Local and normal stretching vibrational states of H₂O

Classical and semiclassical features of the stretching vibrations on a realistic potential energy surface for the water molecule are examined at energies up to the dissociation limit, Ed ≏ 38000 cm-1. The relative importance of normal, local and irregular motions at different energies is assessed in terms of fractional phase areas in an appropriate Poincaré surface of section. Two limits El ≏ 2200 cm-1 and Ec ≏ 30000 cm-1 are identified, marking the onset of local and irregular motions respectively. Below E L all motions are normal, in the range El < E < Ec the total growth in the phase space is attributed largely to local vibrations, and above Ec irregular motions begin to predominate largely at the expense of local trajectories. Some regular motion of the normal type persist above the dissociation limit. This division of the phase space area is in good agreement with the division of phase space volumes as revealed by the disposition of quantum eigenstates. A quantization procedure for the local motions is developed by the construction of an approximate tunnelling path from one classically degenerate local mode to another. Good agreement with the quantum mechanical eigenvalues is obtained. Finally the forms of the quantized local and normal mode trajectories are discussed in relation to the quantum mechanical wavefunctions.