Predict whether He₂⁺ exist?

In MO diagrams, the orbital with less energy that assists in bonding are known as bonding molecular orbitals. They are more stable than individual atomic orbitals as it senses more nuclei.

The orbitals with comparatively higher energy that detract from bonding are known as anti-bonding molecular orbitals. They are less stable with less electron density between the nuclei.

In the case of He₂ molecule, there are a total of 4 electrons two occupying the bonding MO and the other two occupying anti-bonding MO thus canceling the stability gained by the electrons in the bonding MO. Hence, does not exist. On the other hand, in the case of,He₂⁺ two electrons occupying the bonding MO and only one electron occupying the anti-bonding MO thus giving it net stability. Therefore,He₂⁺ exists.