Topological research on diamagnetic susceptibilities of organic compounds

Abstract

A novel molecular connectivity index, $^{m} \chi \prime$, based on the adjacency matrix of molecular graphs and novel atomic valence connectivities, $\delta ^{\prime }_{i}$, for predicting the molar diamagnetic susceptibilities of organic compounds is proposed. The $\delta ^{\prime }_{i}$ is defined as: $\delta _{i} \prime = \delta _{i} ^{v} \cdot {E_{i} } \mathord{\left/ {\vphantom {{E_{i} } {12.625}}} \right. \kern-\nulldelimiterspace} {12.625}$, where $\delta ^{v}_{i}$ and E_i are the atomic valence connectivity and the valence orbital energy of atom i, respectively. A good QSPR model for molar diamagnetic susceptibilities can be constructed from $^{0} \chi \prime ,^{1} \chi \prime ,^{2} \chi \prime$ and $^{4} \chi ^{\prime }_{p}$ using multivariate linear regression (MLR). The correlation coefficient r, standard error, and average absolute deviation of the MLR model are 0.9918, 5.56 cgs, and 4.26 cgs, respectively, for the 721 organic compounds tested (training set). Cross-validation using the leave-one-out method demonstrates that the MLR model is highly reliable statistically. Using the MLR model, the average absolute deviations of the predicted values of molar diamagnetic susceptibility of another 360 organic compounds (test set) is 4.34 cgs. The results show that the current method is more effective than literature methods for estimating the molar diamagnetic susceptibility of an organic compound. The MLR method thus provides an acceptable model for the prediction of molar diamagnetic susceptibilities of organic compounds.