18.3.2 3D Plot
18.3.2.1 3D Visualization
The 3D spatial visualization of the non-covalent interactions as defined above is
done using the data from the 2D plots as input to construct 3D plots composed of
reduced density gradient isosurfaces.
In a nutshell, a cut-off value of s close to zero, typically s < 0.5, is chosen in order
to recover all the non-covalent interactions in the system, i.e. all the spikes of the 2D
plots. The corresponding reduced density gradient isosurfaces give rise to closed
domains in the molecular space which highlight the spatial localization of the
interactions within the system (see Fig. 18.2c). Since 3D isosurfaces are, by definition, regions of low reduced gradient, the density is nearly constant within these.
At this stage, however, the types of interaction corresponding to the various
isosurfaces are not apparent. In order to discriminate between them, the density
oriented by the sign of λ 2 is further used (as in the 2D plot). A RGB
(red-green-blue) coloring scheme is chosen to rank interactions, where red is used
for destabilizing interactions, blue for stabilizing interactions and green for delocalized weak interactions. The intensity of these colors is associated with a higher
local density and therefore with a stronger interaction.
The isovalue (or cut-off) of s(ρ) chosen for plotting the 3D isosurface determines
which features will appear in the NCI plot as well as their spatial extension. On the
one hand, all NCI spikes do not strictly achieve s = 0, so that a too low isovalue
might miss some of the interactions of interest [60]. On the other hand, too high
isovalues would disclose atomic tails of the density [61]. The cut-off is therefore
chosen from the 2D plot so that all spikes, but only spikes, are captured to render a
meaningful picture which recovers both attractive and repulsive interactions.
18.3.2.2 2D and 3D Shapes
Topological features of the electron density are very stable with respect to the
calculation method. The main effect of different methods on the s versus ρ diagram
is a shift of spikes. The only rule of thumb seems that the same s value should be
used when comparing to each other the various NCI, both in the same or in different
systems, provided a single method was employed to obtain the various electron
densities. This not being the case, different s values are seemingly required to
compare on similar grounds the s-based results for differently computed electron
density (e.g. from wavefunction, multipolar). In other words, a shift of cut-offs is
needed to obtain comparable images. This can be related to the fact that s roughly
behaves like ρ
−1/3 (see Eq. 18.3), so that the effect of the method on the density is
directly followed by the s-value. This information is crucial when moving towards
bigger systems (see Sect. 18.6).
502
C. Narth et al.
18.3.2.1 3D Visualization
The 3D spatial visualization of the non-covalent interactions as defined above is
done using the data from the 2D plots as input to construct 3D plots composed of
reduced density gradient isosurfaces.
In a nutshell, a cut-off value of s close to zero, typically s < 0.5, is chosen in order
to recover all the non-covalent interactions in the system, i.e. all the spikes of the 2D
plots. The corresponding reduced density gradient isosurfaces give rise to closed
domains in the molecular space which highlight the spatial localization of the
interactions within the system (see Fig. 18.2c). Since 3D isosurfaces are, by definition, regions of low reduced gradient, the density is nearly constant within these.
At this stage, however, the types of interaction corresponding to the various
isosurfaces are not apparent. In order to discriminate between them, the density
oriented by the sign of λ 2 is further used (as in the 2D plot). A RGB
(red-green-blue) coloring scheme is chosen to rank interactions, where red is used
for destabilizing interactions, blue for stabilizing interactions and green for delocalized weak interactions. The intensity of these colors is associated with a higher
local density and therefore with a stronger interaction.
The isovalue (or cut-off) of s(ρ) chosen for plotting the 3D isosurface determines
which features will appear in the NCI plot as well as their spatial extension. On the
one hand, all NCI spikes do not strictly achieve s = 0, so that a too low isovalue
might miss some of the interactions of interest [60]. On the other hand, too high
isovalues would disclose atomic tails of the density [61]. The cut-off is therefore
chosen from the 2D plot so that all spikes, but only spikes, are captured to render a
meaningful picture which recovers both attractive and repulsive interactions.
18.3.2.2 2D and 3D Shapes
Topological features of the electron density are very stable with respect to the
calculation method. The main effect of different methods on the s versus ρ diagram
is a shift of spikes. The only rule of thumb seems that the same s value should be
used when comparing to each other the various NCI, both in the same or in different
systems, provided a single method was employed to obtain the various electron
densities. This not being the case, different s values are seemingly required to
compare on similar grounds the s-based results for differently computed electron
density (e.g. from wavefunction, multipolar). In other words, a shift of cut-offs is
needed to obtain comparable images. This can be related to the fact that s roughly
behaves like ρ
−1/3 (see Eq. 18.3), so that the effect of the method on the density is
directly followed by the s-value. This information is crucial when moving towards
bigger systems (see Sect. 18.6).
502
C. Narth et al.