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A very weakly bound van der Waals molecule, observed in cold helium expansions. The absence of an ordinary covalent bond in the elementary molecular orbital model must not be confused with absence of every possible bound dimer.^[ref]

Both Be${}_2$'s occupied bonding and antibonding 2s levels cancel in the simplest diagram. Beryllium's relatively accessible empty 2p orbitals allow mixing and correlated configurations to change that cancellation and produce a weak bond. An s-only single-configuration picture is therefore insufficient; spectroscopy and accurate correlated calculations establish its binding.^[ref]

For He${}_2$, $({\sigma }_{1s}{)}^2({\sigma }_{1s}^{\ast }{)}^2$ similarly gives zero elementary covalent bond order, but the empty-shell excitation gap is much larger and there is no comparable low-energy 2s/2p near-degeneracy. Thus it has no ordinary stable covalent bond.

The literal claim that He${}_2$ does not exist needs qualification: an extraordinarily weak, cold van der Waals helium dimer has been observed. That does not contradict the zero covalent-bond-order diagram.^[ref]

The beryllium dimer and helium dimer illustrate two physically different ways that the elementary bond-order picture can miss weak binding.