Degree-Based Topological Descriptors and Physicochemical Structure–Property Trends in Oligothiophene Derivatives

Abstract

This study presents a graph-theoretical and descriptive structure–property analysis of the linear \(\alpha\)-linked oligothiophenes bithiophene, terthiophene, quaterthiophene, sexithiophene, and octithiophene. From the common edge partition of their hydrogen-suppressed molecular graphs, explicit closed forms are derived for fourteen degree-based descriptors: the first and second Zagreb, forgotten, Yemen, first and second hyper-Zagreb, three redefined Zagreb, Randi´c, Sombor, Yemen–Sombor, geometric–arithmetic, and atom–bond connectivity indices. Numerical values are obtained for all five molecules. Ten physicochemical endpoints reported in PubChem—polar surface area, molecular weight, complexity, XLogP3-AA, heavy-atom count, boiling point, enthalpy of vaporization, flash point, molar refractivity, and molar volume—are analyzed using descriptive linear regression. Every considered index is an affine function of oligomer length; therefore, the fourteen univariate regressions have identical fitted values and goodness-of-fit statistics for a fixed endpoint, although their slopes and intercepts differ. To avoid redundant reporting, the main text provides a compact endpoint-level summary and one representative index model, while all 140 descriptor–endpoint equations are supplied in the supplementary material. The models describe trends within this five-member homologous series and are not presented as externally validated predictive QSPR models.