Highly correlating distance/connectivity-based topological indices: 5. Accurate prediction of liquid density of organic molecules using PCR and PC-ANN

The primary goal of a quantitative structure–property relationship (QSPR) is to identify a set of structurally based numerical descriptors that can be mathematically linked to a property of interest. Recently, we proposed some new topological indices (Sh 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. In this study, the ability of these indices to predict the liquid densities (ρ) of a large and diverse set of organic liquid compounds (521 compounds) has been examined. Ten different Sh indices were calculated for each molecule. Both linear and non-linear modeling methods were implemented using principal component regression (PCR) and principal component-artificial neural network (PC-ANN) with back-propagation learning algorithm, respectively. Correlation ranking procedure was used to rank the principal components and entered them into the models. PCR analysis of the data showed that the proposed Sh indices could explain about 91.82% of variations in the density data, while the variations explained by the ANN modeling were more than 97.93%. The predictive ability of the models was evaluated using external test set molecules and root mean square errors of prediction of 0.0308 g ml−1 and 0.0248 g ml−1 were obtained for liquid densities of external compounds by linear and non-linear models, respectively.