Distance-Related Indexes in the Quantitative Structure−Property Relationship Modeling^†

A comparative study of structure−boiling point modeling for a set of 180 acyclic and cyclic hydrocarbons (DS-180) and two of its subsets (one containing a selection of 76 acyclic and cyclic alkanes (DS-76), and the other containing 104 (DS-104) mono- and polycyclic butanes through octanes) using several known and novel distance-related indices is reported. The distance-related indices used were as follows:  Wiener index, hyper-Wiener index, detour index, hyper-detour index, Harary index, Pasaréti index, Vérhalom index, Wiener-sum index, inverse Wiener-sum index and the product-form version of the Wiener index. Additional indices used were the total number of paths, the Hosoya Z index, the total walk count index, the number of carbon atoms, and the number of rings in the hydrocarbon. The best models for predicting the boiling points of 76, 104, and 180 acyclic and cyclic alkanes contain the natural logarithm of the cross-products of the Hosoya and detour index and of the Pasaréti index and the number of rings. This result extends earlier work by us^2,7 and Rücker and Rücker⁸ on the use of the Wiener, detour, and Hosoya indices in modeling boiling points of alkanes and cycloalkanes. It also supports later work by Rücker and Rücker⁹ on the use of the descriptor combination for the same purpose.