach we have improved these QSPRs by reducing the standard deviation by almost 50%. In addition, the current approach permits the illustration of the similarities and differences among the different descriptors studied, indicating possible directions for searching new optimal molecular descriptors.