*3.4. The IR*<sup>2</sup> ··· *HD Dimers*

3.4.1. The IR2 ··· HF and IR2 ··· HCN Dimers

Due to the fairly large similarity in the values of the C-H-D angle, i.e., the local geometry of the C··· H-D hydrogen bond, in the HF and HCN dimers, it is convenient to consider these dimers together. The fully optimized structures of the dimers IR2 ··· HF and IR2 ··· HCN are shown in Figure 5 along with the obtained values of dissociation energy, distance C··· H, angle C-H-D and value of the electron density at the bond critical point of the C··· H hydrogen bond.

**Figure 5.** The IR2 ··· HF and IR2 ··· HCN (R = Me, *<sup>i</sup>* Pr, *<sup>t</sup>* Bu, Ph, Mes, Dipp, Ad) dimers. The values of the dissociation energy are given in bold, while the three values refer to the length of the hydrogen bond, the C-H-D angle and the value of the electron density at the bond critical point of the C··· H-D hydrogen bond.

First, let us note that, as with the I··· HF and I··· HCN dimers (Figure 4), the HF dimers are much stronger than their HCN counterparts. The dissociation energies are in the 17.5–19.9 kcal/mol range while the HCN dimer values are only 9.4–11.4 kcal/mol. In the former case, the strongest complex is IDipp2 ··· HF, and the weakest is IPh2 ··· HF, while in the latter, the strongest complex is also the one involving IDipp2, but the weakest dimer is formed by IMe2 instead. Much greater strength of hydrogen bonds C··· H in IR2 ··· HF dimers than IR2 ··· HCN is also visible in much smaller distances H··· C (1.599–1.632 Å vs 2.055–2.105 Å), much higher values of *ρ*bcp (0.073–0.079 a.u. vs 0.027–0.030 a.u.), much greater extensions of the H-D bond (0.075–0.088 Å vs 0.031–0.040 Å) and much higher values of the *<sup>ν</sup>*HD stretching vibration frequency red-shift (from −1591 up to −1814 cm−<sup>1</sup> vs. from −462 up to −548 cm<sup>−</sup>1). It is worth noting that although the dimers involving Ad (i.e., IAd2 ··· HF and IAd2 ··· HCN) are not the strongest (although the difference compared to their counterparts involving Dipp is small, especially in the case of the HCN dimer), the effect of extending the proton-donor bond and red-shift values are in these systems greatest. Therefore, it can be concluded that together with IDipp2, IAd2 also forms strong C··· H hydrogen bonds, which have the greatest impact on the characteristics of HF and HCN proton-donor molecules. It is also worth noting that for both HF and HCN, the dissociation energies obtained for the dimers shown in Figure 5 are clearly greater than the energies obtained for I··· HF and I··· HCN (16.1 and 8.6 kcal/mol, respectively, as shown in Table 1 and Figure 4), and thus the substitution of hydrogen atoms in both N-H bonds in imidazol-2-ylidene even by methyl groups increases the strength of the dimer. This can most likely be explained by the weak inductive effect of these groups, which increases the charge on lone electron pairs.

It may be asked why the systems with IDipp2 and IAd2 are characterized by the highest values of dissociation energies (of course also the shortest H··· C distances and the highest *ρ*bcp, Δ*d*HD and red-shift values). Very often, the increase in dimer strength is due to the presence of additional competing interactions, the presence of which is often suggested by the significant non-linearity of the dominant hydrogen bond, as was the case with the dimers I··· H2O, I··· MeOH and I··· NH3 shown in Figure 4 and discussed earlier. However, the reference to the C-H-D angle value can be very deceptive because these values for both IDipp2 and IAd2 are exactly 180◦, so the C··· H-D hydrogen bonds in the dimers of these carbenes with HF and HCN are linear. What is more, interestingly, carbenes IPh2, and especially IMes2, are characterized by a distinct nonlinearity of C··· H-D hydrogen bonds. In these cases, the non-linearity may indeed result from the presence of other competing interactions which affect the alignment of the proton-donor molecule and thus also the geometry of the C··· H-D hydrogen bond.

In order to search for such competitive interactions, the determination of a molecular graph defined by QTAIM [110–112] may be a particularly helpful tool. Figure 6 presents molecular graphs of several selected IR2 ··· HF and IR2 ··· HCN dimers.

As can be clearly seen, in each of the examples, the molecular graph shows the presence of accompanying interatomic interactions, which are indicated by color-coded arrows. IPh2 ··· HF is a simple example in which the molecular graph suggests the presence of two accompanying C-H··· F type hydrogen bonds. A similar situation occurs in the slightly larger IMes2 ··· HF, where the proton-donating C-H bond is derived from one of the methyl groups in the mesityl group. Both these bonds should be very weak, which is suggested by low electron density values (ca. 0.008 a.u.). Using Equation (1) gives the value of −1.0 kcal/mol. In contrast, in the IMes2 ··· HCN dimer, a similar pair of bond paths indicates the presence of CH··· C-type hydrogen bonds, which should be even weaker (*ρ*bcp amounts to ca. 0.0034 a.u. only, and therefore, the bonding effect is negligible) than C-H··· F. The IAd2 ··· HF dimer is a very simple example of a system featuring a C··· F tetrel bonding pair. This time the binding energy value is significant (ca. −1.4 kcal/mol), suggesting that the pair of these interactions may contribute significantly to the overall binding effect of the dimer.

The presence of 2,6-diisopropylphenyl (Dipp) substituent allows a particularly large number of accompanying interactions [80]. Apart from pairs of hydrogen bonds of the type C··· H-F (or C··· H-C in IDipp2 ··· HCN), both these dimers, i.e., IDipp2 ··· HF and IDipp2 ··· HCN, experience the presence of bond paths between the hydrogen atom of a C-H bond and the carbene carbon atom. Therefore, this result suggests that apart from the dominant C··· H-D hydrogen bond (D = F or C), the carbene carbon atom engages in two additional C··· H-C hydrogen bonds, which, however, should be very weak (ca. −0.9 and −1.1 kcal/mol in IDipp2 ··· HF and IDipp2 ··· HCN, respectively). In the case of IDipp2 ··· HCN, the molecular graph also suggests the presence of a pair of *intra*molecular hydrogen bonds of the C-H··· N type, as nitrogen atoms belong to the imidazol-2-ylidene ring. Since the values of *ρ*bcp are significant (ca. 0.016 a.u.), the use of Equation (1) yields the value of ca. −2.8 kcal/mol. Apart from the aforementioned accompanying hydrogen bonds, the molecular graphs of dimers IDipp2 ··· HF and IDipp2 ··· HCN also show the presence of numerous C-H··· H-C interactions, which, however, seems to be a fairly common feature in the case of crowded systems with many C-H bonds [80,125–127].

**Figure 6.** Molecular graphs of selected IR2 ··· HF and IR2 ··· HCN dimers. Arrows show the presence of bond paths for some accompanying interatomic interactions (hydrogen bonds—red, tetrel bonds brown, and C-H··· H-C contacts—yellow). Large balls represent atoms (hydrogen—white, carbon gray, nitrogen—blue, and fluorine—light green) and small balls represent critical points (bond critical points—light green, ring critical points—red, and cage critical points—blue).

As shown (Figure 6), molecular graphs suggest the presence of many different interactions, including intermolecular ones. Their role in the overall binding of the system and their influence on the overall structure is not easy to quantify, although there are many descriptors for individual, i.e., local, interactions [116]. One such descriptor is the electron density value determined at the bond critical point of a given interaction, which, as already mentioned, best correlates with the binding energy [116]. In the case of IR2 ··· HF and IR2 ··· HCN dimers, the estimates based on Equation (1) show that these interactions should be much weaker than the dominant C··· H-D hydrogen bond. Nevertheless, also taking into account their large number, it is highly likely that their presence can influence the overall structure of the dimer. In particular, their presence can significantly influence the angle values as they are generally associated with small force constants.
