Abstract
This report examines the interpretation of the Graph Derivative Indices (GDIs) from three different perspectives (i.e., in structural, steric and electronic terms). It is found that the individual vertex frequencies may be expressed in terms of the geometrical and electronic reactivity of the atoms and bonds, respectively. On the other hand, it is demonstrated that the GDIs are sensitive to progressive structural modifications in terms of: size, ramifications, electronic richness, conjugation effects and molecular symmetry. Moreover, it is observed that the GDIs quantify the interaction capacity among molecules and codify information on the activation entropy. A structure property relationship study reveals that there exists a direct correspondence between the individual frequencies of atoms and Hückel’s Free Valence, as well as between the atomic GDIs and the chemical shift in NMR, which collectively validates the theory that these indices codify steric and electronic information of the atoms in a molecule. Taking in consideration the regularity and coherence found in experiments performed with the GDIs, it is possible to say that GDIs possess plausible interpretation in structural and physicochemical terms.
Highlights
Many mathematical invariants used in the codification of chemical information of molecular structures have in the recent years gained important utility in several research fields [1,2,3]
The Graph Derivative Indices (GDIs) have been previously used in several theoretical applications, providing relevant results fundamentally in QSAR/QSPR studies. [10,11,12] little effort has been destined to the interpretation of these Molecular Descriptors (MDs) in structural and/or physicochemical terms [10,11,12,16]
It was observed that GDIs codify information on molecular symmetry, allow for the characterization of molecular structures with different sizes, are sensitive to structural ramifications, adequately
Summary
Many mathematical invariants used in the codification of chemical information of molecular structures have in the recent years gained important utility in several research fields [1,2,3] These invariants are more advantageous relative to physicochemical parameters customarily employed in describing, for instance, the hydrophobic, steric and/or electronic effects due modifications of substituents in a molecule (e.g., the Hammett’s sigma constant); because they are able to quantify greater chemical information on molecules and usually yield better performance in studies on structure-property/activity relationships, similarity/diversity, virtual screening, among others. Some of the authors of the present work defined a new family of TIs based on the concept of the discrete derivative (derivative of a molecular graph), which was denominated Graph Derivative Indices (GDI) [10,11] These GDIs have been applied in several Quantitative Structure/Property Relationship (QSAR/QSPR) studies showing satisfactory results [10,11,12]. A group of carefully designed experiments to corroborate the veracity of the propositions made in the GDIs interpretation will be reported
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