Figure 3. Symmetry-unique key valence functions (and occupation numbers where appropriate) from analysis of the SCGVB(6) description of the D 3h[MgH3Mg]+ cation. Also shown are QTAIM bond paths.
Much the same turns out to be true for the dominant valence functions generated by means of DAFH analysis for the MgMg and HHH domains (see the first two images in the second row of Figure 3). Even the two occupation numbers of 0.19 and 1.79, representing the relative contributions to each Mg−H−Mg bonding unit from the MgMg and HHH domains, respectively, are much the same as in the beryllium systems. Unsurprisingly, the corresponding valence LNOs, DAFH functions and SCGVB orbitals for the D 3h[HeMgH3MgHe]+ cation (see Figure S7 in the Supporting Information) turn out to be difficult to distinguish by eye from those for [MgH3Mg]+. Similarly, except for small changes in occupation numbers, we found that changing the level of theory had negligible effects on the valence LNOs and DAFH functions (see Figures S8 and S9 in the Supporting Information for depictions of the various LNOs).
The QTAIM bond paths for the D 3h[MgH3Mg]+ cation are depicted in the third image in the second row of Figure 3. (As before, the ring and cage critical points have not been displayed.) The pattern is the same as we saw for the D 3h[BeH3Be]+ cation, confirming the similarity between these two systems: there are curved bond paths linking Mg and H atoms, as well as linking H atoms, but there is no MgMg bond path. As can be seen from the third image in the second row of Figure S7 in the Supporting Information, the basic pattern in the central moiety is unchanged upon capping the ‘bare’D 3h[MgH3Mg]+ cation with He atoms. The values of SEDI(Mg,Mg) and of W MgMg for theD 3h[MgH3Mg]+ cation turn out to be just 0.039 and 0.033, respectively, providing further confirmation of the absence of any significant direct metal-metal bonding.
As was the case for the corresponding beryllium systems, there is no evidence in the forms of any of the valence LNOs, DAFH functions or SCGVB orbitals, or in bond indices and QTAIM analysis, for any significant direct MgMg bonding in the D 3h[MgH3Mg]+ and [HeMgH3MgHe]+ cations at their all-electron CCSD(T)/cc‑pVQZ geometries. As before, we conclude that the two positively-charged metal centres are held together with a short MM distance by the three negatively-charged H centres, with a stabilizing contribution from three equivalent sets of highly polar 3c‑2e M−H−M bonding character.
We also briefly examined the ‘mixed’ system, i.e. theC 3v [BeH3Mg]+ cation, for which geometrical parameters and total energies are presented in Tables S2 and S3 in the Supporting Information, respectively. As might have been expected, the resulting valence LNOs, DAFH functions and SCGVB orbitals (see Figures S10 to S13 in the Supporting Information) turn out to be ‘mixed’, closely resembling those for theD 3h[BeH3Be]+ cation on the beryllium side of the 3c‑2e Be−H−Mg bonding units and resembling those for theD 3h[MgH3Mg]+ cation on the magnesium side.
We observe that the BeMg separation in theD 3h[BeH3Mg]+ cation is shorter byca . 0.04 Å than was found for the BeMgO2 ring[11] but, consistent with the situation in the D 3h[BeH3Be]+ and [MgH3Mg]+ cations, we find that there is no BeMg QTAIM bond path (see Figures S10 and S11 in the Supporting Information, but one small difference is that there are also no longer any bond paths linking the H atoms in the ‘mixed’ case). The values of SEDI(Be,Mg) and of W BeMg of just 0.031 and 0.027, respectively, provide further confirmation of the absence of any significant direct metal-metal bonding in theC 3v [BeH3Mg]+ cation, in spite of the short BeMg separation.