However, the applicability of the Thom’s CT in the framework of the QTAIM has
been found to be limited to intramolecular chemical processes since no topological
changes are found in the electron density when two atoms separate. Subsequently
Silvi and Krokidis [135], as a generalization of Bader’s work, have developed the
joint use of electronic localization function ELF and Thom’s CT. In this context, the
mechanism of a given chemical reactions can be rationalized in terms of chemical
events, namely: bond forming or breaking processes, creation and annihilation of
electron pairs. This analysis allows us to understand the electronic structure and
related properties of the reactants as the reaction takes place, providing a nice guide
to elucidate the mechanism of chemical reactions and further understanding of the
chemical reactivity. This methodology proposed is known as bonding evolution
theory (BET). Changes in the control parameters defining the reaction pathway (such
as the nuclear coordinates and the electronic state) can lead to different topologies of
the ELF. Therefore, according to the theory of dynamical systems, a system can be
considered structurally stable if a small perturbation is only possible for values of the
control parameters comprised into well-defined ranges, namely structural stability
domains (SSDs), where all the critical points are hyperbolic and separated by
catastrophic points in which at least one critical point is non-hyperbolic. Therefore,
according to the BET, the reaction pathway of a given chemical system goes from a
given ELF-SSD to another by means of bifurcation catastrophes occurring at the
turning points. The bifurcation catastrophes occurring at these turning points are
identified according to Thom’s classification [133, 134]. In this way, a chemical
reaction can be understood as a sequence of chemical events (ELF-SSDs) and
separated by bifurcation points. Only three types of bifurcation catastrophes have
been found in chemical reactivity: (i) the fold catastrophe, corresponding to the
creation or annihilation of two critical points of different parity; (ii) the cusp
catastrophe, which transforms one critical point into three (and viceversa) such as in
the formation or the breaking of a covalent bond; (iii) the elliptic umbilic, in which
the index of a critical point changes by two. The identification of the turning points
connecting the ELF-SSDs along the reaction pathway allows a rigorous characterization of the sequence of electron pair rearrangements taking place during a
chemical transformation, such as multiple bond forming/breaking processes,
creation/annihilation of lone pairs, transformations of double bonds into single ones
or vice versa, and other electronic rearrangements. Details of the Thom’s classification in chemical reactions have been described in detail elsewhere [103].
A plethora of chemical rearrangements have been studied by BET: cycloadditions
[103, 136–139], cyclization [140–142], S N 2 reaction [143], Nazarov reaction [144],
Cope reaction [145], Cope rearrangement of semibullvalene [146], the reaction of
uranium ions with N 2 O in the gas phase [147], the reaction of Mn
+ with small
molecules [148], or inorganic reactions involving Mo complexes [149, 150]. Also,
some reviews on the applicability of BET to understand and rationalize chemical
reactivity have been published [138, 151–153], including the study of the bonding
changes along solid-solid phase transitions [154].
10 Quantum Chemical Topology Approach …
263
been found to be limited to intramolecular chemical processes since no topological
changes are found in the electron density when two atoms separate. Subsequently
Silvi and Krokidis [135], as a generalization of Bader’s work, have developed the
joint use of electronic localization function ELF and Thom’s CT. In this context, the
mechanism of a given chemical reactions can be rationalized in terms of chemical
events, namely: bond forming or breaking processes, creation and annihilation of
electron pairs. This analysis allows us to understand the electronic structure and
related properties of the reactants as the reaction takes place, providing a nice guide
to elucidate the mechanism of chemical reactions and further understanding of the
chemical reactivity. This methodology proposed is known as bonding evolution
theory (BET). Changes in the control parameters defining the reaction pathway (such
as the nuclear coordinates and the electronic state) can lead to different topologies of
the ELF. Therefore, according to the theory of dynamical systems, a system can be
considered structurally stable if a small perturbation is only possible for values of the
control parameters comprised into well-defined ranges, namely structural stability
domains (SSDs), where all the critical points are hyperbolic and separated by
catastrophic points in which at least one critical point is non-hyperbolic. Therefore,
according to the BET, the reaction pathway of a given chemical system goes from a
given ELF-SSD to another by means of bifurcation catastrophes occurring at the
turning points. The bifurcation catastrophes occurring at these turning points are
identified according to Thom’s classification [133, 134]. In this way, a chemical
reaction can be understood as a sequence of chemical events (ELF-SSDs) and
separated by bifurcation points. Only three types of bifurcation catastrophes have
been found in chemical reactivity: (i) the fold catastrophe, corresponding to the
creation or annihilation of two critical points of different parity; (ii) the cusp
catastrophe, which transforms one critical point into three (and viceversa) such as in
the formation or the breaking of a covalent bond; (iii) the elliptic umbilic, in which
the index of a critical point changes by two. The identification of the turning points
connecting the ELF-SSDs along the reaction pathway allows a rigorous characterization of the sequence of electron pair rearrangements taking place during a
chemical transformation, such as multiple bond forming/breaking processes,
creation/annihilation of lone pairs, transformations of double bonds into single ones
or vice versa, and other electronic rearrangements. Details of the Thom’s classification in chemical reactions have been described in detail elsewhere [103].
A plethora of chemical rearrangements have been studied by BET: cycloadditions
[103, 136–139], cyclization [140–142], S N 2 reaction [143], Nazarov reaction [144],
Cope reaction [145], Cope rearrangement of semibullvalene [146], the reaction of
uranium ions with N 2 O in the gas phase [147], the reaction of Mn
+ with small
molecules [148], or inorganic reactions involving Mo complexes [149, 150]. Also,
some reviews on the applicability of BET to understand and rationalize chemical
reactivity have been published [138, 151–153], including the study of the bonding
changes along solid-solid phase transitions [154].
10 Quantum Chemical Topology Approach …
263