  Understanding the Raman spectroscopy at the atomistic level is important for
the elucidation of dynamical processes in liquid water. Because the
polarizability (or its time derivative) is often a highly nonlinear function of
coordinates or/and momenta, we employ the linearized semiclassical initial
value representation for quantum dynamical simulations of liquid water (and
heavy water) under ambient conditions based on an ab initio based, flexible,
polarizable model (the POLI2VS force field). It is shown that quantum dynamical
effects play a critical role in reproducing the peaks in the intermediate
region between the librational and bending bands, those between the bending and
stretching bands, and the double-peak in the stretching band in the
experimental isotropic Raman spectrum. In contrast, quantum dynamical effects
are important but less decisive in the anisotropic Raman spectrum. By
selectively freezing either the intramolecular O-H stretching or H-O-H bending
mode, we demonstrate that the peak in the intermediate region (2000-2400 cm-1)
of the isotropic Raman spectrum arises from the interplay of the stretching and
bending motions while a substantial part of the peak in the same intermediate
region of the anisotropic Raman spectrum may be attributed to the combined
motion of the bending and librational modes.
