Low-frequency depolarized Raman-spectral density of liquid water from femtosecond optical Kerr-effect measurements:: Lineshape analysis of restricted translational modes

A high-quality depolarized Raman-spectrum is obtained in the frequency range 0 less than or equal to omega less than or equal to 600 cm(-1) by Fouriert-ransformation of time-resolved dual-color heterodyne-detected optical Kerr-effect data of liquid water at 0 C. The time-resolution was sufficient to fully capture the restricted translational and part of the hindered rotational region of the Raman spectrum. This low-temperature spectrum is used to test the applicability of stochastic line broadening theories. A conventional Kubo line shape analysis indicates that restricted translational modes involving hydrogen-bond bending and stretching motions are predominantly in the slow modulation limit at temperatures close to the melting point. However, a pronounced residual ne structure exists which cannot be fully accounted for by the theory in its standard form. Instead, we propose to apply a modified Kubo model based on truncating its continued-fraction representation at a finite order N including a convolution with a quasi-static structural inhomogeneity in the liquid. In particular, a quantitative agreement of our experimental data with such an inhomogeneous N-state random-jump model is interpreted with a discrete size distribution of aggregates which can interconvert on a time scale of about 500 fs by breaking and making of hydrogen bonds.