Insights from domain-averaged Fermi hole (DAFH) analysis and multicenter bond indices into the nature of Be(0) bonding

The nature of the bonding interactions in the recently synthesized first stable neutral complex of so-called zero-valent beryllium (i.e. formally Be(0)) is investigated using the analysis of domain-averaged Fermi holes (DAFHs) and of multicenter bond indices. It is shown that both of these types of analysis, which have previously proved useful for various molecules with nontrivial bonding patterns, basically corroborate the appealing model suggested in the original study to explain the stability of the complex (except for a more realistic specification of the actual valence state of the Be atom). Nevertheless, as well as confirming the anticipated dominance of three-center two-electron pi bonding in the central C-Be-C fragment, reinforced by the existence of two donor-acceptor Be-C sigma bonds, a more detailed scrutiny of the multicenter bond indices also reveals somewhat unexpected features which suggest also the existence of delocalized 3c-4e sigma bonding in the C-Be-C skeleton.