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Bond-based linear indices of the non-stochastic and stochastic edge-adjacency matrix. 1. Theory and modeling of ChemPhys properties of organic molecules

Abstract

Novel bond-level molecular descriptors are proposed, based on linear maps similar to the ones defined in algebra theory. The kth edge-adjacency matrix (E k) denotes the matrix of bond linear indices (non-stochastic) with regard to canonical basis set. The kth stochastic edge-adjacency matrix, ES k, is here proposed as a new molecular representation easily calculated from E k. Then, the kth stochastic bond linear indices are calculated using ES k as operators of linear transformations. In both cases, the bond-type formalism is developed. The kth non-stochastic and stochastic total linear indices are calculated by adding the kth non-stochastic and stochastic bond linear indices, respectively, of all bonds in molecule. First, the new bond-based molecular descriptors (MDs) are tested for suitability, for the QSPRs, by analyzing regressions of novel indices for selected physicochemical properties of octane isomers (first round). General performance of the new descriptors in this QSPR studies is evaluated with regard to the well-known sets of 2D/3D MDs. From the analysis, we can conclude that the non-stochastic and stochastic bond-based linear indices have an overall good modeling capability proving their usefulness in QSPR studies. Later, the novel bond-level MDs are also used for the description and prediction of the boiling point of 28 alkyl-alcohols (second round), and to the modeling of the specific rate constant (log k), partition coefficient (log P), as well as the antibacterial activity of 34 derivatives of 2-furylethylenes (third round). The comparison with other approaches (edge- and vertices-based connectivity indices, total and local spectral moments, and quantum chemical descriptors as well as E-state/biomolecular encounter parameters) exposes a good behavior of our method in this QSPR studies. Finally, the approach described in this study appears to be a very promising structural invariant, useful not only for QSPR studies but also for similarity/diversity analysis and drug discovery protocols.

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Correspondence to Yovani Marrero-Ponce.

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Dedicated to Professor Ernesto Estrada for his many contributions to the graph-theoretical chemistry and specifically by the relevant extension of well-known atom-based mathematical invariants to bond-level relationship.

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Marrero-Ponce, Y., Martínez-Albelo, E.R., Casañola-Martín, G.M. et al. Bond-based linear indices of the non-stochastic and stochastic edge-adjacency matrix. 1. Theory and modeling of ChemPhys properties of organic molecules. Mol Divers 14, 731–753 (2010). https://doi.org/10.1007/s11030-009-9201-5

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Keywords

  • TOMOCOMD-CARDD software
  • Edge-adjacency matrix
  • Stochastic linear map
  • Non-stochastic and stochastic bond-based linear index
  • QSPR study
  • Physicochemical property
  • Antibacterial activity
  • Octane isomers
  • 2-Furylethylene derivative