*3.3. Imidazol-2-Ylidene Complexes*

Compared to all other molecules, imidazol-2-ylidene is distinguished by the presence of highly polar N-H bonds (Figure 3), which are good proton donors and therefore can eagerly form hydrogen bonds as long as there is an atom with good proton-acceptor properties, such as O, N or a halogen atom, in their presence.

**Figure 3.** Map of the electrostatic potential (in a.u.) of imidazol-2-ylidene: −0.06, red; −0.03, yellow; 0.00, green; 0.03, cyan; 0.06, blue.

The stable dimers between imidazol-2-ylidene and HF, HCN, H2O, MeOH or NH3 are shown in Figure 4.

In the case of HF and HCN, the obtained hydrogen bonds are linear, the former of which is very strong, which is expressed by a large value of the determined dissociation (16.1 kcal/mol) and binding (−13.7 kcal/mol) energies, a short distance C··· H (1.676 Å) and a fairly high value of the electron density determined at the critical point (*ρ*bcp) of this bond (0.065 a.u.). In addition, the formation of the C··· H-F hydrogen bond leads to a significant elongation of the H-F bond (+0.061 Å) and a very large red-shift of its stretching vibration frequency (−1317 cm−1). On the other hand, the interaction in the I··· HCN dimer is almost half as weak (8.6 kcal/mol), which is also related to the much longer C··· H distance (2.138 Å) and the much lower *ρ*BCP value (0.025 a.u.). The elongation of the C-H bond in HCN and the red-shift of its stretching vibration frequency are only +0.029 Å and −397 cm<sup>−</sup>1, respectively.

**Figure 4.** Imidazol-2-ylidene dimers with HF, HCN, NH3, H2O and MeOH. The values of the dissociation energy are given in bold, while the three values next to the interaction shown refer to the length of the hydrogen bond, its angle and the value of the electron density at the bond critical point.

As can be seen in Figure 4, unlike I··· HF and I··· HCN, in the remaining systems, i.e., I··· NH3, I··· H2O and I··· MeOH, the C··· H-D hydrogen bond is not linear due to the presence of another hydrogen bond. The presence of this accompanying hydrogen bond results not only from the presence of a strongly polar N-H bond in the imidazol-2-ylidene molecule, but above all from the presence of the D atom having an easily accessible lone electron pair. This possibility leads to the formation of the N-H··· O hydrogen bond in the dimers I··· H2O and I··· MeOH and N-H··· N in the I··· NH3 dimer. Importantly, this situation, i.e., the simultaneous presence of two strong hydrogen bonds, means that the determined values of the dissociation energy do not represent strengths of the C··· HD hydrogen bonds only, because, as representing intermolecular interactions globally, they should rather be assigned to both the hydrogen bonds, i.e., C··· H-D and the accompanying one. Moreover, it is not easy to extract energy values for individual bonds. Nevertheless, as already mentioned in the Theoretical Methods section, Emamian et al. [116] have recently shown that among many wave function-based HB descriptors (including those based on QTAIM), the electron density determined at the bond critical point of HB best correlates with the binding (in fact, interaction) energy of this HB, giving Equation (1). As a result, they proposed using this equation for a quick estimate of the energy of hydrogen bonds forming networks [116]. Using this proposal, in the case of the I··· NH3 dimer, the value is −4.6 kcal/mol for the N-H··· N hydrogen bond and only −1.7 kcal/mol for C··· H-N. Thus, the N-H··· N bond is definitely stronger than N-H··· C, which is also expressed in a definitely shorter distance H··· N (2.066 Å) than H··· C (2.521 Å). However, in the case of I··· H2O and I··· MeOH dimers, the O-H··· C bond is definitely stronger (−5.3 and −5.5 kcal/mol, respectively) than the accompanying N-H··· O bond (−1.9 and −2.4 kcal/mol, respectively). This is also reflected in shorter C··· H distance (2.035 Å) than H··· O (2.319 and 2.313 Å, respectively).

The dimers I··· NH3, I··· H2O and I··· MeOH are good simple examples clearly showing that imidazol-2-ylidene willingly forms accompanying hydrogen bonds by the strongly polar N-H bond. The formation of such bonds is particularly easy when the D atom has lone electron pairs readily available, as is the case, for example, of N and O atoms. The formation of these bonds is prevented after replacing the H atoms in both N-H bonds with non-polar R substituents. However, in addition to the frequently mentioned steric effects, this type of modification of the imidazol-2-ylidene molecule may lead to other accompanying secondary interactions, which is discussed in the other subsections.
