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I understand that Be2 cannot exist, since it has as many electrons in the antibonding as in the bonding orbitals.

But it seems to me that since the next electron would go into the πu orbital, which is a bonding orbital, Be2- would have a bond order of 0.5, and Be22- would have a bond order of 1, since it would have 4 in bonding (2 in σ and 2 in π)and only 2 in the σ*.

Could Be2- or Be22- at least theoretically be produced? In other words, would the energy released by forming a bond be sufficient to counterbalance the energy needed to stabilize the negative charge gained?

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