Differentiation of alkyl radicals: A route through chemical graph theory

Abstract

AbstractAlkyl radicals play important roles such as intermediary metabolism, cell damage/injury and death leading to potential mutations. The present investigation using chemical graph theory studied two sets of carboxyl radicals, that is, deprotonated (DPro, radical) and protonated (Pro, radical anion) forms of 5‐ethyl heptanoic acid and 5‐ethenyl hept‐6‐enoic acid (Set I) radicals and 6‐ethyl octanoic acid and 6‐ethenyl oct‐7‐enoic acid (Set II) radicals. The study reveals that the largest eigenvalue (LEV) spectra of the adjacency matrix have a unique value, where the spectra increase from DPro to Pro and from single to double bonded alkyl radical structures, thus forming a scoring function for molecular topological indices. This topological index is presented as a measure for molecular connectivity/branching, where the index is used to predict the refractivity of a series of carboxyl radicals. The statistical correlation coefficient obtained for quantitative structure–property relationship between chemical structure (alkyl radical) and its physical property (refractivity) through heat maps are excellent and ranges within 0.97–0.99. It is further discovered that the vector component of the LEV gives an insight to its structural details, where it captures the node with the highest degree along with the important weighted node, that holds the complete structure (i.e., the radical site), in case of the Pro radical structures. Node centrality, which captures the structural makeup, divides DPro radical T‐shaped structures into two subunits for the signal transduction of important biological process like oral toxicity. Size of the largest clusters is also studied, illustrating the parameter to be less sensitive for differentiating the CC double bonds in the Pro radicals. To our knowledge, this is the first study where pattern recognition has been exemplified through the lower‐diagonal‐upper decomposition matrix of the chemical graph that forms a fingerprint signature to differentiate the alkyl radicals. The present study innovatively digitalizes the chemical structures of alkyl radicals that enables the discovery of structure–property relationship reflected by their molecular branching through machine learning.