A three-parameter wave function for the hydrogen molecule ion

In minimizing the electronic energy of the ground state of the hydrogen molecule ion H 2 + with respect to the parameters p , α and β in the elaborated Guillemin-Zener wave function ψ = (1 + pR ξ) exp(-α R ξ) cosh(β R η) we have located two minima, corresponding to p > 0 and p < 0. We confirm Bhalla and Khubchandani's calculations for p < 0, but find that better results are obtained when p > 0 (the energy being then as low as that corresponding to the most successful variational wave function published up to now). We also report calculations in which the flexibility of the variation process is restricted so that the `local' energy Hψψ is finite at the nuclei.