The use of graph-theoreticaltopological indices in quantitative structure–property/activity relationships (QSPR/QSAR) has become a powerful tool for predicting physical properties and biological activities of organic compounds as well as for molecular design in recent years because they can be derived directly from the molecular structures without any experimental effort [1-3]. Recently, we proposed some new topological indices based on the distance sum and connectivity of a molecular graph that derived directly from two-dimensional molecular topology for use in QSAR/QSPR studies [4,5]. In this study, the ability of these indices to predict the normal boiling point (NBP) and molar refractivity (MR) of a large set of organic compounds (394 compounds) belonging to a diverse type of compounds consisting of alkanes, alkenes, ethers, amines, alcohols, alkylbenzenes, and alkylhalides has been examined. Ten different Sh indices were calculated for each molecule. Both linear and nonlinear modeling were implemented using principal component regression (PCR) and principal component-artificial neural network (PC-ANN) with back-propagation learning algorithm, respectively. Principal component analysis of the Sh data matrix showed that the six and seven PCs could explain 97.49% and 99.22% of variances in the Sh data matrix for NBP and MR, respectively. PCR analysis of the data showed that proposed Sh indices could explain about 97.52% and 99.52% of variations; while the variations explained by the ANN modeling were more than 99.00% and 99.82% in the NBP and MR data, respectively. The linear and nonlinear models could predict the NBP and MR of molecules with the respective root mean square errors lower than 9.69 and 0.660 for linear model and 6.17 and 0.416 for nonlinear model, respectively.
