or related to the electron density and, in the case of LDM, also to electron delocalization information related to the electron-pair density as well.
In this new approach we draw on the strengths of two sub-fields of theoretical
chemistry: Bader’s Quantum Theory of Atoms in Molecules (QTAIM) to extract
physically meaningful descriptors from the electron density and related properties
and Chemical Graph Theory which led the way in abstracting the chemical graph in
matrices followed by mathematical treatment to extract matrix invariants for the
purpose of correlating with and predicting experimental properties of compounds.
This new approach is promising and wide reaching, with possible applications
ranging from predicting physicochemical properties of series of molecules to their
corrosion protective abilities passing by as diverse problems as quantifying aromaticity to possibly providing a practical tool for assessing the quality of newly
developed basis sets of electronic structure calculations such as new DFT
functionals.
A book is presently being written by the authors about LDMs and their uses
[104]. This book will contain extensive data that support the basic claim of this
chapter, that is, that LDMs are a molecular fingerprinting tool that can provide a
basis for robust QSAR-type studies.
Acknowledgments 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.
References
1. Dmitriev IS (1981) Molecules without chemical bonds (English Translation). Mir Publishers,
Moscow
2. Balaban AT (1976) Chemical applications of graph theory. Academic Press, New York
3. Balaban AT (1985) Applications of graph theory in chemistry. J Chem Inf Comput Sci
25:334–343
4. Hall LH, Kier LB (1976) Molecular connectivity in chemistry and drug research. Academic
Press, Boston
5. Bonchev D, Rouvray DH (1991) Chemical graph theory: introduction and fundamentals.
OPA, Amsterdam
6. Balasubramanian K (1994) Integration of graph theory and quantum chemistry for
structure-activity relationship. SAR & QSAR Eviron Res 2:59–77
7. Diudea MD, Gutman I, Lorentz J (1999) Molecular topology. Nova Science Publishers Inc,
Hauppauge NY
8. Janezić D, Milicević A, Nikolić S, Trinajstić N (2007) Graph theoretical matrices in
chemistry. In: Mathematical chemistry monographs, vol 3. University of Kragujevac,
Kragujevac
9. Todeschini R, Consonni V (2009) Molecular descriptors for chemoinformatics, 2nd Edn,
vols. I and II). Wiley-VCH Weinheim, Weinheim
10. Bader RFW (1990) Atoms in molecules: a quantum theory. Oxford University Press, Oxford
11. Popelier PLA (2000) Atoms in molecules: an introduction. Prentice Hall, London
84
C.F. Matta et al.
In this new approach we draw on the strengths of two sub-fields of theoretical
chemistry: Bader’s Quantum Theory of Atoms in Molecules (QTAIM) to extract
physically meaningful descriptors from the electron density and related properties
and Chemical Graph Theory which led the way in abstracting the chemical graph in
matrices followed by mathematical treatment to extract matrix invariants for the
purpose of correlating with and predicting experimental properties of compounds.
This new approach is promising and wide reaching, with possible applications
ranging from predicting physicochemical properties of series of molecules to their
corrosion protective abilities passing by as diverse problems as quantifying aromaticity to possibly providing a practical tool for assessing the quality of newly
developed basis sets of electronic structure calculations such as new DFT
functionals.
A book is presently being written by the authors about LDMs and their uses
[104]. This book will contain extensive data that support the basic claim of this
chapter, that is, that LDMs are a molecular fingerprinting tool that can provide a
basis for robust QSAR-type studies.
Acknowledgments 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.
References
1. Dmitriev IS (1981) Molecules without chemical bonds (English Translation). Mir Publishers,
Moscow
2. Balaban AT (1976) Chemical applications of graph theory. Academic Press, New York
3. Balaban AT (1985) Applications of graph theory in chemistry. J Chem Inf Comput Sci
25:334–343
4. Hall LH, Kier LB (1976) Molecular connectivity in chemistry and drug research. Academic
Press, Boston
5. Bonchev D, Rouvray DH (1991) Chemical graph theory: introduction and fundamentals.
OPA, Amsterdam
6. Balasubramanian K (1994) Integration of graph theory and quantum chemistry for
structure-activity relationship. SAR & QSAR Eviron Res 2:59–77
7. Diudea MD, Gutman I, Lorentz J (1999) Molecular topology. Nova Science Publishers Inc,
Hauppauge NY
8. Janezić D, Milicević A, Nikolić S, Trinajstić N (2007) Graph theoretical matrices in
chemistry. In: Mathematical chemistry monographs, vol 3. University of Kragujevac,
Kragujevac
9. Todeschini R, Consonni V (2009) Molecular descriptors for chemoinformatics, 2nd Edn,
vols. I and II). Wiley-VCH Weinheim, Weinheim
10. Bader RFW (1990) Atoms in molecules: a quantum theory. Oxford University Press, Oxford
11. Popelier PLA (2000) Atoms in molecules: an introduction. Prentice Hall, London
84
C.F. Matta et al.