  We review recent results of molecular dynamics simulations of two models of
liquid water, the extended simple point charge (SPC/E) and the
Mahoney-Jorgensen transferable intermolecular potential with five points
(TIP5P), which is closer to real water than previously-proposed classical
pairwise additive potentials. Simulations of the TIP5P model for a wide range
of deeply supercooled states, including both positive and negative pressures,
reveal (i) the existence of a non-monotonic ``nose-shaped'' temperature of
maximum density (TMD) line and a non-reentrant spinodal, (ii) the presence of a
low temperature phase transition. The TMD that changes slope from negative to
positive as P decreases and, notably, the point of crossover between the two
behaviors is located at ambient pressure (temperature approx 4 C, and density
approx 1 g/cm^3). Simulations on the dynamics of the SPC/E model reveal (iii)
the dynamics at negative pressure shows a minimum in the diffusion constant $D$
when the density is decreased at constant temperature, complementary to the
known maximum of D at higher pressures, and (iv) the loci of minima of D
relative to the spinodal shows that they are inside the thermodynamically
metastable regions of the phase-diagram. These dynamical results reflect the
initial enhancement and subsequent breakdown of the tetrahedral structure and
of the hydrogen bond network as the density decreases.
