Calculation of vibrational energy levels of triatomic molecules with the C 2v and C s symmetries by summing divergent series of the Rayleigh-Schrödinger perturbation theory

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The Rayleigh-Schrodinger perturbation theory is applied to calculation of vibrational energy levels of triatomic molecules with the C2v and Cs symmetries: SO2, H2S, F2O, HOF, HOCl, and DOCl. Particular attention is given to the states coupled by anharmonic resonances; for such states, the perturbation theory series diverge. To sum these series, the known methods of Pade, Pade-Borel, and Pade-Hermite and the method of power moments are used. For low-lying levels, all the summation methods give satisfactory results, while the method of quadratic Pade-Hermite approximants appears to be more efficient for high-excited states. Using these approximants, the structure of singularities of the vibrational energy, as a function in the complex plane, is studied.