Large-order dimensional perturbation theory for diatomic molecules within the Born-Oppenheimer approximation
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 Req, 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 Req. 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 Padé-Borel approximants with modifications that explicitly model known singularity structure.