  The local structure of liquid water as a function of temperature is a source
of intense research. This structure is intimately linked to the dynamics of
water molecules, which can be measured using Raman and infrared spectroscopies.
The assignment of spectral peaks depends on whether they are collective modes
or single molecule motions. Vibrational modes in liquids are usually considered
to be associated to the motions of single molecules or small clusters. Using
molecular dynamics simulations we find dispersive optical phonon-like modes in
the librational and OH stretching bands. We argue that on subpicosecond time
scales these modes propagate through water's hydrogen bond network over
distances of up to two nanometers. In the long wavelength limit these optical
modes exhibit longitudinal-transverse splitting, indicating the presence of
coherent long range dipole-dipole interactions, as in ice. Our results indicate
the dynamics of liquid water have more similarities to ice than previously
thought.
