of interacting particles, known as the many-body problem [17, 18] has stimulated
the development of a number of general approximation techniques.
As it was emphasized by Löwdin [19] “Quantum chemistry deals particularly
with the electronic structure of atoms, molecules, and condensed matter, and
describes it in terms of electronic wave patterns of standing waves. It deals also
with collisions between atoms and molecules and with the study of chemical
reactivity”. In quantum chemistry, the fundamental model of chemical bond is
based on one-determinant electronic structure methods like Hartree-Fock or
Kohn-Sham density functional theory (DFT). However, despite the contemporary
high standards in determination of geometrical parameters, questions of chemical
bond are still highly controversial. This problem can be traced back to the lack of a
clear and unambiguous definition of a bond in quantum mechanics. Therefore, a
chemical bond together with other essential concepts such as electron shells, lone
pairs, aromaticity, atomic charges, (hyper-) conjugation, strain, etc. have been
getting fuzzier over time, yet invaluably useful concepts [20–23], which are of
essential importance for practical chemistry leading to constructive ideas and
developments when appropriately used and defined, have been developed. In the
Faraday Discussions 135 [24], which took place in September 2006 in Manchester,
a number of methods have been suggested (Chemical Concepts from Quantum
Mechanics) without laying an end to the debate. Many concepts, including
chemical bond, cannot be derived from theory reduction from the principles of
quantum mechanics, because they were introduced heuristically as ordering criteria,
as it was remarked by Primas [25].
What is a chemical bond? and how should we define chemical bond? are still a
critical questions for chemical community, and remain as an active area of research
[26–43]. For example, the controversy about the existence of a sextuple bond or not
in Cr 2 , and more recently the existence or not of a quadruple bond in C 2 [44–46], as
well as the nature of hydrogen bonding [47, 48]. In this sense, chemical bonds have
even been compared to unicorns: mythical creatures of which everyone knows how
they look, despite nobody ever having seen one [49]. Very recently, the different
methods of defining and describing chemical bonds have been highlighted in a
two-volume book dedicated to the chemical bond [50]. But it is important to
remark, as noted by Frenking and Caramori [48]: “The physical nature of chemical
bonding is quite complicated [51]. It is in most cases not necessary for a synthetic
chemist to engage in elaborate quantum-chemical investigations. Standard calculations will usually provide sufficient information to classify a new compound and
design new experiments”.
10.2 Electron Density
The electron density is related to the molecular Hamiltonian, and hence is the
ultimate source of all properties in the ground- and excited states. In addition,
descriptors and/or indexes derived from the electron density possess physical and
10 Quantum Chemical Topology Approach …
259
the development of a number of general approximation techniques.
As it was emphasized by Löwdin [19] “Quantum chemistry deals particularly
with the electronic structure of atoms, molecules, and condensed matter, and
describes it in terms of electronic wave patterns of standing waves. It deals also
with collisions between atoms and molecules and with the study of chemical
reactivity”. In quantum chemistry, the fundamental model of chemical bond is
based on one-determinant electronic structure methods like Hartree-Fock or
Kohn-Sham density functional theory (DFT). However, despite the contemporary
high standards in determination of geometrical parameters, questions of chemical
bond are still highly controversial. This problem can be traced back to the lack of a
clear and unambiguous definition of a bond in quantum mechanics. Therefore, a
chemical bond together with other essential concepts such as electron shells, lone
pairs, aromaticity, atomic charges, (hyper-) conjugation, strain, etc. have been
getting fuzzier over time, yet invaluably useful concepts [20–23], which are of
essential importance for practical chemistry leading to constructive ideas and
developments when appropriately used and defined, have been developed. In the
Faraday Discussions 135 [24], which took place in September 2006 in Manchester,
a number of methods have been suggested (Chemical Concepts from Quantum
Mechanics) without laying an end to the debate. Many concepts, including
chemical bond, cannot be derived from theory reduction from the principles of
quantum mechanics, because they were introduced heuristically as ordering criteria,
as it was remarked by Primas [25].
What is a chemical bond? and how should we define chemical bond? are still a
critical questions for chemical community, and remain as an active area of research
[26–43]. For example, the controversy about the existence of a sextuple bond or not
in Cr 2 , and more recently the existence or not of a quadruple bond in C 2 [44–46], as
well as the nature of hydrogen bonding [47, 48]. In this sense, chemical bonds have
even been compared to unicorns: mythical creatures of which everyone knows how
they look, despite nobody ever having seen one [49]. Very recently, the different
methods of defining and describing chemical bonds have been highlighted in a
two-volume book dedicated to the chemical bond [50]. But it is important to
remark, as noted by Frenking and Caramori [48]: “The physical nature of chemical
bonding is quite complicated [51]. It is in most cases not necessary for a synthetic
chemist to engage in elaborate quantum-chemical investigations. Standard calculations will usually provide sufficient information to classify a new compound and
design new experiments”.
10.2 Electron Density
The electron density is related to the molecular Hamiltonian, and hence is the
ultimate source of all properties in the ground- and excited states. In addition,
descriptors and/or indexes derived from the electron density possess physical and
10 Quantum Chemical Topology Approach …
259