One-Center Perturbation Approach to Molecular Electronic Energies. II. Exact Wavefunctions and Energies for H2+-Like Molecular Puffs

The exact solution is given for the problem of the ground state of one electron moving in the potential field V(r) = —Z/r>, produced by an effective nuclear charge Z uniformly spread over a sphere of radius R, with r> the greater of R and the electron's distance r from the sphere center. The lowest eigenvalue and corresponding eigenfunction are tabulated as functions of R and Z. For the case corresponding to the spherical approximation to H2+ at its equilibrium distance, R = 1, Z = 2, the energy is found to be −1.018502 a.u., in agreement with previous variational calculations of Cohen and Coulson, Howell and Shull, and Houser, Lykos, and Mehler.