Excited stretching vibrations of water: the quantum mechanical picture

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Abstract
Quantum mechanical eigenvalues derived from a Morse oscillator basis are reported for stretching vibrational states of H2O with total quantum numbers ν = ν1 + ν3 = 0–8, on the Sorbie-Murrell potential. Spectroscopic absorption intensities for all interstate transitions were calculated in a bond dipole model. The dominant feature of the eigenvalue spectrum is a pattern of local mode doublets, such that linear combinations of the component wavefunctions for doublets with splittings less than 10 cm-1 are localized in the bond directions. The timescales for intramolecular energy transfer derived from these splittings increase along the most strongly localized progression from 0·5 ps at ν = 1 to 30 ns at ν = 8. This most localized progression is substantially the most strongly coupled in absorption to the ground state. The strongest transitions in general are subject to a bond excitation rather than a normal coordinate excitation selection rule Δn = ± 1. The relative intensities of particular pairs of transitions, one of which is allowed and the other forbidden by normal coordinate selection rules, gives a third measure of the localization in different doublets which is well correlated with the local mode splitting and the qualitative localization of the wave-function.