Confused ice:
New light on the hydrogen bond?

Although the ice we find in the freezer, or outside in the winter, is familiar to us, it has many strange attributes. The fact that it floats on its liquid phase - water - is unusual for a solid, yet this behaviour is reasonably well understood in terms of the nature of the hydrogen bonding that joins water molecules together in both the liquid and ice phases.

Figure 1: Ice Ih.

 Like all crystals, ice contains molecules which are arranged in a regular repeating crystal lattice, as shown in figure 1. Each water molecule consists of one oxygen and two hydrogen atoms, with an HOH angle of 104.5°. These link together to form a structure in which each water molecule connects to four others in an approximately tetrahedral arrangement. The intermolecular linkages are hydrogen bonds - an intermolecular interaction that is relatively weak, but which is very important, occurring in many biological molecules including proteins and DNA.

This ice structure - as well as other ice structures found at higher pressures - can be thought of in terms of in terms of (a) the underlying oxygen framework; and (b) how the hydrogens are distributed between these oxygens.

The hydrogen decoration of the oxygen frameworks must fulfil the topological constraints of the Bernal-Fowler rules. These state that (a) each oxygen is associated with two hydrogen atoms, consistent with the existence of individual water molecules, (b) each O-O hydrogen bond accommodates one, and only, one hydrogen, and (c) each water molecule links to four neighbours through hydrogen bonding. Within these constraints, there are (in general) a number of ways in which the hydrogens can be distributed on a four-co-ordinated oxygen framework, or to make an equivalent statement, there are a number of ways in which the water molecules can be oriented. These arrangements may be ordered (e.g. ferroelectric, antiferroelectric), or disordered (e.g. where there is no periodicity of the orientations that coincides with the periodicity of the oxygen framework). Subject to crystallographic symmetry constraints, there are also possibilities of intermediate partially ordered states.

This is illustrated in figure 2(a), which shows the six possible orientations that a water molecule can adopt such that it donates two and accepts two hydrogen bonds to and from its neighbours respectively. Figure 2(b) shows schematically in two dimensions both an orientationally ordered (here ferroelectrically ordered) and an orientational disordered structure. Note that the space-time average structure, as determined by diffraction, will be the average of all the orientations in a given structure. Thus, a fully disordered structure will appear as a tetrahedral network of oxygen atoms with two hydrogen atoms per O-O bond; the probability of finding a hydrogen at each site is, however, only 50% (figure 2(c)). For a partially ordered structure, these probabilities will depart from 50%.

Figure 2a.

Figure 2b.

Figure 2c.

The hydrogen arrangements must follow a set of chemically-determined rules. These were first elucidated by Bernal and Fowler in 1933. Briefly, they tell us that:

Within these rules, the hydrogens can be arranged in ordered or disordered ways. In 'normal' ice Ih, they are disordered. As we reduce temperature, they remain disordered - though thermodynamics tells us they should order.

Why the hydrogens do not order spontaneously in ice Ih at low temperature is because the orientations of the water molecules become 'frozen in' - they don't have enough energy to move to the ordered structure. This kind of behaviour is found in several of the high-pressure ice structures, though in some (e.g. ices VII - disordered - and VIII - ordered) order-disorder transitions can occur at temperatures above the 'freezing in' temperature.

We have been studying the hydrogen disorder in several of the high-pressure ice structures, using neutron scattering. The reason we use neutrons rather than X-rays is that the hydrogen atom (or in our case, for technical reasons, the deuterium atom) is far more visible to neutrons than it is to X-rays. In particular, we have concentrated on the hydrogen order/disorder situations in ices III, IV, V, and XII. This work has been done using neutron beam lines at the world's most powerful sources of neutrons, the Institut Laue-Langevin, Grenoble, France, and the ISIS Pulsed Neutron Source at the Rutherford Appleton Laboratory in the UK.

Figure 3: Unstrained and strained sites.

Figure 4: Strain example: Ice III.

Conventional wisdom tells us that the hydrogen disorder is determined by the degree of strain that water molecules feel when occupying particular sites in the crystal. Figure 3 shows examples of an ideally unstrained site and a strained site. In actual ice structures, if we concentrate on one particular water molecule site and compare the OOO angle for the hydrogen bonded neighbours with the inherent HOH angle of 104.5°, we find a range of 'mismatches' - some OOO angles can be as low as 80° and some as high as 140° (see figure 4 which shows some of these mismatches for ice III). We might expect the largest mismatches to be associated with the greatest local strain, and hence these sites would be occupied less than those showing less strain. If we try to rationalise the hydrogen partial ordering in terms of preferential occupation of the lower strain sites, however, we find the situation is rather more complicated. In fact, we are unable to explain our observed ordering in these terms, and so we need to look for another driving force. This we now think relates to repulsive non-bonded interactions between molecules. These can be between hydrogens of neighbouring molecules, or between oxygens and hydrogens, or between neighbouring non-bonded oxygens. Two of these repulsive interactions are shown schematically in figure 5.

Figure 5: Repulsive interaction example.

Thus, we believe that the driving forces to hydrogen ordering in all those ices that show disorder (which is most of them) are rather more complicated than was originally thought. The potential involvement of repulsive interactions is consistent with earlier work of Hugh Savage, who rationalised for the first time the orientational structures of water molecules close to biological interfaces. The fact that we need these interactions to rationalise the much simpler ice systems means that we can use ices to improve our understanding of the hydrogen bond that is ubiquitous in much of chemistry and biology.

Selected references

W. F. Kuhs, C. Vettier, D.V. Bliss and J.L. Finney
"Structure and hydrogen ordering in ices VI, VII and VIII by neutron powder diffraction"
J Chem Phys 81 3612-3623 1984

H F J Savage and J.L. Finney
"Repulsive regularities of water structure in ices and crystalline hydrates"
Nature 322 717-720 1986

C. Lobban, Ph.D. Thesis, University of London, 1998.

The structure and ordering of ices III and V
C. Lobban, J.L. Finney, and W.F. Kuhs
J Chem Phys in press (due out 15 April 2000)