An interpretation of second-order neighborhood Harmonic index

The Topological index serves as a powerful mathematical descriptor, capturing the intricate structural features of molecules and providing insightful analysis in the field of chemical sciences. This communication studies the higher-order Neighborhood Harmonic index ( \(NH_{\alpha }\) $N{H}_{\alpha }$ ) and presents an alternative perspective on the correlation of the second-order Neighborhood Harmonic index ( \(NH_{2}\) $N{H}_2$ ) with the normal boiling point of straight-chain Alkanes and Octane Isomers. Based on the findings of this study, it can be observed that with an increase in the molecular weight of an straight-chain alkane, there is a concurrent elevation in both the normal boiling point and the collective involvement of \(NH_{2}\) $N{H}_2$ along all conceivable internal C–C–C routes. As all the isomers of Octane possess the same molecular weights, we first categorize the isomers into distinct groups and then establish a meaningful connection with their respective normal boiling points. In case of normal boiling point (computed using modified Frost-Kalkwarf equation), it is found that, the proposed index i.e., Second-Order Neighborhood Harmonic index has good predictive ability with a probability of \(90\%\) $90\%$ for absolute relative errors of less than \(6.29\%\) $6.29\%$ . Further, some important mathematical properties of the ( \(NH_{2}\) $N{H}_2$ ) are also presented in the paper.