Chemistry Reference
In-Depth Information
of the
E
i
on unit cell volume in Eqs. (1) and (2) can describe the evolution of the
ice VII/VIII phase boundary with increasing system density. Neglect of vibrations
causes a 10% error in the density-pressure relationship at zero pressure, but that
error decreases with increasing pressure [62].
Oxygen atoms are nearly stationary in proton-ordering transitions. For example,
the transformation of ice Ih to ice XI results in a compression along the
a
- and
c
-axes of only
0
.
36%, respectively, and an elongation of the
b
-axis of
0
.
84% [14]. Similar changes are observed in the proton-ordering transformation
of ice VII in which the
a
- and
c
-axes differ by
−
0
.
75 and
−
−
1
.
0 and 2
.
0%, respectively. The
lattice constants change by
3
.
3% for
a
and
c
, respectively, when ice
III is cooled from 250 to 165 K to form ice IX [45]. The distortion of the unit cell
in the low-temperature phase has been neglected in theoretical work to date.
+
0
.
4 and
−
B. Energetics of H-Bond Arrangements in Ice
The options for describing the delicate energy differences among H-bond isomers
in ice are empirical potentials and
ab initio
methods. Common empirical potentials
have been notably unsuccessful in describing H-bond order-disorder phenomena
in ice [36, 64-66], although there is no reason to be pessimistic that future improve-
ments in water models will lead to more successful prediction, as discussed below
in Section II.B.3. Initial results have shown that even modest levels of electronic
density functional theory can correctly predict the H-bond topology of the low-
temperature structures of ice and provide a qualitative estimate of the transition
temperatures.
1. Empirical Potentials
Enormous effort has been devoted to devising analytic potential models (i.e., “em-
pirical potentials”) capable of describing the structural and dynamic properties
of water, and substantial improvements have been made since the first computer
simulations of liquid water [67, 68]. Initial tests of the predictions of various avail-
able water models at the time by Morse, Rice [69, 70] Townsend et al. [71] found
varying quality of structure predictions. The
inter
variant of the MCY potential
[72] gave reasonable ice structures, while the ST2 potential [73] revealed serious
flaws. More recently, Sanz et al. [74] calculated the entire phase diagram of the
TIP4P [75] and SPC/E [76] water models (with the exception of ice X, which these
models are incapable of describing). Although the phase boundaries are shifted
to lower temperature by roughly 40 K, the TIP4P model gave a particularly good
account of the phase diagram and, although not nearly as successful, the phase
diagram of the SPC/E model bore some resemblance to experiment.
While current empirical potentials show some hope of reproducing the melting
lines of the various ice phases and transitions between ice phases with different
oxygen atom positions, these potentials do not capture the energetics of the H-bond
