As exchange is usually less long-range than classical electrostatics, it is not
surprising that a
x
XN tends toward 0 for large separation distances. Conversely, it
becomes predominant at small distances (smaller than approximately 2.4 Å, corresponding to a
x
XN
[ 1). For instance, for F…N = 2.0 Å, E
x
FN = −48.9 kcal/mol
(while E
cl
FN = +19.6 kcal/mol). This hierarchy also holds for the other halogens, as
exemplified by the bromine case: E
x
BrN ¼ À115:3 kcal=mol (while E
cl
BrN ¼
À103:1 kcal=mol for Br…N = 2.0 Å).
At such distances, the use, as an interpretative tool, of the molecular electrostatic
potential (which is simply the Gâteaux derivative of the molecular classical electrostatic energy functional with respect to the electron density) becomes arguable
since classical electrostatics does not exclusively drive the studied interactions. This
Graph 16.6 Interaction exchange energy (left) and a
x
XN ¼
E
x
XN
E cl
XN
ratio (right) for the X…N primary
interaction as a function of the X…N distance for the Cl 3 COX…NH 3 complexes
Graph 16.7 Interaction
energy due to dispersion for
the X…N primary interaction
as a function of the X…N
distance for the Cl 3 COX…
NH 3 complexes
16 Following Halogen Bonds Formation …
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