Dihydrogen bonds density

In the framework of AIM theory, which well be used extensively to describe dihydrogen bonds, the situation above corresponds to the electron density distribution in the H2 molecule, where the pc parameter takes the very large value 1.857 au and the Laplacian, V pc, is strongly negative ( —34.15 au). These data have been obtained by ab initio calculations at the MP2/6-31G level [4],... 

THE NATURE OF DIHYDROGEN BONDING THE TOPOLOGY OF ELECTRON DENSITY AND CONTRIBUTIONS TO TOTAL BONDING ENERGY... 

Figure 3.17 Electron density at the bond critical point (in an) versus intermolecular distance (in A) obtained for hydrogen-bonded (HB) and dihydrogen-bonded (DHB) complexes. Solid circles and triangles correspond to B3LYP calculations. Open circles and triangles represent MP2 calculations. The solid and dashed lines are fittings to the exponential function for B3LYP and MP2, respectively. (Reproduced with permission from ref. 31.)...

Interactions between two hydrogen atoms separated by a distance of less than 2.4 A can be formulated as dihydrogen bonds if they correspond to criteria based on the topology of the electron density in the H- H directions The pc values should be small, and the V pc values should be small and positive. 

Topology of Electron Density in Dihydrogen-Bonded Systems from Diffraction Data... 

Figure 5.12 Linear relationship between the interaction energy and the electron density at the H- -H bond critical point found for the dihydrogen bonds shown in Structure 5.6. (Reproduced with permission from ref. 16.)...

Figures 5.20 illustrates the equilibrium and transition-state structures obtained for these complexes. As shown, the L1H-H20 complex in equilibrium state 1 shows an intramolecular dihydrogen bond with a very short H- H distance of 1.580 A calculated at the MP2/6-311++G(2d,2p) level. The topological analysis of the electron density on the H- H direction has resulted in the small pc and positive V pc values (0.0388 and 0.0453 an, respectively) typical of dihydrogen bonding. In contrast, no dihydrogen bonding was observed in the LiH-H2S molecule (3), where the corresponding hydrogen atoms are strongly remote.

A topological analysis of the electron density in the framework of AIM theory, performed for the systems in Figure 6.2, has completely confirmed their formulation as dihydrogen-bonded complexes. In accord with the AIM criteria, the pc and V pc parameters at the bond critical points found in the H- - -H directions are typical of dihydrogen bonds 0.042 and 0.057 au for complex LiH HF and 0.046 and 0.048 au for complex NaH- - -HF, respectively. The presence of the bond critical points can be well illustrated by the molecular graph in Figure 6.3, obtained for the HCCH H-Li complex by Grabowski and co-workers [8]. 

For comparison, the authors have probed a complex formed by the same proton-donor molecule and molecular hydrogen. In this very weak complex, HCCH- - (H2), the H- - (H2) distance has been calculated as 2.606 A (i.e., significantly larger than the sum of the van der Waals radii of H). It is extremely interesting that a topological analysis of the electron density also leads to the appearance of the bond critical point in the H- - (H2) direction. However, the Pc and V pc values are very small (0.0033 and 0.0115 au, respectively) compared with those in the HCCH- - -HLi complex (0.0112 and 0.0254 au, respectively). The most important conclusion of this comparison is There is no evident borderline between the dihydrogen-bonded complexes and the van der Waals systems. 

TABLE 6.10. Energy Contributions to the Total Energy of Three Dihydrogen-Bonded Complexes with Methanol and Electronic Density Parameters in the H- -H Directions"... 

NH4-CH4]+ complex in the gas phase [36]. Topological analysis of the electron density performed in the framework of AIM theory shows the bond critical points on the H- H directions with pc values of 0.013 an. It is interesting that the electron density in this complex is larger than that obtained for the BH4 - CH4 dihydrogen-bonded system (pc = 0.007 an), the CH4 molecule of which acts as a proton donor. In accordance with the electronic density, the H- H distances in the BH4 - H4C complex were remarkably longer than 2.4 A (2.797, 2.929,... 

AIM topological analysis of the electron density performed for two complexes and for isolated components is shown in Table 6.15. The bond critical points found in the H H directions are characterized by the small electronic density with Pc = 0.002 and 0.009 au in the CILj- HF and SilLj- HF systems, respectively. The Laplacian, V pc, is also small but takes positive values in accordance with the AIM criteria for dihydrogen bonding. 

CORRELATION RELATIONSHIPS AMONG ENERGETIC, STRUCTURAL, AND ELECTRON DENSITY PARAMETERS OF INTERMOLECULAR DIHYDROGEN-BONDED COMPLEXES... 

As mentioned previously, AIM theory suggests a more accurate formulation of dihydrogen bonding, based on the topology of the electron density analyzed in... 

Figure 8.9 Electron density p at bond critical points found in the H- H directions versus the H- H distance in an H2 molecule and dihydrogen-bonded complexes of Li-H, BeH2, BH3, BH4, LiCCH, and CH4 with various proton-donor components HE, HNF3+, HNH3+, HNC, HCN, HCCSiHs, HCCH, HCCF, HCCCH3, HCCLi, and CH4. The taboo domain between 0.9 and 1.15 A, shown as the rectangle, corresponds to the case when the dihydrogen-bonded complexes are not stable enough to yield a free H2 molecule, or are nonexistent. (Reproduced with permission from ref. 18.)...

Figure 9.7 Contour plot of the electron density for bifurcated S-H- -(H-B)2 dihydrogen bonds. The bond critical points are indicated as squares. (Reproduced with permission from ref. 8.)...

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