analysis of the same-spin pair probability density and thus generates basins of
localized electron pairs [125–127]. The integration of the electron density over the
ELF basin yields the basin population, that is, the amount of electron density in the
chemical bond [128–130].
As Silvi et al. [131] stated: “… the ELF topological analysis provides a mathematical bridge between quantum mechanics and chemistry which relies on the one
hand on the statistical interpretation and on the other hand on the theory of
dynamical system. This approach shares the dynamical system theory as common
mathematical method with the Atoms in Molecules theory, the difference being the
nature of the potential function and therefore the nature of the investigated properties. The QTAIM theory is rightly claimed to be rooted in physics rather than in
chemistry and its partition scheme aims accordingly to define open quantum systems within which the virial theorem holds.”
10.4 The Bonding Evolution Theory
The analysis of the electronic structure at the stationary points concomitantly with
the description of the possible reaction pathways associated with the chemical
rearrangements are undoubtedly one of the most relevant applications of modern
computational chemistry; nevertheless accurate geometries, energies, as well as
other observables properties cannot always be guaranteed from quantum chemical
calculations. Likewise, there is no physical observable corresponding to the
chemical bond and their rearrangement along a given chemical reaction (which
corresponds to the essence of the chemical reactivity). Such concepts cannot be
unambiguously defined in pure quantum theory, and therefore, qualitative concepts
are of essential importance for practical chemistry.
In spite of Hohenberg–Kohn theorem guarantees that all the molecular information is encoded in the electron density, the physical description of chemical
systems requires additional postulates for extracting observable information in
terms of atomic contributions. This is achieved by the QTAIM introduced by Bader,
providing a quantum topological partitioning of the molecular space into chemically transferable molecular fragments for which the energy and all other measurable properties can be precisely defined [132]. The introduction of concepts such as
bond path in the framework of QTAIM allows the description of the evolution of
the electronic structure along a reaction pathway, and hence, to understand a given
chemical rearrangement following the redistribution of the electron density along
the reaction pathway connecting the stationary points. Thus, Bader and co-workers
pioneered the study of the evolution of the electron density in chemical reactions
considering the structural changes in this scalar field according to the Thom’s
catastrophes theory (CT) [97, 133, 134].
262
J. Andrés et al.
localized electron pairs [125–127]. The integration of the electron density over the
ELF basin yields the basin population, that is, the amount of electron density in the
chemical bond [128–130].
As Silvi et al. [131] stated: “… the ELF topological analysis provides a mathematical bridge between quantum mechanics and chemistry which relies on the one
hand on the statistical interpretation and on the other hand on the theory of
dynamical system. This approach shares the dynamical system theory as common
mathematical method with the Atoms in Molecules theory, the difference being the
nature of the potential function and therefore the nature of the investigated properties. The QTAIM theory is rightly claimed to be rooted in physics rather than in
chemistry and its partition scheme aims accordingly to define open quantum systems within which the virial theorem holds.”
10.4 The Bonding Evolution Theory
The analysis of the electronic structure at the stationary points concomitantly with
the description of the possible reaction pathways associated with the chemical
rearrangements are undoubtedly one of the most relevant applications of modern
computational chemistry; nevertheless accurate geometries, energies, as well as
other observables properties cannot always be guaranteed from quantum chemical
calculations. Likewise, there is no physical observable corresponding to the
chemical bond and their rearrangement along a given chemical reaction (which
corresponds to the essence of the chemical reactivity). Such concepts cannot be
unambiguously defined in pure quantum theory, and therefore, qualitative concepts
are of essential importance for practical chemistry.
In spite of Hohenberg–Kohn theorem guarantees that all the molecular information is encoded in the electron density, the physical description of chemical
systems requires additional postulates for extracting observable information in
terms of atomic contributions. This is achieved by the QTAIM introduced by Bader,
providing a quantum topological partitioning of the molecular space into chemically transferable molecular fragments for which the energy and all other measurable properties can be precisely defined [132]. The introduction of concepts such as
bond path in the framework of QTAIM allows the description of the evolution of
the electronic structure along a reaction pathway, and hence, to understand a given
chemical rearrangement following the redistribution of the electron density along
the reaction pathway connecting the stationary points. Thus, Bader and co-workers
pioneered the study of the evolution of the electron density in chemical reactions
considering the structural changes in this scalar field according to the Thom’s
catastrophes theory (CT) [97, 133, 134].
262
J. Andrés et al.