Figure 9 . Exponential correlations between the cooperative
energy E coop and the ratio of changes of the
halogen bonding distance to the changes of the pnicogen bonding distance
Δr(hal…N)/Δr(N…P).
Since the pnicogen bonding is the same in the trimer, the cooperative
energy varies depending on the strength in X…CN-Ph-CN or
Y…Br-Ph-CN. In most cases, the cooperative effect becomes more
prominent when the additional interaction in X…CN-Ph-CN or
Y…Br-Ph-CN is larger. As can be seen in Figure 10, a good linear
relationship is found between the halogen bonding interaction in
X…CN-Ph-CN (X=dihalogen compounds, including F2,
Cl2, Br2, FCl, FBr, BrCl, ClBr) and the
percentage of E coop to the total interaction
energy ΔE total. The E coopdecrease in the order of
F2<BrCl*<Cl2<Br2<ClBr*<FCl*<FBr*,
which is in good agreement with the order of Vmax values
of the σ-hole on the halogen atoms as discussed above. Combined with the
studies of Zhang et al.[44], it is found
that the cooperative energy and its percentage to
ΔE total are both smaller when the benzenoid
derivatives are served as the bridge molecule than the heterocyclic
systems. This may be due to the fact that the mutual effect of the
interaction is weakened through the aromaticity of phenyl ring, while
the strength is still very strong through the bond of the heterocyclic
ring. Therefore, the interplay between the two interaction is strongly
influenced by bonding characteristic of the bridge molecule, in addition
to the strength of both interactions.
Table 6. The total interaction in the ternary complex
(∆E(ABC)), the interaction energy of the halogen/triel bond (∆E(AB)) and
pnicogen bond (∆E(BC)), and cooperative energy
(E coop) in the ternary complexes (Unit:
Kcal/mol).