Abstract
A renormalization of the $D$-dimensional Hamiltonian is developed to ensure that the large-$D$ limit corresponds to a single well at any value of the internuclear distance $R.$ This avoids convergence problems caused by a symmetry-breaking transition that is otherwise expected to occur when $R$ is approximately equal to the equilibrium bond distance ${R}_{\mathrm{eq}},$ with larger $R$ giving a double well. This symmetry breaking has restricted the applicability of large-order perturbation theory in $1/D$ to cases where $R$ is significantly less than ${R}_{\mathrm{eq}}.$ The renormalization greatly extends the range of $R$ for which the large-order expansion can be summed. A numerical demonstration is presented for H${}_{2}^{+}.$ The $1/D$ expansions are summed using Pad\'e-Borel approximants with modifications that explicitly model known singularity structure.
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