It has recently been found that the origins of all the baffling properties of pure water, mentioned above, can be understood through the simple recognition of the importance of variable outer neighbor interactions derived from the bending, not the breaking, of hydrogen bonds at the second-neighbor level. This idea [19] about the possible importance of ice-II-like hydrogen-bond bending outside the ordinary tetrahedral bonding regions suggests that a very explicit rearrangement of O···O outer bonding may take place in the liquid with increasing temperature and pressure without a significant change of the inner tetrahedral structure. The close-range structural properties of the pure liquid should then be closely related to those in the most stable ice polymorphs, particularly Ih, II, III. In all the most stable crystalline polymorphs, including these three, a well defined "cage" of five water molecules with nearest-neighbor O···O distances of ~ 2.8 Å exists [20]. From structural studies, a similar cage, though of course dynamically rapidly fluctuating [21], is found in the liquid. Its relative persistence from supercooled temperatures to near 100° C is the origin of the high boiling point of this material. Some of these structural ideas about the liquid actually follow the very early concepts of Tammann [22], the discoverer of ice II. However, as evidenced by the failure to cite either of the two early seminal papers [19,22] on this topic, modern authors have been hesitant to adopt this view. The important aspect here is the explicit structural information that is available from the polymorph crystallography, blurred to some extent in the recent descriptions of the liquid in terms of low- and high-density amorphs, LDA and HDA [23], and still more recently in the much less explicit description in terms of low- and high-density liquid forms, LDL and HDL [24].

The persistence of the tetrahedral "cage" in all condensed forms of water means that the behavior of the liquid on a molecular-level scale has to do not just with the nearest-neighbor tetrahedral structure, the central theme of all previous investigations, but also with O···O non-hydrogen-bonded neighbors farther out. The outer structural features found in the energetically most stable ice polymorphs, or equivalently LDA and HDA (see Ref. [5] for our early recognition of this), can occur in the liquid with very little energy expense [20] to create a dynamically variable non-nearest-neighbor structure that has never been explicitly considered in liquid water studies. The most important feature of this non-nearest-neighbor bonding is the presence of and interconversion between two nearly equienergetic forms — a trigonometrically specific 4.5 Å second-neighbor O···O distance from regular tetrahedral bonding and a compact higher density bent hydrogen bonded O···O distance near 3.5 Å.

In passing, it should be mentioned that it is these outer neighbor variations that remove the liquid water problem from the realms of small cluster experiments [25], small molecule quantum theory [26-28] and ordinary liquid state theory. They are precisely the features that have caused the confusion among molecular scientists that has existed about this problem over the decades. For example, the seemingly huge size of a 1000-molecule water cluster corresponds to a spherical droplet with diameter less than 40 Å, where nearly half the molecules reside on the surface. Intuition would then say that, even in this size cluster, "edge effects" would prevent an accurate assessment of any outer bonding characteristics of the type we believe to be important in the liquid. An even larger minimum size might be inferred from the experimental study of fairly large supercooled water clusters containing 4000-6000 molecules [29]. So many molecules may be required that the necessary experiments or high-level quantum mechanics are no longer possible to carry out using currently available methods.

It is a simple matter to see why the quantum mechanically difficult outer structural characteristics of the condensed phases of water are so crucial to their understanding. In ice II and III, structural differences surrounding the ordinary 5-molecule tetrahedron give rise to densities that are 30% higher than the density of ice Ih! Yet, the inner bonding is essentially identical to that in ice Ih [20,30]. Thus, in spite of almost universal concentration in water studies on the nearest four-neighbor tetrahedron, this aspect alone cannot possibly differentiate these condensed phase structures. It cannot be responsible for the remarkable structural variations among the ice polymorphs, or in the liquid. This is the reason that we have believed, in agreement with some early comments of Bosio, et al. [31], that it is the structural behavior in the "outer" non-hydrogen-bonded regions that is at the root of the unusual properties of water.

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