Analysing spectral parameters of decane—A graph theoretical perspective

Abstract

Hydrocarbons are one of the subclasses of organic compounds that comprise exactly of hydrogen and carbon. Alkanes are one of the types of hydrocarbons that have chemical formula $C_n{H}_{2n+2}$. Isomers are molecules with identical chemical formula but different structural arrangements, leading to variations in their spectral properties as their corresponding molecular graphs also differ in structure. This exploration is motivated by the understanding that variations in structural configurations manifest as differences in spectral properties, as evidenced by alterations in their respective molecular graphs. Alkanes with ten carbon atoms are called decanes. Our study employs a multifaceted approach, encompassing the determination of spectral properties and the calculation of eigenvalue-based entropy for the $C_{10}{H}_{22}$ decane isomers. This analysis is undertaken with the goal of unravelling the intricate relationships between structural variations and corresponding spectral bounds. Notably, our investigation extends beyond the realm of molecular structures to draw connections with physico-chemical properties. Through meticulous comparison of the obtained spectral data with the known characteristics of $C_{10}{H}_{22}$ isomers, we unveil interesting correlations among the characteristics. We establish that the spectral gap, a key parameter in our study, intriguingly exhibits a maximal correlation with the refractive index of the isomers. This finding not only enhances our understanding of the spectral intricacies of decane isomers but also underscores the practical implications of such research. The correlation between spectral gap and refractive index opens avenues for predicting and manipulating the optical properties of hydrocarbons, offering potential applications in diverse fields, from materials science to optics. In essence, this study bridges the gap between molecular structure and macroscopic properties, shedding light on the intricate interplay between isomeric variations and their consequential effects on spectral characteristics.