It was shown by Baber and Hassé(1) that the Schrödinger equation for the single electron in H+2 with fixed nuclei is separable in spheroidal coordinates. The separated equations were integrated by Bates, Ledsham and Stewart (2) and their solutions may be regarded as exact. However, several attempts have been made to derive approximate solutions for this, which is the simplest of all molecular problems, generally with the hope that it might be possible to extend the analysis to larger diatomic systems. Recently a single-centre expansion has been much favoured, since it avoids the difficult two-centre integrals; but unfortunately this advantage has been offset by the fact that the rate of convergence for the lowest states has been rather slow since the deviations of diatomic H+2 from the united-atom H+e are serious. But successful approximations to some excited states suggest that a single-centre approach may still be useful, provided that the trial functions are suitably chosen.