chemical meanings, and can be obtained both experimentally and by means of
theoretical calculations, except for properties that require the full density matrix
obtainable only from quantum mechanical calculations. Combined experimental
and theoretical charge density studies rely on the analysis of electron density distributions obtained from quantum chemical calculations, ρ calc (r), and from experimental X-ray diffraction data, ρ exp (r) [52–55]. The comparison of the topological
parameters of ρ calc (r) and ρ exp (r) provides important information for the interpretation of experimental results and allows to evaluate the accuracy of the experimental data. A direct comparison between both electron density distributions is
biased because they are subjected to different sources of errors. The electron density
ρ exp (r) is, for example, affected by systematic experimental errors and the model
ambiguities introduced during the reconstruction of a static electron density distribution from the measured X-ray scattering factors.
Recently, Gavezzotti [56] has reviewed the physical principles of chemical
bonding from the Feynman perspective. The answer of this question: What binds
atoms together? was provided by Feynman [57]: “The force on a nucleus in an
atomic system is shown to be just the classical electrostatic force that would be
exerted on this nucleus by other nuclei and by the electrons’ charge distribution”.
Being that the electron density is the observable common to both the experimental
and theoretical approaches, it has become logical to focus on the observable itself,
rather than on a model density, to confront and mutually validate them and their
densities [58]. But the most important reason for studying the total density has been
the increasing popularity of the so-called topological studies of bonding, that is,
those made in terms of the study of the gradient vector field of a scalar function
containing information on bonding [58]. Accurate X-ray diffraction experiments
allow for a reconstruction of the electron density distribution of solids and molecules in a crystal.
The concept of molecular orbitals [59], the valence bond theory [60], related
natural bond orbitals approach [61] and the valence shell electron pair repulsion
concept [62] have provided quite reliable predictions of chemical structures, i.e.
molecular geometries, while Woodward–Hoffmann rules [63], Fukui’s frontier
molecular orbital theory [64], analysis based on valence bond theory [65] or Marcus
theory [66] have been helpful for our current understanding of chemical reactivity.
Advanced theories in science, as chemistry and/or physics, to be sustainable need to
have a mathematical support to give basic concepts of the theory. Furthermore, the
scalar fields based on electron density are experimentally amenable and thereby
provide a clear-cut bridge between theory and experiment. Collar and Hall [67], and
Bader [68] have provided the foundations of the topological analysis of
one-electron charge densities. The path-breaking works due to Bader and
co-workers have generated an active research area based on the study of the
topology of molecular scalar fields. It is aimed at providing an understanding of
molecular structure and reactivity [69]. Likewise, Nasertayoob and Shahbazian [70]
have presented the mathematical foundations of the dynamical aspects of topological analysis of the electronic charge densities.
260
J. Andrés et al.
theoretical calculations, except for properties that require the full density matrix
obtainable only from quantum mechanical calculations. Combined experimental
and theoretical charge density studies rely on the analysis of electron density distributions obtained from quantum chemical calculations, ρ calc (r), and from experimental X-ray diffraction data, ρ exp (r) [52–55]. The comparison of the topological
parameters of ρ calc (r) and ρ exp (r) provides important information for the interpretation of experimental results and allows to evaluate the accuracy of the experimental data. A direct comparison between both electron density distributions is
biased because they are subjected to different sources of errors. The electron density
ρ exp (r) is, for example, affected by systematic experimental errors and the model
ambiguities introduced during the reconstruction of a static electron density distribution from the measured X-ray scattering factors.
Recently, Gavezzotti [56] has reviewed the physical principles of chemical
bonding from the Feynman perspective. The answer of this question: What binds
atoms together? was provided by Feynman [57]: “The force on a nucleus in an
atomic system is shown to be just the classical electrostatic force that would be
exerted on this nucleus by other nuclei and by the electrons’ charge distribution”.
Being that the electron density is the observable common to both the experimental
and theoretical approaches, it has become logical to focus on the observable itself,
rather than on a model density, to confront and mutually validate them and their
densities [58]. But the most important reason for studying the total density has been
the increasing popularity of the so-called topological studies of bonding, that is,
those made in terms of the study of the gradient vector field of a scalar function
containing information on bonding [58]. Accurate X-ray diffraction experiments
allow for a reconstruction of the electron density distribution of solids and molecules in a crystal.
The concept of molecular orbitals [59], the valence bond theory [60], related
natural bond orbitals approach [61] and the valence shell electron pair repulsion
concept [62] have provided quite reliable predictions of chemical structures, i.e.
molecular geometries, while Woodward–Hoffmann rules [63], Fukui’s frontier
molecular orbital theory [64], analysis based on valence bond theory [65] or Marcus
theory [66] have been helpful for our current understanding of chemical reactivity.
Advanced theories in science, as chemistry and/or physics, to be sustainable need to
have a mathematical support to give basic concepts of the theory. Furthermore, the
scalar fields based on electron density are experimentally amenable and thereby
provide a clear-cut bridge between theory and experiment. Collar and Hall [67], and
Bader [68] have provided the foundations of the topological analysis of
one-electron charge densities. The path-breaking works due to Bader and
co-workers have generated an active research area based on the study of the
topology of molecular scalar fields. It is aimed at providing an understanding of
molecular structure and reactivity [69]. Likewise, Nasertayoob and Shahbazian [70]
have presented the mathematical foundations of the dynamical aspects of topological analysis of the electronic charge densities.
260
J. Andrés et al.