  One of the most promising frameworks for understanding the anomalies of cold
and especially supercooled water is that of two-structure thermodynamics, in
which water is viewed as a non-ideal mixture of two interconvertible local
structures. The non-ideality of this mixture may give rise, at very low
temperatures, to a liquid-liquid phase transition (LLPT) and a liquid-liquid
critical point (LLCP), at which thermodynamic response functions diverge.
Various versions of the "two-structure equation of state" (TSEOS) based on this
concept have shown remarkable agreement with both experimental data in real
water and simulation results. However, recent experiments probing supercooled
water at negative pressures reveal the inadequacy of extrapolations of
equations of state developed for positive pressures, and have begun to shed
additional light on the source of the anomalies of supercooled water. We have
analyzed simulation results for the TIP4P/2005 model over a broad range of
positive and negative pressures from ambient temperature to deep supercooling.
We find that by explicitly incorporating a liquid-vapor spinodal into a
two-structure equation of state, we are able to match the simulation data in
TIP4P/2005 with striking accuracy. In particular, our equation of state
reproduces the observed lines of minima and maxima in the density, isothermal
compressibility, and isobaric heat capacity. Contrary to scenarios in which a
retracing spinodal accounts for the thermodynamic anomalies of water, we find
that the liquid-vapor spinodal in this model continues monotonically to lower
pressures as temperature is decreased, influencing but not giving rise to the
locus of density maxima and other thermodynamic anomalies. We explain the
behavior of TIP4P/2005 in terms of two phenomena: the competition between two
local structures and a monotonic liquid-vapor spinodal.
