  We present the results of molecular dynamics simulations of the extended
simple point charge (SPC/E) model of water to investigate thethermodynamic and
dynamic properties of stretched and supercooled water. We locate the liquid-gas
spinodal, and confirm that the spinodal pressure increases monotonically with
$T$, supporting thermodynamic scenarios for the phase behavior of supercooled
water involving a ``non-reentrant'' spinodal. The dynamics at negative pressure
show 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. We locate the loci of minima of $D$ relative to the spinodal,
showing that the locus is inside the thermodynamicaly 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.
