Cages of Water Coordinating Kr in Aqueous Solution Randall A. LaViolette* and Kristina L. Copeland Idaho National Engineering and EnVironmental Laboratory, P.O. Box 1625, Idaho Falls, Idaho 83415-2208 Lawrence R. Pratt* Theoretical DiVision, Los Alamos National Laboratory, P.O. Box 1663, Los Alamos, New Mexico 87545 ReceiVed: July 8, 2003; In Final Form: October 1, 2003 Using molecular simulation and inherent structure ideas, we study the coordination number statistics for a Kr atom dissolved in liquid water with a classical force field. We quench compact Kr(H 2 O) n clusters extracted from the liquid. In order that stable cage structures enclosing the Kr atom be obtained with high probability upon quenching of the coordinating water, more water molecules than the mean liquid phase hydration number should be included. The stable enclosing cluster structures obtained here are not simply related to the cage structures of clathrate hydrates. These results confirm the central features of the coordination number distribution of the recent ab initio molecular dynamics work of Ashbaugh et al. [Biophys. Chem. 2003, 105, 321-336], and that distribution is further characterized in the wings of the previous results. In contradiction to a simple clathrate structure hypothesis, no magic number features are observed under the conditions of the present work. 1. Introduction Hydrophobic effects are a fundamental issue in a physical chemical understanding of biomolecular structure, stability, and function. 1 Embedded in the enormous literature 2-5 is a surprising lack of consensus on molecular mechanisms of hydrophobic effects. 6-13 In view of the wide-spread availability of simulation calcula- tions, the necessity of a valid molecular mechanism in a classic sense of physical chemistry, i.e., understanding on a molecular level as well as predicting, might be questioned. But if most current theories are not mostly false, then different mechanisms should be anticipated for low temperatures in contrast to high temperatures, 14,15 for low pressures in contrast to high pressures, 16-18 and for inert gas molecule solutes in contrast to macromolecular and amphiphilic solutes solutes. 7-9 A valid molecular mechanism is nontrivial. Such a mechanism might be expected to develop from justifiable and tested molecular theories. In fact, the most completely worked out and tested theories 3,5,19 have suggested unexpected mechanistic connec- tions. As an example, we note here that those recent theories suggest that the temperature of entropy convergence can be validly estimated as with R σ denoting the coefficient of thermal expansion along the coexistence curve. 3,5,19 This parameter R σ is distinctive of liquid water, being typically more than 5 times smaller for water than for common organic solvents. 20 A “clathrate-like” mechanistic view, either an orthodox or reformed picture, 19 has widespread appeal but recently was reexamined critically. 19 The present paper gives the results of further study of critical issues raised there. Specifically, using simulation tools we search for magic number features in the coordination number distributions of a ideal hydrophobic solute (Kr) that might be suggestive of hydration structures of clathrate type. Additionally, we characterize more precisely the stability of the inner shell structures observed in conventional simulation studies of Kr in liquid water solution. The wide-spread use of the euphemism “clathrate-like” does not imply that it has an accepted quantitative identification nor does it have accepted quantitative consequences for solution thermodynamics. 19 Often, “clathrate-like” directs attention to orientational preferences for water molecules proximal to hydrophobic groups. 19 The perspective of the present work is that average radial ordering of those proximal water molecules would be expected to be as important as the average orientational ordering, perhaps more so. But that radial ordering is typically not considered when “clathrate-like” is employed as a mecha- nistic descriptor; where that radial ordering has been examined with care, it is distinctively “clathrate-unlike”. 19 An extension of that average radial structure information is provided by inner shell hydration number distributions, some- times called “quasi-component distributions”. 19 Being a distribu- tion, such a quantity presents more information than just the mean value. In this respect “clathrate-like” has been assumed 21 to imply specifically that mean inner shell occupancies should be quantized in jumps of four water molecules, as suggested by crystal structures of clathrate hydrates. 22 This idea has the important virtues of a simple, definite hypothesis. A related idea is that the corresponding quasi-component distribution should exhibit structuring, i.e., magic numbers, corresponding to these quanta. Previous ab initio molecular dynamics study of Kr(aq) 19 did not find any magic number structuring. 2. Methods The analysis that we bring newly to the problem of understanding cage structures that might be involved in hydra- * Corresponding authors. E-mail: R.A.L., yaq@inel.gov; L.R.P., lrp@lanl.gov. T ≈ 1 2R σ 11267 J. Phys. Chem. A 2003, 107, 11267-11270 10.1021/jp0359687 CCC: $25.00 © 2003 American Chemical Society Published on Web 11/25/2003