Express the bond order as an integer or fraction.
Use simple LCAO (linear combination of atomic orbitals) MO theory. Li(0) 2s^1 Overlap of the two 2s AOs results in a
σ bonding MO that is lower in energy than the constituent 2s AOs and an antibonding σ* MO that is at a higher energy than the 2s AOs. Each MO can hold two e⁻s and hence for Li2 the MO scheme is σ(↑↓) σ*(0) Li2 is present the extent of ~1% in Li(g). Removal of one e⁻ from Li2 to give Li2+ results in an MO scheme of σ(↑)σ*(0)
Bond Order = ½[Σ (bonding e⁻) – Σ (antibonding e⁻)] = ½[(σ(1e⁻)] = 0.5. It is bound and should be observed in the gas phase.
Likewise Li2^- has an MO scheme of σ(↑↓) σ*(↑) and also a bond order of 0.5 and again should be observed in the gas phase. For reasons I won’t go into Li2^- should be less stable than Li2^+.
Mo Energy Diagram