positive or negative. Within the NCI framework, the sign of λ 2 (i.e. the perpendicular plane) enables identification of the interaction type. Attractive interactions
appear at λ 2 < 0 whereas in the cases where λ 2 is positive (as in rings or cages),
usually several atoms interact but are not bonded, which corresponds to steric
crowding according to classical chemistry.
Both van der Waals interactions and hydrogen bonds show negative values of λ 2
at the critical point (with k 2 ’ 0 for van der Waals interactions and even λ 2 ≥ 0 on
the surface). This can be attributed to the homomorphic virial path associated with
the bonding direction, which defines a line along which the potential-energy density
is maximally negative. Conversely, non-bonding interactions, such as steric
crowding, result in density depletion, such that λ 2 > 0. Analogously, the homeomorphism ensures that these critical points (both ring and cages points) identify
lines of minimally-negative potential-energy density.
18.3 Interpreting NCI
18.3.1 The 2D Plot
Once the second eigenvalue has been introduced to separate attractive from
repulsive interactions, it is necessary to categorize the interactions by their strength.
This can be done thanks to the properties of the corresponding critical points.
Characteristic densities of van der Waals interactions are much smaller than densities at which hydrogen bonds appear. However, steric clashes and hydrogen bonds
(HBs) span similar density ranges and overlap in plots of s(ρ). This is illustrated for
the phenol dimer in Fig. 18.2a, b. This is a hydrogen-bonded complex that exhibits
non-bonding interactions within each benzene ring and a stacking interaction
between the benzene rings. We thus have the three main types of interactions: van
der Waals, HB and steric clashes. Whereas van der Waals is well-differenciated
because it appears at smaller densities, the steric clash and the hydrogen bond
spikes overlap in Fig. 18.2a.
The interaction type can be distinguished if the s(ρ) diagrams are modified by
plotting sign(λ 2 )ρ as the abscissa. Analysis of the sign of λ 2 thus helps to discern
between the different types of weak interactions, whereas the density itself provides
information about their strength; both are combined in the value of sign(λ 2 )ρ. When
the Hessian eigenvalues are considered, the different nature of these interactions is
made clear: the benzene-ring interactions remain at positive values, whereas the
hydrogen bond now lies at negative values, within the attractive regime. The NCI
spikes nearest zero density correspond to weakly-attractive dispersion interactions
between the phenyl rings.
500
C. Narth et al.
appear at λ 2 < 0 whereas in the cases where λ 2 is positive (as in rings or cages),
usually several atoms interact but are not bonded, which corresponds to steric
crowding according to classical chemistry.
Both van der Waals interactions and hydrogen bonds show negative values of λ 2
at the critical point (with k 2 ’ 0 for van der Waals interactions and even λ 2 ≥ 0 on
the surface). This can be attributed to the homomorphic virial path associated with
the bonding direction, which defines a line along which the potential-energy density
is maximally negative. Conversely, non-bonding interactions, such as steric
crowding, result in density depletion, such that λ 2 > 0. Analogously, the homeomorphism ensures that these critical points (both ring and cages points) identify
lines of minimally-negative potential-energy density.
18.3 Interpreting NCI
18.3.1 The 2D Plot
Once the second eigenvalue has been introduced to separate attractive from
repulsive interactions, it is necessary to categorize the interactions by their strength.
This can be done thanks to the properties of the corresponding critical points.
Characteristic densities of van der Waals interactions are much smaller than densities at which hydrogen bonds appear. However, steric clashes and hydrogen bonds
(HBs) span similar density ranges and overlap in plots of s(ρ). This is illustrated for
the phenol dimer in Fig. 18.2a, b. This is a hydrogen-bonded complex that exhibits
non-bonding interactions within each benzene ring and a stacking interaction
between the benzene rings. We thus have the three main types of interactions: van
der Waals, HB and steric clashes. Whereas van der Waals is well-differenciated
because it appears at smaller densities, the steric clash and the hydrogen bond
spikes overlap in Fig. 18.2a.
The interaction type can be distinguished if the s(ρ) diagrams are modified by
plotting sign(λ 2 )ρ as the abscissa. Analysis of the sign of λ 2 thus helps to discern
between the different types of weak interactions, whereas the density itself provides
information about their strength; both are combined in the value of sign(λ 2 )ρ. When
the Hessian eigenvalues are considered, the different nature of these interactions is
made clear: the benzene-ring interactions remain at positive values, whereas the
hydrogen bond now lies at negative values, within the attractive regime. The NCI
spikes nearest zero density correspond to weakly-attractive dispersion interactions
between the phenyl rings.
500
C. Narth et al.