Nevertheless a “molecular structure” is also defined by a geometry (disposition, i.e.
Cram-Dreiding structures) [17]. As the smallest constituent of a—pure substance in
French, the Lavoisier’s language—a molecule is assigned to a particular molecular
structure corresponding to an equilibrium geometry and corresponding energy
(as ultimately determined by iterative resolution of the Schrödinger equation), and
to a temperature-dependent chemical potential (as determined from the Boltzmann
distribution of states) [18].
In a first attempt to go from topology to geometry, the spatial extension of the
bonding and non bonding pairs has been accounted for by the model of Sidgwick
and Powell [19] involving both shared and unshared groups having the same size
which is uniquely determined by the type of spatial arrangement considered.
Gillespie and Nyholm have substantially improved this model explaining the
arrangement of the pairs around of a given centre as due to the exclusion principle
[20]. The repulsion depends on the type of pairs considered, for example a lone pair
is more repulsive than a bonding pair, and on the electronegativity of the ligands. In
the earliest version of the Valence Shell Electron Pair Repulsion (VSEPR) model
[21], the valence pairs are considered as points on a sphere the arrangement of
which is found by maximizing the least distance between any pair of points. The
points on a sphere were replaced in a first time by tangent spherical electronic
domains attracted by the central positive core and further by ellipsoid, “pear” and
“egg” shaped domains of different sizes [22]. Electron pair domains are defined as a
charge cloud which occupies a given region of space and excludes other pairs from
this region as a consequence of the Pauli exclusion principle. This electron pair
domain version of VSEPR emphasizes the shape and size of the domains rather
than the magnitude of their mutual repulsion. In addition to bond and lone pair
domains, Gillespie considers single electron domains which are expected to be
smaller than an electron pair domain [23]. The VSEPR model is very successful in
predicting qualitatively the shape of molecules. It enables to understand many
features of the molecular geometry in a qualitative fashion.
The Lewis’ and VSEPR models are finally simple to understand and to apply,
they provide very convincing explanations of the molecular structure and suffer few
exceptions. They have consequently acquired a central place in chemical education.
Both rely on the hypothesis of the formation of individualized localized electron
pairs which is not an experimental fact and which remains questionable from a strict
theoretical point of view. Beyond covalence, actually, the nature of the interactions
between atoms (i.e. the “absolute edge weight” of the molecular graph, see below)
can indeed be appraised on a purely phenomenological basis (“sharing and pairing”
of formal “electronic” quanta) [24].
The aim of this chapter is to give the consistency between the following chapters
gathered in this Volume. It consists in an introduction of the topological analysis
methods which enable the recovery of the different concepts used in the chemical
description of the matter in the spirit of Lewis’ model as well as to go deeper into
their contents. After a reminder of the links between chemistry and topology
introducing the two types of discrete and continuous topological approaches, the
general spirit of these approaches is presented in the subsequent sections.
4
B. Silvi et al.
Cram-Dreiding structures) [17]. As the smallest constituent of a—pure substance in
French, the Lavoisier’s language—a molecule is assigned to a particular molecular
structure corresponding to an equilibrium geometry and corresponding energy
(as ultimately determined by iterative resolution of the Schrödinger equation), and
to a temperature-dependent chemical potential (as determined from the Boltzmann
distribution of states) [18].
In a first attempt to go from topology to geometry, the spatial extension of the
bonding and non bonding pairs has been accounted for by the model of Sidgwick
and Powell [19] involving both shared and unshared groups having the same size
which is uniquely determined by the type of spatial arrangement considered.
Gillespie and Nyholm have substantially improved this model explaining the
arrangement of the pairs around of a given centre as due to the exclusion principle
[20]. The repulsion depends on the type of pairs considered, for example a lone pair
is more repulsive than a bonding pair, and on the electronegativity of the ligands. In
the earliest version of the Valence Shell Electron Pair Repulsion (VSEPR) model
[21], the valence pairs are considered as points on a sphere the arrangement of
which is found by maximizing the least distance between any pair of points. The
points on a sphere were replaced in a first time by tangent spherical electronic
domains attracted by the central positive core and further by ellipsoid, “pear” and
“egg” shaped domains of different sizes [22]. Electron pair domains are defined as a
charge cloud which occupies a given region of space and excludes other pairs from
this region as a consequence of the Pauli exclusion principle. This electron pair
domain version of VSEPR emphasizes the shape and size of the domains rather
than the magnitude of their mutual repulsion. In addition to bond and lone pair
domains, Gillespie considers single electron domains which are expected to be
smaller than an electron pair domain [23]. The VSEPR model is very successful in
predicting qualitatively the shape of molecules. It enables to understand many
features of the molecular geometry in a qualitative fashion.
The Lewis’ and VSEPR models are finally simple to understand and to apply,
they provide very convincing explanations of the molecular structure and suffer few
exceptions. They have consequently acquired a central place in chemical education.
Both rely on the hypothesis of the formation of individualized localized electron
pairs which is not an experimental fact and which remains questionable from a strict
theoretical point of view. Beyond covalence, actually, the nature of the interactions
between atoms (i.e. the “absolute edge weight” of the molecular graph, see below)
can indeed be appraised on a purely phenomenological basis (“sharing and pairing”
of formal “electronic” quanta) [24].
The aim of this chapter is to give the consistency between the following chapters
gathered in this Volume. It consists in an introduction of the topological analysis
methods which enable the recovery of the different concepts used in the chemical
description of the matter in the spirit of Lewis’ model as well as to go deeper into
their contents. After a reminder of the links between chemistry and topology
introducing the two types of discrete and continuous topological approaches, the
general spirit of these approaches is presented in the subsequent sections.
4
B. Silvi et al.