  We present molecular dynamics simulations of the SPC/E model of water to
probe the dynamic properties at temperatures from 350 K down to 190 K and
pressures from 2.5GPa (25kbar) down to -300MPa (-3kbar). We compare our results
with those obtained experimentally, both of which show a diffusivity maximum as
a function of pressure. We find that our simulation results are consistent with
the predictions of the mode-coupling theory (MCT) for the dynamics of weakly
supercooled liquids -- strongly supporting the hypothesis that the apparent
divergences of {\it dynamic} properties observed experimentally may be
independent of a possible thermodynamic singularity at low temperature. The
dramatic change in water's dynamic and structural properties as a function of
pressure allows us to confirm the predictions of MCT over a much broader range
of the von Schweidler exponent values than has been studied for simple atomic
liquids. We also show how structural changes are reflected in the wave-vector
dependence of dynamic properties of the liquid along a path of nearly constant
diffusivity. For temperatures below the crossover temperature of MCT (where the
predictions of MCT are expected to fail), we find tentative evidence for a
crossover of the temperature dependence of the diffusivity from power-law to
Arrhenius behavior, with an activation energy typical of a strong liquid.
