As suggested in a previous study under the title "Simple Relationship Between the Properties of Isotopic Water", viscosity results verify the fact that the structural properties of liquid H 2 O and D 2 O are nearly identical once a zero-point-energy-induced thermal offset effect is taken into account. This means that the viscosities of these two isotopic forms must be compared at different temperatures, rather than at the same temperature. Only in this way can the expected (M D 2 O /M H 2 O ) 1/2 viscosity ratio be retrieved. Application of this most simple idea, with no additional parameter adjustment, to H 2 O viscosity data, or equivalently to any of the existing empirical viscosity equations for H 2 O, leads to D 2 O viscosities having better than 1% accuracy over a wide temperature range. This isotopic correlation concept has also been used here to predict viscosities of liquid T 2 O, no viscosity data apparently being available for this substance.

Cho et al. Reply: It appears to us that Velasco et al. [1] have misconstrued the intent of our paper [2]. The purpose of using the overly simple 1D model in the first place was merely to verify that an appropriately chosen double-well potential can produce a realistically behaving pressure-dependent density maximum. The calculation was meant further to provide a valid yet understandable physical picture for the properties of this important substance, none then existing, and to give possible insights for later 3D computations.However, the 3D calculations performed by Velasco et al. used a potential model that is not closely related to any 3D model conceived or suggested by us. When they find no evidence for a density anomaly using such a model, they incorrectly conclude that the key to the density anomaly is not the multiple-well potential. They further claim that the analytic work of Stell and Hemmer (SH) [3] excludes the possibility of anomalous behavior from multiple-well potentials in 3D systems. As far as we can see, SH made no comments on such phenomena in 3D models at all. In fact, contrary to this point of view, Bell et al.[4] did find density maxima in 3D models with double-well potentials, but their particular choice of potentials gave an incorrect pressure dependence.Apparently, Velasco et al.[1] simply used our unmodified 1D potential in their 3D calculations. In our paper we stated that, "the water-water potential in computational models should be modified in such a way that it can provide a subsidiary second-neighbor oxygen-oxygen minimum near 3.4 Å, while keeping intact under appropriate thermodynamic conditions the open tetrahedral structure." This cannot be done by assuming a spherically symmetric double-well potential as in Ref. [1].A strong angular dependence [5] of the water-water potential enters in 3D because the normal O-H · · · O hydrogen bond must be present only within a narrow range of angles so as to allow the formation of a normal oxygen-oxygen van der Waals minimum near 3.4 Å. Kamb [6] has already discussed the possible necessity of these van der Waals interactions to offset energy losses caused by hydrogen bonds bending to form the much more compact O · · · O · · · O angles in the dense polymorph structures. Coulomb interactions employed in all commonly used potential models [7], and, of course, the Velasco et al. potential, have far too broad an angular dependence. Since the potential of Velasco et al. does not have close to the form we suggested, it is not surprising to us that no density anomalies were found.It is our opinion that the 3.4 Å potential minimum must be present in order to promote the formation of highdensity ice-II-like structure known to occur in the real liquid. See the differential scattering curves in Fig. 5 of Ref. [8]. A correctly behaving intermediate range 3D potential has been devised in our laboratory [9]. In this three-site model, H · · · H interactions have a standard

No previous concept has explained all the intricate structural features of liquid water which occur in the radial distribution function (RDF) as a function of temperature and pressure. Using an outerstructure two-state model, successful in explaining all the anomalies of water, the RDF and its sensitivity to temperature and pressure can be reproduced. The crossings of these RDF's at specific distances confirm the precise two-state nature of this important liquid.

Articles you may be interested inTemperature, pressure, and isotope effects on the structure and properties of liquid water: A lattice approachThe steep non-Arrhenius temperature dependence at low temperatures of the shear viscosity of water and its backwards-sounding increased fluidity under pressure for temperatures below 33°C are two of the anomalies of this liquid that have been known for a very long time. The purpose of the present paper is to show how these two important characteristics of water emerge quantitatively from an explicit two-state outer-neighbor mixture model that we have used to explain many other properties of this substance. It will be shown here that both of these viscosity anomalies are directly related to the steep variations with temperature and pressure of the fractional compositions of ice-Ih-type bonding and ice-II-type bonding in the two-state mixture. This compositional dependence has already been obtained in earlier work from the variations of the density and the isothermal compressibility of water with temperature. The viscosity analysis presented here thus helps to unify further all the properties of this liquid under a single, very simple structural characteristic.