a r(X…N) represents the intermolecular distance between the boron / halogen atom and the nitrogen atom in the triel / halogen bonds of the ternary complexes, and X refers to the boron or halogen atom.
b Δr(X…N) and Δr(N…P) refers to the changes of the distance of r(X…N) and r(N…P) in ternary complexes relative to the binary complexes, respectively.
c Δr(X…N)/Δr(N…P) refers to the ratio between Δr(X…N) and Δr(N…P).
d ΔE bin, ΔE int, and E def refers to the total binding energy, interaction energy, and the deformation energy of the ternary complex. Energies are given with the BSSE correction.
When forming trimolecular complexes of X…CN-Ph-CN…PO2F, all hal…N (hal=F, Cl, Br) and N…P distances in the trimers are larger than those in the dimers, which suggests that both halogen bond and pnicogen bond becomes weaker relative to the isolated bimolecular complexes. For example, the N…P distance in CN-Ph-CN…PO2F is 1.954 Å, and the Br…N distance in FBr…CN-Ph-CN is 2.438 Å. With the formation of FBr…CN-Ph-CN…PO2F complex, the two distances are both elongated to 1.974 and 2.475 Å, respectively. In such type of ternary complexes, the elongation of the halogen bonding length is more prominent than the pnicogen bonding distance.
When the additional interaction is triel bond, the N…P distances X…CN-Ph-CN…PO2F increase to 1.969 and 1.967 Å for X=BH3 and BF3, respectively. It can be seen that there is a clear change in the geometry for the B-containing molecule, which deviates from the planar trigonal structure in the isolated monomer to tetrahedral geometry in the complexes. This is also observed in several triel-bonded complexes[44, 49], indicating strong π-hole triel bonding interaction. To confirm the reliability of the computational methods, we have also calculated the structures of BF3…HCN, and the results indicate that the B…N distance is predicted to be 2.408 Å at the B2PLYP-D3/6-311+G**, which compares favorably with the data obtained from the microwave spectra experiment (2.473±0.029 Å)[58]. Here, for our selected system, the B…N distance is calculated to be 1.543 and 1.824 Å in BH3…CN-Ph-CN, and BF3…CN-Ph-CN complexes, respectively. The differences of the geometries between BH3 and BF3 systems here compare well with those of other nitrile…BH3 complexes and their BF3 counterparts[59], which indicate that BF3 complexes are weaker with longer B…N distance and smaller N…B-X angles. This is consistent with the earlier findings that BH3 is a stronger Lewis acid than BF3, which is partly due to the backbonding effect [60]. When these two dimers form the trimers complexes with PO2F, one could expect that the B…N distance will become larger, as the CN-Ph-CN acts as Lewis acids in both triel bond and pnicogen bond in the complexes. But surprisingly, the observed changes are different from the expected behaviors. That is, the B…N distance is contracted to be 1.537 Å for the former and elongated to be 2.405 Å for the latter, although the N…P distances become larger in both complexes in comparison with the CN-Ph-CN…PO2F dimer. To ensure the validity of the calculated unusual variation of the B…N distance, we have reoptimized the structure of the complexes at the wB97XD/6-311+G** level, and the same trend is observed. That is, the value of B…N distance decreases from 1.559 Å in dimer to 1.552 Å in trimer for the BH3-involving complexes, while it increases from 1.814 Å in dimer to 2.422 Å in trimer for the BF3-involving complexes. Besides, it is worth mentioning that for the halogen bonded binary complexes in the research systems, as shown in Table S1, the proportion of the deformation energyE def is smaller than 15% of the binding energy, while for the triel bonded binary complex, E defis similar to or even much greater than the binding energy, and for BF3…CN-Ph-CN complex, E defis approximately three times greater than the binding energy. However, upon formation of the ternary complexes, the deformation for the BF3-involving trimolecular complexes become smaller than those of BH3 complexes, with the angle of F-B…N changing from 101.10° in dimer to 93.53° in trimer. The deformation is large if the angle has a larger derivation with 90°. These changes may be arising from the influence of the pnicogen bond in the ternary complex.
When the additional N…Br halogen bond is formed by introducing the nitrogen bases into the Br-Ph-CN…PO2F complexes, the binding distance of N…Br and N…P are both shortened in comparison with those in binary complex, which indicates that both halogen bond and pnicogen bond are reinforced from binary to ternary complexes. As seen from both the binding energy and interaction energy, the strength of the halogen bonding between the N-bases and Br-Ph-CN increase in the sequence HCN<NH3<NHCH2<NH2CH3, which is inconsistent with the values of Vmin,N from the ESP analysis.

3.2.3 Cooperative Energy

The total interaction energy (ΔE (ABC) or ΔE total) and the cooperative energyE coop, as well as the two-body terms are all summarized in Table 6, which are obtained at B2PLYP/jun-cc-pVTZ level for all studied systems. The values of E coop are positive for X…CN-Ph-CN…PO2F trimers, and this means that the strength of both halogen (or triel) bonding and pnicogen bonding interaction decrease upon the formation of the ternary complexes, which is also termed as the negative synergistic effect or diminutive effect[60]. When the halogen bond is introduced into CN-Ph-CN…PO2F complexes, the E coop ranges from 0.23 to 2.01 kcal/mol for the systems we studied. As for the Y…Br-Ph-CN…PO2F, the negativeE coop values reveal that the interactions are strengthened in trimer in comparison with the sum of the halogen bonding and the pnicogen bonding interactions in dimers, and this can be called positive synergistic effect. The E coopcorresponds to -1.32 to -1.65 kcal/mol. These findings related to the cooperative effect are consistent with the variations of the intermolecular distance as discussed above. As displayed in Figure 9, it is interesting to find that the ratio of the changes of the halogen bonding distance to the changes of the pnicogen bonding distance, i.e. Δr(hal…N)/Δr(N…P), show exponential correlation with the cooperative energy E coop, and the correlation coefficient R2 is 0.927. This indicates that, for two given type of the interactions, the greater the cooperative effect, the smaller for the difference between the variations of the two interaction distances.