QSPR modeling of hydroxypropyl beta-cyclodextrin using reverse-degree-based molecular topological indices

Abstract

Topological indices are mathematical quantities used to describe the structural characteristics of chemical molecules. In this work, we investigate a class of Reverse-Degree Molecular Topological Indices (RDTIs), which utilize the reciprocal of vertex degrees to characterize molecular structures. Several reverse-degree topological indices are employed to study hydroxypropyl beta-cyclodextrins (HPβCDs) - cyclic oligosaccharides widely used in pharmaceutical formulations and drug delivery systems. HPβCDs are also applied across various industries owing to their unique physicochemical properties, including enhanced aqueous solubility, improved stability, and increased bioavailability of drugs. The aim of this study is to develop and analyze the Reverse-Degree Molecular Topological Indices, which serve as molecular descriptors in computational chemistry for quantifying the structural complexity of molecules. These indices depend on the degree of atoms within the molecular graph. A graph-theoretical edge-partitioning approach is adopted to model the molecular topology of HPβCDs. Closed-form mathematical expressions are derived for several key reverse-degree topological indices, including the reverse first and second Zagreb indices, reverse first and second hyper Zagreb indices, reverse first, second, and third redefined Zagreb indices, reverse symmetric division degree index, reverse harmonic index, and their corresponding polynomial forms. The obtained results contribute to a deeper understanding of the structure–property relationships in hydroxypropyl beta-cyclodextrins and can facilitate the prediction of their physicochemical and functional properties.