distinguish chemically bonded atoms from non bonded pairs (for a diatomic
molecule the Poincaré-Hopf relation imposes a BCP at any internuclear distance).
The process of the creation-annihilation of electronic domains, as depicted by ELF,
has been formalized in the Bonding Evolution Theory (BET) of Krokidis et al. [77].
This method has been widely applied to investigate organic chemistry reaction
mechanisms [80–86].
1.5 Conclusion
In the following nineteen chapters, the relevance of topology in chemistry is
addressed.
The first section presents the latest methodological advances in the topological
analysis of molecular structure and reactivity. The first four chapters by Paul L.
A. Popelier, Shant Shahbazian, Carlo Gatti et al. and Cherif F. Matta et al, deal with
the most recent developments and extensions of the topological analysis of the
electron density (QTAIM). In particular, a direct link between QTAIM and
chemical graph theory is provided by the localization-delocalization and electron
density-weighted connectivity matrices described by Chérif F. Matta et al.. The
chapter by Ángel Martín Pendás et al. highlights emergent interests in forgotten
scalar and vector fields for topological analyses within the gradient dynamical
system theory. The current density vector field is more specifically considered by
Paolo Lazzeretti, while the Fukui function gradient field, enabling the definition of
the chemically reactive regions of a molecule and thus providing a measure of the
chemical reactivity, is envisaged by Patricio Fuentealba et al. Other topological
tools relevant for the analysis of chemical reactivity and reaction mechanisms, are
discussed in the next two chapters by Paul Mezey and Juan Andrés et al.
respectively.
The second section focuses on applications of topological analysis for the
characterization of p-electron delocalization and aromaticity. The chemical graph
theory approach is here shown to remain more topical than ever. In spite of the
development of advanced quantum chemical tools beyond Hartree-Fock, DFT or
multi-configurational methods, a direct understanding of computational results
often requires recourse to the methods of graph theory or Hückel Molecular
Orbitals (HMOs). While aromaticity is certainly one of the “most basic topological
concept” in chemistry (specific effect of the cyclic character of p-systems in
molecules), it has long suffered from a lack of clear-cut definition. The merit of the
discrete graph theory level is first illustrated by Ivan Gutman and Slavko
Radenkovic delineating the scope of approaches based on the counting of Kekulé
structure types for the prediction of the “observable aromatic character” of benzenoids, in particular around the perylene family. From a more general standpoint,
Miquel Solà et al. address the relevance of the basic “counting rules of aromaticity”
in a systematic manner. The main application of graph theory in quantum chemistry
is the use of the adjacency matrix as a Hückel Hamiltonian. Within this context,
1 Topological Approaches of the Bonding in Conceptual Chemistry
17
molecule the Poincaré-Hopf relation imposes a BCP at any internuclear distance).
The process of the creation-annihilation of electronic domains, as depicted by ELF,
has been formalized in the Bonding Evolution Theory (BET) of Krokidis et al. [77].
This method has been widely applied to investigate organic chemistry reaction
mechanisms [80–86].
1.5 Conclusion
In the following nineteen chapters, the relevance of topology in chemistry is
addressed.
The first section presents the latest methodological advances in the topological
analysis of molecular structure and reactivity. The first four chapters by Paul L.
A. Popelier, Shant Shahbazian, Carlo Gatti et al. and Cherif F. Matta et al, deal with
the most recent developments and extensions of the topological analysis of the
electron density (QTAIM). In particular, a direct link between QTAIM and
chemical graph theory is provided by the localization-delocalization and electron
density-weighted connectivity matrices described by Chérif F. Matta et al.. The
chapter by Ángel Martín Pendás et al. highlights emergent interests in forgotten
scalar and vector fields for topological analyses within the gradient dynamical
system theory. The current density vector field is more specifically considered by
Paolo Lazzeretti, while the Fukui function gradient field, enabling the definition of
the chemically reactive regions of a molecule and thus providing a measure of the
chemical reactivity, is envisaged by Patricio Fuentealba et al. Other topological
tools relevant for the analysis of chemical reactivity and reaction mechanisms, are
discussed in the next two chapters by Paul Mezey and Juan Andrés et al.
respectively.
The second section focuses on applications of topological analysis for the
characterization of p-electron delocalization and aromaticity. The chemical graph
theory approach is here shown to remain more topical than ever. In spite of the
development of advanced quantum chemical tools beyond Hartree-Fock, DFT or
multi-configurational methods, a direct understanding of computational results
often requires recourse to the methods of graph theory or Hückel Molecular
Orbitals (HMOs). While aromaticity is certainly one of the “most basic topological
concept” in chemistry (specific effect of the cyclic character of p-systems in
molecules), it has long suffered from a lack of clear-cut definition. The merit of the
discrete graph theory level is first illustrated by Ivan Gutman and Slavko
Radenkovic delineating the scope of approaches based on the counting of Kekulé
structure types for the prediction of the “observable aromatic character” of benzenoids, in particular around the perylene family. From a more general standpoint,
Miquel Solà et al. address the relevance of the basic “counting rules of aromaticity”
in a systematic manner. The main application of graph theory in quantum chemistry
is the use of the adjacency matrix as a Hückel Hamiltonian. Within this context,
1 Topological Approaches of the Bonding in Conceptual Chemistry
17