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.