Vibrational spectroscopy of HOD in liquid D2O. II. Infrared line shapes and vibrational Stokes shift

We present semiclassical calculations of the infrared line shapes for the three intramolecular vibrations of dilute HOD in liquid ${\mathrm{D}}_2\mathrm{O}.$ In these calculations the vibrations of HOD are treated quantum mechanically, and the rotations and translations of all the molecules are treated classically. The approach and model, which is based on earlier work of Oxtoby and of Rey and Hynes, was discussed in detail in Paper I, on vibrational energy relaxation in the same system, of this series. A novel feature of our approach is a self-consistent renormalization scheme for determining the system and bath Hamiltonians for a given vibrational state of the HOD molecule. Our results for the line shapes are in reasonable agreement with experiment. We also explore the extent to which the frequency fluctuations leading to the line shape are Gaussian. Finally, we calculate the vibrational Stokes shift for the OH stretch fundamental. Our result, which is nonzero only because the specification of the bath Hamiltonian depends on the vibrational state of the HOD molecule (as a result of the self-consistent renormalization scheme), is 57 cm⁻¹, in good agreement with the experimental number of 70 cm⁻¹.