  Water is an ubiquitous liquid that has several exotic and anomalous
properties. Despite its apparent simple chemical formula, its capability of
forming a dynamic network of hydrogen bonds leads to a rich variety of physics.
Here we study the vibrations of water using molecular dynamics simulations,
mainly concentrating on the Raman and infrared spectroscopic signatures. We
investigate the consequences of the temperature on the vibrational frequencies,
and we enter the details of the hydrogen bonding coordination by using
restrained simulations in order to gain quantitative insight on the dependence
of the frequencies on the neighbouring molecules. Further we consider the
differences due to the different methods of solving the electronic structure to
evaluate the forces on the ions, and report results on the angular
correlations, isotopic mixtures HOD in H$_2$O/D$_2$O and and the dielectric
constants in water.
