  Water is a complex structured liquid of hydrogen-bonded molecules that
displays a surprising array of unusual properties, also known as water
anomalies, the most famous being the density maximum at about $4^\circ$C. The
origin of these anomalies is still a matter of debate, and so far a
quantitative description of water's phase behavior starting from the molecular
arrangements is still missing. Here we provide a simple physical description
from microscopic data obtained through computer simulations. We introduce a
novel structural order parameter, which quantifies the degree of translational
order of the second shell, and show that this parameter alone, which measures
the amount of locally favored structures, accurately characterizes the state of
water. A two-state modeling of these microscopic structures is used to describe
the behavior of liquid water over a wide region of the phase diagram, correctly
identifying the density and compressibility anomalies, and being compatible
with the existence of a second critical point in the deeply supercooled region.
Furthermore, we reveal that locally favored structures in water not only have
translational order in the second shell, but also contain five-membered rings
of hydrogen-bonded molecules. This suggests their mixed character: the former
helps crystallization, whereas the latter causes frustration against
crystallization.
