In this paper, the quantum energy levels and the level's splitlings of the first exciting state and the second exciting states generated by OH and HOH stretching vibrations of water molecules and vapour and liquid water have been studied by a new self-trapping dynamical theory and the quantized perturbation theory in weak disperse limit. The results obtained are consistent with experimental data, and are better as compared with that of normal model and the localized model. Thus, this method of self-trapping theory is found to be a good method for calculating quanturn vibrational levels of molecules.
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