Perturbation Treatment of the Ground State of H2+

Rayleigh—Schrödinger perturbation calculations are carried out for the ground state of the H₂⁺ molecular ion. The zeroth‐order wavefunction for this problem is chosen to be the Guillemin and Zener variational function $$\mathrm{\psi =N[}\exp {\mathrm{(-\alpha r}}_{\mathrm{A}}{\mathrm{-\beta r}}_{\mathrm{B}}\mathrm{)+}\exp {\mathrm{(-\beta r}}_{\mathrm{A}}{\mathrm{-\alpha r}}_{\mathrm{B}}\mathrm{)].}$$ The energies through third order and the expectation value E(1) of the Hamiltonian calculated with the wavefunction accurate through first order are computed for various choices of the parameters. For the optimum choices of both α and β, we obtain for all separations values of E(1) which agree almost perfectly with the accurate series calculations of Bates, Ledsham, and Stewart. Also the values of the wavefunction accurate through the first order agree almost perfectly at most points in configuration space with Bates et al.