Localization-Delocalization Matrices and Electron Density-Weighted Adjacency/Connectivity Matrices: A Bridge Between the Quantum Theory of Atoms in Molecules and Chemical Graph Theory

  • Chérif F. MattaEmail author
  • Ismat Sumar
  • Ronald CookEmail author
  • Paul W. AyersEmail author
Part of the Challenges and Advances in Computational Chemistry and Physics book series (COCH, volume 22)


Chemical graph theory (CGT) starts by defining matrices that represent the molecular graph then proceed to extract numbering-independent matrix invariants to be used as molecular descriptors in empirical quantitative structure to activity (or property) relationships (QSAR/QSPR). Two proposed matrix representations of molecular structure are presented in this chapter as alternatives to simple connectivity molecular graphs. Firstly, it is proposed to use a more “nuanced” connectivity matrix by weighing the “ones” entered in a CGT molecular graph matrix by the bond critical point electron densities associated with each bond path to yield what we term the “electron density-weighted adjacency/connectivity matrices (EDWAM/EDWCM)”. In a second approach, it is proposed to use the localization and delocalization indices of the quantum theory of atoms in molecules (QTAIM) to construct a richer representation of the molecular graph, a “fuzzy” graph, whereby an edge exists between any two atoms (measured by the delocalization index between them) whether they share a bond path or not. Such a fuzzy graph is represented by what we term “electron localization-delocalization matrix (LDM)”. We show that the LDM representations of a series of molecules provide a powerful tool for robust QSAR/QSPR modeling.


Quantitative Structure Activity Relationship Molecular Graph Bond Critical Point Quantitative Structure Property Relationship Bond Path 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.



The authors thank Dr. Todd A. Keith, Professor Lou Massa, Dr. Nenad Trinajstić, Dr. Sonja Nikolić, and Mr. Matthew J. Timm for helpful discussions. Financial support of this work was provided by the Natural Sciences and Engineering Research Council of Canada (NSERC), Canada Foundation for Innovation (CFI), Saint Mary’s University, McMaster University, and Mount Saint Vincent University.


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© Springer International Publishing Switzerland 2016

Authors and Affiliations

  1. 1.Department of Chemistry and PhysicsMount Saint Vincent UniversityHalifaxCanada
  2. 2.Department of ChemistryDalhousie UniversityHalifaxCanada
  3. 3.Department of ChemistrySaint Mary’s UniversityHalifaxCanada
  4. 4.Department of ChemistryMcMaster UniversityHamiltonCanada
  5. 5.TDA Research, IncWheat RidgeUSA

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