Calculations of low-lying quartet states of He-2(-) are reported, in which
a positively charged core He-2(+) holds two remote electrons in antibonding
orbitals, i.e, spending most time either side of and away from the central
nodal plane, of similarly large RMS extent. A previously reported 4 Pi(u)
state is reinterpreted and shown to be a Rydberg state. Further, a (4)Phi(u
) state and a (4)Pi(g), the lowest state of this category, are reported. Th
e calculation, performed in prolate spheroidal coordinates, is variational,
utilizing one-electron diatomic-molecule-type orbitals, in full configurat
ion interaction.