Beryllium systems
We start by considering the nature of the SCGVB(6) descriptions of the
bonding in the D 3h[MH3M]+ cation. Although these
calculations were carried out without imposing any symmetry relations
amongst the active orbitals, we found in each case that the converged
solution features two sets of three symmetry-related orbitals, with each
‘pair’ being primarily associated with a particular Be−H−Be linkage.
Symmetry-unique active orbitals \(\phi_{1}\) and \(\phi_{2}\) forD 3h[BeH3Be]+ are depicted as the
first two images in the top row of Figure 2. The remaining active
orbitals for this cation are related to these two by successive\({\hat{C}}_{3}\) rotations around the principal axis. Whereas SCGVB
orbital \(\phi_{1}\) has distinct three-centre BeHBe character, orbital\(\phi_{2}\) is somewhat more localized on the H atom. The orbital
overlap \(\left\langle\phi_{1}\middle|\phi_{2}\right\rangle\) is
0.846 and we find that the perfect-pairing mode of spin coupling
dominates the total active space spin function \(\Theta_{0,0}^{6}\),
with a weight of 98.3% in the Kotani basis, so that the spins
associated with \(\phi_{1}\) and \(\phi_{2}\) are predominantly coupled
to a singlet. All of this means that the SCGVB(6) description of theD 3h[BeH3Be]+ cation corresponds
primarily to three equivalent highly polar three‑centre two‑electron
(3c‑2e) M−H−M bonding units, each reminiscent of those in diborane.
As can be seen from Figures S2 and S3 in the Supporting Information, the
corresponding SCGVB(6) orbitals for theD 3h[NgBeH3BeNg]+ cations
(Ng = He, Ne) are rather difficult to distinguish by eye from those for
the ‘bare’ system; taken together with the dominance of the
perfect-pairing mode of spin coupling, the SCGVB(6) descriptions for
each of the ‘capped’ systems again corresponds primarily to three
equivalent highly polar 3c‑2e Be−H−Be bonding units.