*3.5. Relationship between Dimer Strength and the C*··· *H Distance*

As has been shown in the previous subsections, many of the dimers considered here have some secondary interactions accompanying the leading C··· H-D hydrogen bond. The strength of at least some of them may be considerable. Therefore, one should not expect a good overall (i.e., for all the IR2 ··· HD dimers) correlation between the dissociation energy, *D*0, and the distance C··· H. Moreover, good correlations are also not to be expected even in cases where individual proton-donor molecules are considered. Of course, the exception here is HF, and perhaps HCN, which more often forms linear or nearly linear C··· H hydrogen bonds (Table 1). This is confirmed in Figure 11 (left), where it is shown that the *<sup>R</sup>*<sup>2</sup> (coefficient of determination) values for the linear correlation between *<sup>D</sup>*<sup>0</sup> and *<sup>d</sup>*C···<sup>H</sup> are very poor for NH3 (even with the rejection of the clearly outlier point for I··· NH3), H2O and MeOH (0.217, 0.319, 0.550, respectively) and much better for HCN (0.886) and especially for HF (0.930).

**Figure 11.** The dependence of either the dissociation energy (**left**) or the binding energy according to Equation (1) (**right**) on the distance C··· H in the IR2 ··· HD dimers.

This result clearly shows that in the case of more complex dimers, i.e., having more significant intermolecular contacts, one should not expect a good relationship between the dimer dissociation energy and the length of any single intermolecular contact. Rather, a good correlation can be expected in the case of a clearly local parameter, which is the

binding (interaction) energy determined from Equation (1), and therefore based on the electron density value at the critical point of the C··· H-D hydrogen bond. Indeed, as shown in Figure 11 (right), for HF, MeOH and NH3, the linear correlations between *Eb* and *<sup>d</sup>*C···<sup>H</sup> are very good (*R*<sup>2</sup> > 0.98) and only slightly worse for HCN and H2O (0.968 and 0.962, respectively). Importantly, for all the IR2 ··· HD dimers, an excellent exponential relationship, *Eb* = −755.8 *<sup>e</sup>*−2.38 *<sup>d</sup>*C···<sup>H</sup> , has been found (black curve in Figure 11). This result is not unexpected as a good common exponential relationship between *ρ*bcp and the hydrogen bond length has been found for both different X and Y atoms in the X-H··· Y hydrogen bond [128–131].
