The new topological indices (Sh indices) based on the distance sum and connectivity of a molecular graph, previously developed by our team, were extended to predict the two physicochemical properties including normal boiling point (NBP) and molar refractivity (MR), of a large set of organic compounds consisting of alkanes, alkenes, ethers, amines, alcohols, alkylbenzenes, and alkylhalides. The sets of molecular descriptors were derived directly from the two-dimensional molecular structure of the compounds based on graph theory. Both linear and nonlinear modelings were implemented by using principal component regression (PCR) and principal component-artificial neural network (PC-ANN) with back-propagation learning algorithm, respectively. Eigenvalue and correlation-ranking procedures were used to rank the principal components and entered them into the models. Principal component analysis of Sh data matrix showed that the respective six and seven PCs could explain 97.49% and 99.22% of variances in the Sh indices. PCR analysis of the NBP and MR data demonstrated that the proposed Sh indices could explain about 97.52% and 99.52% of variations, while the variations explained by the PC-ANN modeling were more than 99.00% and 99.82%, respectively. The predictive ability of the models were evaluated using an external test set for NBP and MR of molecules with the respective root-mean-square errors lower than 9.69 K and 0.660 cm3 mol-1 for linear model and 6.17 K and 0.416 cm3 mol-1 for nonlinear model.
