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 2 Σ + electron resonances of the H 2 - 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 ) 2 Σ u + and (1sσ g )(2pσ u ) 2 2 Σ g + .