The potential usefulness of some newly proposed topological indices (Sh indices) has been examined by their application to the prediction of 15 different properties of a large number of alkanes (C2 through C10, a total of 149 molecules). Ten different indices (Sh1 through Sh10) and a novel one (Sh index) were calculated for each molecule by different combination of the connectivity and distance sum vectors. The alkanes× properties studied included boiling point (BP), density (D), molar refraction (MR), refraction index (RI), critical temperature (CT), critical pressure (CP), surface tension (ST), molar volume (MV), heat capacity (HC), enthalpy (E), heat of vaporization (HV), heat of atomization (HA), standard heat of formation (HF), heat of formation in liquid (HFL), and heat of formation in gas (HFG). First, the novel Sh index and the Randic connectivity index were used to simply correlate them to the properties of alkane molecules. Except with D, ST and RI, in all other cases, the Sh index produced high correlation coefficients. Besides, in almost all cases, the Sh index resulted in higher correlations than the Randic index. In order to predict the properties of alkanes more accurately, the PCR analysis was employed to drive multiparametric equations between the Sh indices and alkane properties. It was found that the stepwise procedure for factor selection, which was in accordance with the correlation ranking procedure, produced more convenient models in comparison with the eigen-value ranking procedure. The advantages of the resulting QSPR models obtained by the use of Sh indices, over some other proposed models, were lower number of variables and higher prediction power.
