  Ice nucleation is a phenomenon that, despite the relevant implications for
life, atmospheric sciences, and technological applications, is far from being
completely understood, especially under extreme thermodynamic conditions. In
this work we present a computational investigation of the homogeneous ice
nucleation at negative pressures. By means of the seeding technique we estimate
the size of the ice critical nucleus Nc for the TIP4P/Ice water model. This is
done along the isotherms 230, 240, and 250 K, from positive to negative
pressures until reaching the liquid-gas kinetic stability limit (where
cavitation cannot be avoided). We find that Nc is nonmonotonic upon
depressurization, reaching a minimum at negative pressures in the doubly
metastable region of water. According to classical nucleation theory we
establish the nucleation rate J and the surface tension gamma, revealing a
retracing behavior of both when the liquid-gas kinetic stability limit is
approached. We also predict a reentrant behavior of the homogeneous nucleation
line. The reentrance of these properties is related to the reentrance of the
coexistence line at negative pressure, revealing new anomalies of water. The
results of this work suggest the possibility of having metastable samples of
liquid water for long times at negative pressure provided that heterogeneous
nucleation is suppressed.
