“Thomas [71] and Dirac [72] imagined that the kinetic and exchange energies of
systems of many electrons could be locally modeled by their uniform electron gas
energy densities”. The electron density is a scalar field that can be experimentally
accessed [55] in principle and contains all necessary information for the ground
state of the molecular system, according to the Hohenberg–Kohn [73, 74] theorems
of DFT [75]. There is growing interest in explaining chemical phenomena arising
from the structure of the charge density. One branch of this developing research
field is the so-called conceptual DFT [76, 77], which has provided rigorous definitions for various chemical concepts such as electronegativity [78] and hardness,
[79] as well as relating changes within the density to frontier orbital concepts
through the Fukui function [80]. Calculations based on the seminal idea of Kohn
[81] are now an integral component of almost all areas of chemistry, physics and
materials sciences [82–84]. Although the exact functional form of the quantum
mechanical part of the electron–electron interaction (also referred to as the
exchange–correlation interaction) is not known, our ability to derive reasonable
approximations to this functional has made DFT an enormously practical tool
[85, 86].
10.3 Quantum Chemical Topology Analysis
In recent years, the topological analysis of the three-dimensional scalar fields [87–
95], such as electron density [55, 67, 92, 95–97], the Laplacian of the electron
density [68, 92], the electron localization function (ELF) [94, 98], and molecular
electrostatic potential, have been widely used to discern chemical structure and
reactivity. This procedure, named quantum chemical topology (QCT) [99] has been
utilized for the study of chemical structure and reactivity [100–106]. Since its
origins, the well-known approach of the ‘‘atoms in molecules’’ quantum theory
(QTAIM), has evolved to be an invaluable tool for the chemical interpretation of
quantum mechanical data, which relies on the properties of the electron density ρ(r)
when atoms interact. Excellent reviews on QTAIM methods have been published
elsewhere [69, 96, 107–109].
QTAIM starts from a particular division of real space into atomic basins. Given
the appropriate operator density, any quantum mechanical observable can be
integrated within the atomic basins, giving rise to the partition of properties into
additive atomic contributions. QTAIM represents molecular structure and bonding
as consequence of the charge-density topology and geometry. However, it is
important to note that there is some controversy on the applicability of QTAIM
[110–120]. Basically, their criticisms are focused on the arbitrariness of the theory,
the ambiguity of the topological construction and lack of predictive capabilities. For
such reason, more complex topologies such as the topology of the electron localization function (ELF) have been used [98, 121–124]. ELF performs a topological
10 Quantum Chemical Topology Approach …
261
systems of many electrons could be locally modeled by their uniform electron gas
energy densities”. The electron density is a scalar field that can be experimentally
accessed [55] in principle and contains all necessary information for the ground
state of the molecular system, according to the Hohenberg–Kohn [73, 74] theorems
of DFT [75]. There is growing interest in explaining chemical phenomena arising
from the structure of the charge density. One branch of this developing research
field is the so-called conceptual DFT [76, 77], which has provided rigorous definitions for various chemical concepts such as electronegativity [78] and hardness,
[79] as well as relating changes within the density to frontier orbital concepts
through the Fukui function [80]. Calculations based on the seminal idea of Kohn
[81] are now an integral component of almost all areas of chemistry, physics and
materials sciences [82–84]. Although the exact functional form of the quantum
mechanical part of the electron–electron interaction (also referred to as the
exchange–correlation interaction) is not known, our ability to derive reasonable
approximations to this functional has made DFT an enormously practical tool
[85, 86].
10.3 Quantum Chemical Topology Analysis
In recent years, the topological analysis of the three-dimensional scalar fields [87–
95], such as electron density [55, 67, 92, 95–97], the Laplacian of the electron
density [68, 92], the electron localization function (ELF) [94, 98], and molecular
electrostatic potential, have been widely used to discern chemical structure and
reactivity. This procedure, named quantum chemical topology (QCT) [99] has been
utilized for the study of chemical structure and reactivity [100–106]. Since its
origins, the well-known approach of the ‘‘atoms in molecules’’ quantum theory
(QTAIM), has evolved to be an invaluable tool for the chemical interpretation of
quantum mechanical data, which relies on the properties of the electron density ρ(r)
when atoms interact. Excellent reviews on QTAIM methods have been published
elsewhere [69, 96, 107–109].
QTAIM starts from a particular division of real space into atomic basins. Given
the appropriate operator density, any quantum mechanical observable can be
integrated within the atomic basins, giving rise to the partition of properties into
additive atomic contributions. QTAIM represents molecular structure and bonding
as consequence of the charge-density topology and geometry. However, it is
important to note that there is some controversy on the applicability of QTAIM
[110–120]. Basically, their criticisms are focused on the arbitrariness of the theory,
the ambiguity of the topological construction and lack of predictive capabilities. For
such reason, more complex topologies such as the topology of the electron localization function (ELF) have been used [98, 121–124]. ELF performs a topological
10 Quantum Chemical Topology Approach …
261