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.