through which molecules recognize themselves and establish how molecules will
approach and eventually pack together.
During the last decade, non-covalent interactions have also raised a great deal of
interest in the context of self-assembly [36] and crystallization [37], whose
underlying general rules are at the moment too far away to be fully rationalized and
understood [38]. Knowledge of such rules would in principle allow to build from
scratch (even complex) materials exhibiting the desired properties [29, 39, 40].
Although it can not be ignored that a given observed structure is generally the
outcome of a “drawing” among a plethora of energetically similar, but structurally
dissimilar options [41], understanding intermolecular non-covalent interactions and
their mutual interplay in the supramolecular assemblies is nonetheless a fundamental step in making progress in structural prediction and evolution.
18.1.2.1 Weak Interactions: The Need for a New Approach
Non-covalent interactions are frequently visualized using distance-dependent contacts, generally without consideration of hydrogen atoms [42–44]. Hydrogen-bonds
can be identified from the molecular geometry [45] and from ELF [46], while
grid-based calculations from classical force fields are used to model van der Waals
interactions [47]. The crucial role of weak interactions can also be analyzed in an
indirect manner through property computations (from population to electrostatic
moments) [48]. However, these fluctuations are not easily visualized. In other words,
a visual quantum chemical approach was conspicuously missing in this scenario.
Let’s look at an example to clearly pinpoint the state of the art of topological
approaches to weak interactions. The image provided by QTAIM and ELF of benzene
dimer is provided in Table 18.1. Let’s first focus on a given benzene molecule: The
electron density shows maxima (cusps) for the C and H atoms, whereas C–H and C–C
bonds are represented by BCPs (in red). ELF, instead, provides a picture based on
electron localization, so that isosurfaces appear around nuclei and bonds. In both
cases the chemical structure is revealed as expected from chemical intuition.
However, the ELF picture is obviously more intuitive thanks to the isosurfaces.
Now, if we take a look at the complete system, the stacking dimer, we can see
that intermolecular BCPs appear along with a ring critical point (second order
saddle point, in yellow). The fact that interactions are related to saddle points,
locates them on the interatomic surfaces, so that they highlight interatomic contact,
but they do not have an associated region within this approach. Moreover, the
critical points unite pairs of C atoms, which is not the chemical picture we have of a
stacking interaction: it should appear as a benzene to benzene interaction.
The VSEPR regions of benzene dimer are clearly identified by ELF, but nothing is
seen for the inter-benzene stacking interaction.
In other words, both approaches fail to correctly provide a picture of delocalized
interactions. Thus, it is the aim of this chapter to introduce such a tool, show its
advantages over previous theories and its ability to provide a complete and holistic
vision of non-covalent interactions and their changes directly from the electron density.
18 A Complete NCI Perspective: From New Bonds to Reactivity
495
approach and eventually pack together.
During the last decade, non-covalent interactions have also raised a great deal of
interest in the context of self-assembly [36] and crystallization [37], whose
underlying general rules are at the moment too far away to be fully rationalized and
understood [38]. Knowledge of such rules would in principle allow to build from
scratch (even complex) materials exhibiting the desired properties [29, 39, 40].
Although it can not be ignored that a given observed structure is generally the
outcome of a “drawing” among a plethora of energetically similar, but structurally
dissimilar options [41], understanding intermolecular non-covalent interactions and
their mutual interplay in the supramolecular assemblies is nonetheless a fundamental step in making progress in structural prediction and evolution.
18.1.2.1 Weak Interactions: The Need for a New Approach
Non-covalent interactions are frequently visualized using distance-dependent contacts, generally without consideration of hydrogen atoms [42–44]. Hydrogen-bonds
can be identified from the molecular geometry [45] and from ELF [46], while
grid-based calculations from classical force fields are used to model van der Waals
interactions [47]. The crucial role of weak interactions can also be analyzed in an
indirect manner through property computations (from population to electrostatic
moments) [48]. However, these fluctuations are not easily visualized. In other words,
a visual quantum chemical approach was conspicuously missing in this scenario.
Let’s look at an example to clearly pinpoint the state of the art of topological
approaches to weak interactions. The image provided by QTAIM and ELF of benzene
dimer is provided in Table 18.1. Let’s first focus on a given benzene molecule: The
electron density shows maxima (cusps) for the C and H atoms, whereas C–H and C–C
bonds are represented by BCPs (in red). ELF, instead, provides a picture based on
electron localization, so that isosurfaces appear around nuclei and bonds. In both
cases the chemical structure is revealed as expected from chemical intuition.
However, the ELF picture is obviously more intuitive thanks to the isosurfaces.
Now, if we take a look at the complete system, the stacking dimer, we can see
that intermolecular BCPs appear along with a ring critical point (second order
saddle point, in yellow). The fact that interactions are related to saddle points,
locates them on the interatomic surfaces, so that they highlight interatomic contact,
but they do not have an associated region within this approach. Moreover, the
critical points unite pairs of C atoms, which is not the chemical picture we have of a
stacking interaction: it should appear as a benzene to benzene interaction.
The VSEPR regions of benzene dimer are clearly identified by ELF, but nothing is
seen for the inter-benzene stacking interaction.
In other words, both approaches fail to correctly provide a picture of delocalized
interactions. Thus, it is the aim of this chapter to introduce such a tool, show its
advantages over previous theories and its ability to provide a complete and holistic
vision of non-covalent interactions and their changes directly from the electron density.
18 A Complete NCI Perspective: From New Bonds to Reactivity
495