For completeness, one can mention that others local descriptors have been
designed over the years (ellipticity, various density energies like the G c and K c
kinetic, potential V c , Hamiltonian H c ones at BCP, reduced density gradient variation
rates [98], DFT-based local descriptors [99]…). Besides, following the appearance
and disappearance of critical points also constitutes an efficient way of describing the
mechanism of chemical transformations (see Ref. [100] for a recent example).
16.2.3 Computational Details
Consistently with our previous works, and as recommended by Kozuch and Martin
[101], the ωB97X-D exchange-correlation functional [102] was used in conjunction
with the triple-ζ aug-cc-pVTZ basis set. Potential energy surfaces were explored
through relaxed energy scans on the X…N (X being any halogen) distance with a
stepsize equal to 0.07 Å. All DFT calculations were carried out using the Gaussian 09
software [103], while Keith’s AIMAll program [104] was used for the whole topological analysis.
16.3 Unravelling Halogen Bond Formation
with the QTAIM-IQA Approach
As first examples, we will consider the Cl 3 COX…NH 3 complexes (X = F, Cl, and
Br) that belong to the R 3 COX…NH 3 family, which was studied by Politzer [56]
and recently revisited by us within the framework of conceptual DFT [67] and
density Laplacian maps [68].
16.3.1 Potential Energy Surfaces
The potential energy surface along the X…N distance coordinate for the three
complexes is represented in Graph 16.1.
It clearly appears that an energy minimum (from the SCF energy point of view) is
located in the chlorine and bromine cases, while the curve exhibits an overall
repulsive interaction between the two moieties for X = F.
1 Consistently with the
higher bromine electrophilicity and its higher polarizability, the complexation energy
is larger for Br than for Cl. Noticeably, while bromine is in general a bigger atom
than chlorine, the equilibrium distance for the bromine complex is slightly smaller
than that for the chlorine one: the contraction due to the halogen bond formation is
thus larger.
1
Very small negative values for large separation distances are due to basis set superposition errors.
442
V. Tognetti and L. Joubert
designed over the years (ellipticity, various density energies like the G c and K c
kinetic, potential V c , Hamiltonian H c ones at BCP, reduced density gradient variation
rates [98], DFT-based local descriptors [99]…). Besides, following the appearance
and disappearance of critical points also constitutes an efficient way of describing the
mechanism of chemical transformations (see Ref. [100] for a recent example).
16.2.3 Computational Details
Consistently with our previous works, and as recommended by Kozuch and Martin
[101], the ωB97X-D exchange-correlation functional [102] was used in conjunction
with the triple-ζ aug-cc-pVTZ basis set. Potential energy surfaces were explored
through relaxed energy scans on the X…N (X being any halogen) distance with a
stepsize equal to 0.07 Å. All DFT calculations were carried out using the Gaussian 09
software [103], while Keith’s AIMAll program [104] was used for the whole topological analysis.
16.3 Unravelling Halogen Bond Formation
with the QTAIM-IQA Approach
As first examples, we will consider the Cl 3 COX…NH 3 complexes (X = F, Cl, and
Br) that belong to the R 3 COX…NH 3 family, which was studied by Politzer [56]
and recently revisited by us within the framework of conceptual DFT [67] and
density Laplacian maps [68].
16.3.1 Potential Energy Surfaces
The potential energy surface along the X…N distance coordinate for the three
complexes is represented in Graph 16.1.
It clearly appears that an energy minimum (from the SCF energy point of view) is
located in the chlorine and bromine cases, while the curve exhibits an overall
repulsive interaction between the two moieties for X = F.
1 Consistently with the
higher bromine electrophilicity and its higher polarizability, the complexation energy
is larger for Br than for Cl. Noticeably, while bromine is in general a bigger atom
than chlorine, the equilibrium distance for the bromine complex is slightly smaller
than that for the chlorine one: the contraction due to the halogen bond formation is
thus larger.
1
Very small negative values for large separation distances are due to basis set superposition errors.
442
V. Tognetti and L. Joubert