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The Journal of Physical Chemktry, Vol. 87, No. 21, 1983
others and results in the relation eB = p(3'/')/dW
P. Plummer: (1) Did you fix the monomer geometry at the experimental value or a t that predicted by the basis you used? (2) Since this is not the minimum energy structure for the basis, is that likely to alter your results in a nonuniform way as additional molecules are added? Scheiner: (1)The geometry was fixed a t the experimental geometry: R ( O 0 ) = 2.76 A, r(0H) = 0.97 A, all angles tetrahedral. (2) No I do not think so since a single geometry was used and I do not think the minimum-energy geometry is particularly relevant here. The principal source of error lies in the fact that any basis set such as STO-3G and 4-31G has difficulty accurately calculating dipole moments; hence the necessity for scaling. M. D. Newton: As we discussed privately, I think basis set defects with regard to polarizability might be at least as important as those concerning the permanent dipole in affecting the cooperative enhancement of wz for the linear chains. Scheiner: I agree that polarizability may be an important factor. However, the agreement between scaled STO-3G and 4-31G results is encouraging since even these two basis sets have a large difference in polarizability. I think it is interesting to note also that the slope of the 4-31G curve in Figure 3 is less than that of STO-3G. Since 4-31G is more polarizable, one would a priori expect the results to be more cooperative with a greater slope.
Glass-FormingTendency, Stability of the Amorphous State, and Cryoprotection of Red Blood Cells (P. Boutron) J . Warman: I t is not clear to me how you determined the relative fractions of amorphous and crystalline ice in your samples. Boutron: The quantity of ice crystallized can be deduced from the area of the solidification peak observed in calvimetry, taking account of the variation of the fusion heat of ice with the temperature of the demining heat, etc.
Molecular Dynamics Study of Ice Crystallite Melting (T. A. Weber) P. Plummer: How did you define your melting point? From the E vs. T plot it appears the steep rise begins -200 K and continues to -300 K. Weber: We define our melting point as the maximum of AEIAT. The slope of the curve (Figure 3) does deviate significantly from the harmonic line at 200 K. A line with higher slope could be drawn through the four low temperature points indicating the anharmonic contribution to the heat capacity. The slope starts taking off a t 267 K and reaches its maximum a t 300 K. T. Takahashi: How is the surface boundary condition sensitive to the configuration of liquidlike structure in the H 2 0 molecular sphere? Weber: The surface of the droplet is not sensitive to our wall potential in the present parameterization. An ST2 molecule at 12 A (near the edge of our droplet) experiences a potential of 1.125 X lo-' kcal/mol. The following table of U(r)vs. r shows how weak and slowly varying this function is. r U ( r ) ,kcalimol 6 12
6.9 x 10-13 1.1x lo-'
14
6.1 X
16 18 20
3.4 x 10-4 1.8 X lo-' 1.0
P. Plummer: When you remove your reverse potential do you see substantial evaporation of your cluster? Do you believe, for example, the melting point would decrease if it were removed? Weber: We see only one or two molecules evaporate from the cluster with the wall potential applied. Since the potential is so weak for our size droplet it is hard to believe that anything drastic would occur if we removed the potential.
J. Nagle: Following Takahashi's question, would it be more physical to have your molecules in a small box rather than having your U(r)potential?
Weber: Why invoke a discontinuous wall potential? That would cause continuity problems in integrating the equations of motion. Our wall potential with the current parameterization acts like a hard wall with smoothed edges.
Ice under Pressure: Transitions to Symmetric Hydrogen Bonds (F. H. Stillinger) J. F. Nagle: (1)Is your result that many wave vectors develop soft modes nearly simultaneously consistent with Pauling hypothesis of nearly equal energies for different proton configurations? (2) Can you suggest, based on the soft modes, the kind of ordering that might occur a t low temperatures (assuming equilibrium can be achieved) and can you make contact with the (T- 30 K)-I behavior of the dielectric constant? Stillinger: (1)It is consistent with that hypothesis but does not prove it to be valid for all Bernal-Fowler-Pauling states. (2) An adequate answer would have to be based on a more complete study of relative minima in the many-proton potential hypersurface. In particular, quartic terms would have to be included. Unfortunately, we have not yet carried out such an analysis. It may turn out that the ordering patterns we have already found in the quadratic soft-mode study are still those dominant in the extended (anharmonic) regime about which you inquire.
J. Perez: Concerning the transformation implying soft mode, do you think that the situation of ice can be compared to martensitic transformation, at least in the case of alloys with w-phase (e.g., TiAl)? Stillinger: The connection is an interesting one which we shall keep in mind. My suspicion is that quantum effects are incomparably more important in the ice case because of the small proton mass, and this is probably decisive for the transition to a symmetric-bond form. But perhaps the soft-mode connection will offer some valuable insights.
J. W . Glen: The disappearance of the double-minimum potential affects a second-order transition, but you tell us the transition occurs after the double minimum has disappeared. Could you comment on whether there is evidence of the order of the transition? Stillinger: The two-state Hartree approximation (with fixed oxygens) yields an energy that is continuous and once differentiable with respect to lattice spacing. Its phase transition therefore should be classified as third order. However, it is important to establish in the future what would be the effect of including oxygen-lattice phonon modes. The order of the transition might then change, perhaps even to first order. D. D. Klug: In your ice VI1 calculations you obtain a paraelectric to ferroelectric transition. In infrared experiments at high pressures which we have carried out we find ice VI1 is almost as ordered t w ice VI11 since the line widths are about equal and much less than in ice I. How would this fact modify your prediction regarding ice VIII? Stillinger: As I tried to indicate, the nature of the dominating soft modes for the dense ices VI1 and VI11 depend very sensitively on the fine details of the assumed proton-proton interaction. Pure dipolar interactions with constant dielectric shielding produce ferroelectric ordering, but antiferroelectric order emerges instead when nearest-neighbor protons repel even more strongly. I suspect your experiments suggest that such short-range enhancement of the proton-proton coupling is mandatory.
Small Water Clusters as Theoretical Models for Structural and Kinetic Properties of Ice (M. D. Newton) J . F. Nagle: Would you care to comment upon the effects of the variability with proton configuration of the Bjerrum defect migration activation energy? In particular, would the effective activation energy relevant for dielectric studies be lower than the straight average 3.3 kcal and would there not be some effective channeling of the defect along paths of low activation energy? Newton: Certainly the relevant quantity to focus on is the minimum energy path. From our model per se (Le., (H20)& we clearly f i d a large variation in energies which arises from different possible conformations of the peripheral OH bond, and activation
