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).