**1. Introduction**

In carbenes [1–80], the carbon atom is *sp*2-hybridized. However, unlike the vast majority of organic compounds, in carbenes, it is merely divalent, consequently forming only one (R=C) or at most two (R1R2C) covalent bonds. Thus, two valence electrons remain available, giving the possibility of two spin states, singlet or triplet [5,6,8,70]. In the spin singlet state, both electrons are paired to form a lone electron pair. Additionally, the carbene carbon atom has an unfilled *p*-orbital perpendicular to the *sp*<sup>2</sup> hybrids. While the triplet state is also possible in some carbenes, a number of factors are known to increase singlet stability. The close presence of a strongly electronegative atom, such as, e.g., N, is important here, which stabilizes the singlet state through both the inductive *σ*-electron withdrawing effect and the *π*-electron charge donation from the lone electron pair of this atom to the vacant *p*-orbital of the carbene carbon atom [5,6,8,18,70]. In the case of cyclic carbenes, another factor stabilizing the singlet state is the *π*-electron delocalization within the entire ring, which may be related to its aromaticity, as is the case, for example, in the imidazol-2 ylidene molecule [38]. Another factor that stabilizes the singlet state of a carbene is a low

**Citation:** Jabło ´nski, M. On the Coexistence of the Carbene··· H-D Hydrogen Bond and Other Accompanying Interactions in Forty Dimers of N-Heterocyclic-Carbenes (I, IMe2, I*<sup>i</sup>* Pr2, I*<sup>t</sup>* Bu2, IMes2, IDipp2, IAd2; I = imidazol-2-ylidene) and Some Fundamental Proton Donors (HF, HCN, H2O, MeOH, NH3). *Molecules* **2022**, *27*, 5712. https:// doi.org/10.3390/molecules27175712

Academic Editor: Antonio Caballero

Received: 26 July 2022 Accepted: 29 August 2022 Published: 5 September 2022

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value of the R1–C–R2 angle [3–5]. Naturally, this condition is obviously present in cyclic carbenes. While all of the conditions mentioned so far exist in imidazol-2-ylidene, they need not necessarily occur simultaneously in other N-heterocyclic carbenes (NHCs) [61]. In their case, an important stabilizing factor is the size of the substituents attached to both nitrogen atoms, as larger substituents prevent carbene dimerization [1].

The presence of a lone electron pair on the carbene carbon atom makes carbenes good Lewis bases, showing strongly nucleophilic properties. Carbenes are mainly known for their association with transition metal atoms (see, e.g., refs. [11,30,31,36,55,63]), making them extremely useful compounds in organic, organometallic and materials chemistry as well as homogeneous catalysis [21,30,33,57,61,62,69]. In addition to bonds with metals, however, carbenes quite willingly also form other intermolecular connections, such as hydrogen bonds [9,10,16,19,38,51,56,58], lithium bonds [39,45,46,62,69], beryllium bonds [17,53,54,62,69,73,79], magnesium bonds [14,22,40,41,62,69,73,79], triel bonds [13,20,23,27,69], tetrel bonds [42,65,66,69], pnictogen bonds [47,48,50,69], chalcogen bonds [52,69], halogen bonds [12,15,43,59,69] (in particular to iodine [12,15]), and aerogen bonds [67]. Moreover, in addition to these possibilities resulting from the presence of a lone electron pair, the presence of an empty *p* orbital in singlet carbenes also gives them electrophilic properties that seem to be much less studied [7,24,29,68,71,74,75].

Considering the fundamental role of hydrogen bonds [81–96], it is somewhat surprising that hydrogen bonds involving carbenes are studied only very sporadically [9,10,16,19,38,51,56,58]. Obviously, due to considerable methodological limitations, the first theoretical reports (in 1983 by Pople et al. [9] and then in 1986 by Pople [10]) concerned a simple H2C··· HF dimer. Then, in 1996, Alkorta and Elguero investigated dimers between H2C or F2C and a few simple proton donors [19]. More recently, Jabło ´nski and Palusiak studied hydrogen bonds between carbenes CF2, CCl2 and imidazol-2-ylidene and such proton donors as H2O and HCF3 [38]. In a wonderful extensive work on the application of theoretical methods in the study of carbene chemistry, Gerbig and Ley [56] also mentioned the imidazol-2-ylidene··· HCF3 dimer in which there is C··· H-C hydrogen bonding and the accompanying N-H··· F (both described earlier in ref. [38]). Samanta et al. [58] showed the possibility of the formation of either C··· H-N or C··· H-O hydrogen bonds between the simple heterocyclic derivative of 1,3-di(methyl)imidazol-2-ylidene (IMe2) and MeNH2 or, in particular, MeOH, respectively. In the latter case, the NHC acts as an esterification catalyst activating the alcohol molecule. On the other hand, from the experimental point of view, hydrogen bonding with carbene was first announced by Arduengo et al. [16] in 1995 with the report essentially relating to the C–H–C bridge in a bis(carbene)–proton complex formed by 1,3-di(2,4,6-trimethylphenyl)-imidazol-2-ylidene (IMes2). Much later, in 2011, it was shown that IMes2 and 1,3-di(2,6-diisopropylphenyl)imidazolidin-2-ylidene (SI*<sup>i</sup>* Pr2) can form a C··· H-O type hydrogen bond to 1-hydroxy-2,2,6,6-tetramethyl-piperidine (TEMPO-H) [51]. In addition to crystallographic and NMR studies, results of theoretical calculations were also reported.

As shown above, the theoretical studies for hydrogen bonding involving carbenes have generally been down to very small carbenes, at most imidazol-2-ylidene (I) or 1,3 di(methyl)imidazol-2-ylidene (IMe2). However, there are no theoretical studies in which the imidazol-2-ylidene derivative would contain even larger substituents on both nitrogen atoms. Moreover, the influence of the presence of these substituents on the possible interactions accompanying the leading C··· H-D hydrogen bond has not been investigated yet. This article aims to fill this gap. Namely, this article examines the hydrogen bonds between imidazol-2-ylidene (I) and its seven popular derivatives containing gradually more bulky substituents (methyl = Me, *iso*-propyl = *<sup>i</sup>* Pr, *tert*-butyl = *<sup>t</sup>* Bu, phenyl = Ph, mesityl = Mes, 2,6-diisopropylphenyl = Dipp, 1-adamantyl = Ad) on both nitrogen atoms and five fundamental proton donor molecules (HF, HCN, H2O, MeOH, NH3). The possible combinations form forty dimers, which can be briefly designated as IR2 ··· HD, where R is one of the substituents mentioned previously. The general scheme of the dimers in question is shown in Figure 1.

**Figure 1.** General scheme of the IR2 ··· HD dimers (R = H, Me, *<sup>i</sup>* Pr,*<sup>t</sup>* Bu, Ph, Mes, Dipp, Ad). The colon on the carbene carbon atom represents a lone electron pair.

It should be emphasized that the C··· H-D hydrogen bonds studied here engage the carbene species in their singlet spin states and thus a lone electron pair on the carbene carbon atom (Figure 1) and are therefore considerably distant from hydrogen bonds involving radicals [97,98]. In addition to the description of C··· HD hydrogen bonds, an equally important goal is to analyze the possibility of the emergence of various types of accompanying interactions and their impact on the structure of the obtained dimers. This concerns the important issue of the coexistence of various types of interactions in molecular systems. Recently, the author of the present paper has shown [80] that various types of secondary interactions have a significant effect on the mutual orientation of the ZnX2 molecular plane relative to the imidazol-2-ylidene ring in various types of IR2 carbenes. This result is important because the possible torsion of the planes is usually attributed to the steric effects resulting from the presence of bulky R substituents.
