Abstract
Padé summation of large-order perturbation theory can often yield highly accurate energy eigenvalues for molecular vibrations. However, for eigenstates involved in Fermi resonances the convergence of the Padé approximants can be very slow. This is because the energy is a multivalued function of the perturbation parameter while Padé approximants are single valued, and Fermi resonances occur when a branch point lies close to the physical value of the parameter. Algebraic approximants are multivalued generalizations of Padé approximants. Using the (200) state of H2S and the (400) state of H2O as examples of Fermi resonances, it is demonstrated here that algebraic approximants greatly improve the summation convergence.
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