Nuclear quantum effects lead to an anomalous shift of the volume of hexagonal
ice; heavy ice has a larger volume than light ice. This anomaly in ice
increases with temperature and persists in liquid water up to the boiling
point. We study nuclear quantum effects on the density and compressibility of
several ice-like structures and crystalline ice phases. By calculating the
anisotropic contributions to the stain tensor, we analyze how the
compressibility changes along different directions in hexagonal ice, and find
that hexagonal ice is softer along the x-y plane than the z-direction.
Furthermore, by performing ab initio density functional theory calculations
with a van der Waals functional and with the quasiharmonic approximation, we
find an anomalous isotope effect in the bulk modulus of hexagonal ice: heavy
ice has a smaller bulk modulus than light ice. In agreement with the
experiments, we also obtain an anomalous isotope effect for clathrate hydrate
structure I. For the rest of the ice polymorphs, the isotope effect is: i)
anomalous for ice IX, Ih, Ic, clathrate, and low density liquid-like amorphous
ice; ii) normal at T=0 K and becomes anomalous with increasing temperature for
ice IX, II, high density liquid-like amorphous ices, and ice XV; iii) normal
for ice VIII up to the melting point. There is a transition from an anomalous
isotope effect to a normal isotope effect for both the volume and bulk modulus,
as the density (compressibility) of the structures increases (decreases). This
result can explain the anomalous isotope effect in liquid water: as the
compressibility decreases from melting point to the compressibility minimum
temperature, the difference between the volumes of the heavy and light water
rapidly decreases, but the effect stays anomalous up to the boiling temperature
as the hydrogen bond network is never completely broken by fully filling all
the interstitial sites.Comment: 17 pages, 15 figure
