Statistical Theory of the Hydrogen Molecule-Ion

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Abstract
A version of statistical theory is applied to the hydrogen molecule-ion, with good results for the electronic energies of the lowest attractive and repulsive states. For the former, a binding energy of 0.085 a.u. is obtained with an internuclear distance of 2.10 a.u., to be compared with 0.103 and 2.00 a.u. obtained from the exact solution of Schrödinger's equation. The method employed involves the use of hydrogen atomic orbitals, although when the latter refer to unbound states they are approximated by plane waves.