Chemistry Reference
In-Depth Information
the solid state, deep minima of the potential surface of water are in 1:1 correspon-
dence with the oriented graphs that describe the H-bond topology. Phenomena
like the several known H-bond order-disorder transitions between ice phases can
be understood as discontinuous changes in the H-bond topologies sampled by the
system, while the oxygen lattice changes minimally.
The statistical mechanical description of H-bond order-disorder requires the
relative energies of a large number of H-bond arrangements, growing exponentially
with system size, and therefore present special challenges without appropriate
tools. Since in this case the property of interest is a scalar, it can be related to
topological properties that are invariant to all symmetry operations. In this manner,
the energetic properties of H-bond arrangements can be captured by a handful of
relevant parameters. Physical properties that transform as higher-order tensors,
such as lattice site displacements and dipole moment, can also be treated in an
analogous fashion.
With better techniques and more experience in the synthesis of new phases, the
number of known phases of ice has increased dramatically. Four new phases of
ice have been discovered just since 1998. This will provide a fertile source of new
challenges and opportunities in the theory of H-bond order-disorder in the ices.
Acknowledgments
We gratefully acknowledge support of the National Science Foundation (CHE-0616872) and the
Ohio Supercomputer Center.
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