Application of novel atom-type AI topological indices to QSPR studies of alkanes

Atom-type AI topological indices derived from the topological distance sums and vertex degree further are used to describe different structural environment of each atom-type in a molecule. The multiple linear regression based on combined use of the proposed Xu index and AI indices is performed to develop high quality QSPR models for describing six physical properties (the normal boiling points, heats of vaporization, molar volumes, molar refractions, van der Waals’ constants, and Pitzer's acentric factors) of alkanes with up to nine carbon atoms. For each of six properties, the correlation coefficient r of the final models is larger than 0.995 and particularly the decrease in the standard error (s) is within the range of 45–86% as compared with the simple linear models with Xu index alone. The agreement between calculated and experimental data is quite good. The results indicate the potential of these indices for application to a wide range of physical properties. The role of each of the molecular size and individual groups in the molecules are illustrated by analyzing the relative or fraction contributions of individual indices. The results indicate that the six physical properties of alkanes are dominated by molecular size while AI indices have smaller influence dependent on the studied properties. Moreover, the studies demonstrate that each atomic group contributes an indefinite value to properties dependent on its structural environment in a molecule or other groups present. The cross-validation using the more general leave-n-out method demonstrates the final models to be highly statistically reliable.