*4.4. The Peculiar Case of the AZH (DCR) Dimer*

As previously mentioned, all of the dimers with the exception of AZH (DCR) exhibit a planar or quasi-planar structure. However, the lowest local energy minimum found for the last-mentioned compound adopts a distorted conformation. Based on the aforementioned observations, one might conjecture at first glance that such a geometrical distortion could be understood as a way to alleviate the reduction of aromaticity induced by the formation of the dimers. To explore this idea, two additional conformational isomers were studied, as represented in Figure 9. Both the bent–trans bent–cis structures are bona fide local minima with a non-planar geometry. We performed a constraint optimisation in order to obtain the corresponding planar AZH (DCR) isomer. As shown in Table 5, the bent isomers are almost degenerate in terms of energy, being the bent–cis structure slightly more stable by ≈0.5 kcal/mol. On the other hand, the planar structure is ≈7 kcal/mol less stable than the latter.

**Figure 9.** Different isomers of the AZH (DCR) dimers: bent–trans, bent–cis, planar.

The aromaticity metrics reported in Table 5 indicate that the restriction of the 4 membered rings in AZH to remain in a plane would lead to a further reduction of the aromaticity of the dimer. Moreover, the distortion of the low energy (bent) conformations has a dramatic impact on the QTAIM descriptors. Indeed, the changes in the atomic charges and the delocalisation indices are drastically increased, as reflected by the trends in Δ*Q* and ΔDI values, gathered in Table 6. As it can be seen from the changes in the delocalisation indices in the same chart, the planar isomers lead to a very prominent decrease of the D–H and C–A bond orders while promoting the delocalisation of electrons involved in the D–C and H–A interactions.

**Table 5.** Energies and aromaticity indices for the different isomers of the AZH (DCR) dimers. All values are reported relative to the most stable isomer (bent–cis).


Further information can be obtained through the analysis of the IQA interaction energies, as gathered at the bottom of Table 6. The trends in the *E*int energies reveal that distorting the more stable bent geometry stabilises all the pairwise interactions involved between the terminal atoms participating in the binding. This observation is particularly prominent for the D–C and H–A bonds. The interplay between the exchange-correlation and electrostatic contributions also leads to a moderate stabilisation of the D–H and C–A bonds despite the already mentioned decrease in the DI index. Thus, and in agreement with the aforementioned trends, forcing the planarity of the system further boosts the HB contacts as well as the *π* cloud of electrons through the promotion of the "in-ring" resonant structure. Such an effect is consistent with the enhancement of the anti-aromatic character of the system (top of Figure 7) along with the decrease of the net binding affinities, despite the more favourable hydrogen bonding established between the monomers.

**Table 6.** Change in the QTAIM charges and electron delocalisation indices, in atomic units, upon the formation of the different AZH (DCR) dimers. Some selected changes of IQA interaction energies (in kcal/mol) are reported as well.

