Chemistry Reference
In-Depth Information
18
37
(a)
(b)
16
2
2
48
20
20
18
1
15
1
Figure 16.
(a) An H-bond isomer of a 16-water unit cell of ice VII measuring two primitive unit
cells on each side. Bonds representative of the three second-order graph invariants used to fit the DFT
ene
rg
ies ar
e
shown. (b) The ground-state H-bond isomer of a 32-water unit cell of ice VII measuring
2
√
2
×
2
√
2
×
2 primitive cells on each side corresponding to the experimentally determined ice VIII
structure. Bond pairs representative of the second-order graph invariants, including bond pairs not
possible in the smaller 16-water unit cell, used to fit the DFT energies are shown. Bond 37 connects to
a water molecule in an adjoining cell.
of H-bonds, occurs at nearly constant temperature. All experiments are in gen-
eral agreement on the ice VII/VIII transition temperature, 263-273 K [47, 130],
although hysteresis [131] effects make the precise determination difficult. The
effects of D
2
O on the transformation are negligible at these temperatures, shifting
on the order of a degree [132], indicating quantum effects are minimal. In the ice
Ih/XI transition, the transition temperature shifts from 72 K for H
2
Oto76Kfor
D
2
O. With still higher pressure, the ice VII/VIII transition temperature abruptly
decreases as the mechanism of the transition shifts to proton tunneling across the
shortened H-bonds. Our calculations are pertinent to the temperature-independent
region.
The smallest unit cell we examined was a cubic 16-water unit cell of ice VII,
2 primitive unit cells on each side, as shown in Fig. 16. All first-order invariants
for the 2
2 cell were identically zero for reasons described in Section II.C.
There are eight second-order graph invariants for this cell that were evaluated for
the 52, symmetry-distinct H-bond isomers possible in this unit cell. The electronic
DFT energies are plotted against a linear fit to the 52 energies using three invariants
plus an overall constant. In Fig. 17, perfect agreement is indicated when points lie
on the diagonal line.
N
ext, c
al
culations were performed on a larger ice VII unit cell, measuring
×
2
×
2
√
2
2
√
2
2 primitive cells on each side. As discussed in Section II.C, all
invariants from the smaller cell were also found in the larger unit cell. The DFT
×
×
