Vol. 28, issue 12, article # 1

Duchko A. N. Singularities of complex-valued H2O energy function. Estimating resonances in vibrational energy spectrum of H2O. // Optika Atmosfery i Okeana. 2015. V. 28. No. 12. P. 1051–1058. DOI: 10.15372/AOO20151201 [in Russian].
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High order Rayleigh–Schrödinger perturbation theory and Pade–Hermite algebraic approximants are applied to calculate vibration energy levels of H2O. Quadratic Katz branch points found by second-order algebraic approximants are used to classify resonances between vibrational states of the H2O molecule. Apart from Fermi and Darling–Dennison resonances new resonance perturbations of states were found. Moreover, it was shown that all states with energy higher than 5000 cm–1 are in one resonance polyad. This analysis helped us to improve polyad structure of vibrational states of water molecule.


perburbation theory, divergent series, algebraic approximants, vibrational energy levels, H2O molecule


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