Variational perturbation treatment of the hydrogen molecular ion using the Green function method on the united atom

Abstract We calculated the second‐order perturbed energy and the first‐order perturbed wave function of the hydrogen molecular ion by the Green function method based on a united atom with effective nuclear charge, Z . Since the perturbation is given by ( Z / r ) — (1/ r A ) — (1/ r B ), its magnitude depends on the parameter Z . We obtain an analytical expression for the second‐order perturbed energy as a function of Z and the internuclear distance R . We discuss a variety of methods to determine the best values for Z and to derive the potential energy curve and the force constant for H ; these methods vary in the accuracy of their results.