Electron resonances of the H₂^- ion

The calculation of resonances according to the definitions of Siegert and of Kapur and Peierls is illustrated for s waves of a single particle in a potential well. A variational principle incorporating outgoing-wave boundary conditions is used. It picks out a resonance from the continuum of unbound states and yields simultaneously both the resonance energy and the decay width.

The variational principle is applied to calculate the two simplest ²Σ⁺ electron resonances of the H₂^- ion, both of which go over into H + H^- for large separations of the nuclei. For small separations they have the electronic configurations (1sσ_g)²(2pσ_u) ²Σ_u⁺ and (1sσ_g)(2pσ_u)^{2 2}Σ_g⁺.