Vibrational spectroscopy of HOD in liquid D2O. III. Spectral diffusion, and hydrogen-bonding and rotational dynamics

Time-resolved infrared spectroscopy has the potential to provide unprecedented information about molecular dynamics in liquids. In the case of water, one of the most exciting techniques being developed is transient hole-burning. From experiments on dilute HOD in ${\mathrm{D}}_2\mathrm{O}$ one can obtain the transition frequency time-correlation function for the OH stretch vibration, finding that it decays on a time scale of between 0.5 and 1 ps. In this paper we provide a molecular-level interpretation of this spectral diffusion time-correlation function. First, we verify that for hydrogen-bonded HOD molecules the instantaneous OH frequency is highly correlated with the distance to the (hydrogen-bonded) ${\mathrm{D}}_2\mathrm{O}$ molecule. Second, we show that the instantaneous OH frequency is highly correlated with whether or not the HOD molecule has a hydrogen bond. Finally, we show that the short-time dynamics of the spectral diffusion time-correlation function is due to hydrogen-bond stretching motions, while the longer-time decay observed in the experiments is due to the dynamics of forming and breaking hydrogen bonds. We also present theoretical results that describe recent polarization anisotropy experiments, which measure frequency-dependent rotational dynamics.