Dynamical Aspects of Isomerization and Melting Transitions in [H 2 O] 8 † Daniel Laria, ‡,¶ Javier Rodriguez, ‡ Christoph Dellago, § and David Chandler* ,⊥ Unidad ActiVidad Quı ´mica, Comisio ´ n Nacional de Energı ´a Ato ´ mica, AVenida Libertador 8250, 1429 Capital Federal, Argentina; Departamento de Quı ´mica Inorga ´ nica, Analı ´tica y Quı ´mica-Fı ´sica e INQUIMAE, Facultad de Ciencias Exactas y Naturales, UniVersidad de Buenos Aires, Ciudad UniVersitaria, Pabello ´ n II, 1428, Capital Federal, Argentina; Department of Chemistry, UniVersity of Rochester, Rochester, New York 14627; and Department of Chemistry and Kenneth S. Pitzer Center for Theoretical Chemistry, UniVersity of California, Berkeley, California 94720 ReceiVed: October 25, 2000; In Final Form: December 13, 2000 We present a transition path sampling study of the dynamics of isomerization between the S 4 and the D 2d cubic structures of the water octamer. The reaction mechanism involves a transition state characterized by a distorted face exhibiting a diagonal hydrogen bond. Analysis of an ensemble of trajectories shows that the isomerization requires concerted flips of double proton donor molecules and the interchange between dangling and bonding hydrogens in single proton donor molecules. At a total energy E )-60.5 kcal/mol, we calculated that the characteristic time for the interconversion is of the order of milliseconds. We have also investigated pathways for the melting transition at temperatures T ≈ 200 K. We find that the barrier for solid-liquid interconversions never exceeds 2k B T measured from the liquid side. Such transitions between liquid and solid do not involve the passage over an energetic barrier; instead, the stabilization of the liquid phase is the result of a cancellation between energetic and entropic contributions. I. Introduction Clusters with sizes in the nanometer scale are normally considered as intermediate entities between bulk matter and isolated molecules. From a thermodynamic point of view, clusters are inherently metastable since the most stable con- figurations for a handful of particles within a macroscopic volume in contact with a heat reservoir correspond to fully evaporated states. However, one may extract thermodynamically relevant information, if clusters survive sufficiently long compared to microscopic relaxation times. At low enough temperatures, clusters exhibit solidlike behavior. Under these conditions, their structural and dynamical features do not differ substantially from those of polyatomic molecules: fluctuations of interparticle distances much smaller than their average values and a dynamics characterized by small amplitude vibrations. Depending on interparticle interactions and size, molecular solid clusters may exhibit a manifold of stable structures. As one moves to higher temperatures, but before evaporation becomes important, there is typically a thermal interval where cluster structures look similar to portions of amorphous liquidlike bulk phases. Perhaps, the most clear manifestation of the liquidlike regime is the presence of intracluster diffusion. While the melting temperature of bulk phases is well-defined, interconversions between solid-liquid structures in clusters take place spontaneously over an interval of temperatures. 1-7 At present, there is unambiguous experimental evidence of the existence of solid and liquidlike clusters; 8-11 however, the vast majority of the microscopic details characterizing both environments comes from computer simulations. Melting transi- tions can be localized either by determining the slope of the energy vs temperature curve or by computing relative fluctua- tions in the interparticle distances. 1,12 In many cases, well below the melting temperature, a second kind of structural transforma- tion involving two different stable solidlike structures may also occur. The present paper examines dynamical aspects of these two different kinds of structural transitions, both taking place in the water octamer. The first process is the isomerization between the S 4 and D 2d solid cubic structures characterized by different connectivity patterns of the hydrogen bonds. Recently, these two stable structures have been identified in infrared experiments on isolated water clusters 13 and in experiments involving benzene attached to the water octamer. 14 Second, we investigated dynamical pathways for the melting transition of the octamer. Although there is a large body of investigations devoted to the study of structures of small solid and liquid aqueous clusters, 15-24 very little is known about the dynamics and the mechanisms that drive the interconversion between them. Our methodology relies on the recently developed path sampling method. 26-29 This approach not only provides a route to the computation of rate constants but also allows the characterization of reactive channels and transition states. 30 In contrast to other methods based on biased or constrained dynamics, 31 this new methodology does not require an a priori definition of a reaction coordinate that may preclude proper sampling of all relevant fluctuations governing the dynamics of the reactive process. Instead, it is based on harvesting bias- free reactive pathways joining reactant and product states by sampling appropriate probability distributions of trajectories. This work is organized as follows: in section II we present some relevant details about the model we adopted and a brief † Part of the special issue “William H. Miller Festschrift”. * Corresponding author. ‡ Comisio ´n Nacional de Energı ´a Ato ´mica. ¶ Universidad de Buenos Aires. § University of Rochester. ⊥ University of California. 2646 J. Phys. Chem. A 2001, 105, 2646-2651 10.1021/jp003955c CCC: $20.00 © 2001 American Chemical Society Published on Web 02/14/2001