Calculation of vibrational energy levels of water molecule by summing divergent perturbation theory series

The Rayleigh-Schrödinger perturbation theory is applied to a calculation of vibrational energy levels of the H₂O molecule for isolated states and the states involved in the anharmonic Fermi and Darling-Dennison resonances. It is shown that in spite of the rapid divergence of the perturbation theory series caused by the resonances, the use of the summation methods of Padé, Padé-Borel, and Padé-Hermite and the moments method allows one to obtain quite satisfactory results.