On the Molecular Mechanism of Water Reorientation Damien Laage* ,†,‡ and James T. Hynes †,‡,§ Chemistry Department, Ecole Normale Supérieure, 24 rue Lhomond 75005 Paris, France, CNRS UMR Pasteur, and Department of Chemistry and Biochemistry, UniVersity of Colorado, Boulder, Colorado 80309-0215 ReceiVed: June 13, 2008; ReVised Manuscript ReceiVed: September 4, 2008 We detail and considerably extend the analysis recently presented in Science 2006, 311, 832-835 of the molecular mechanism of water reorientation based on molecular dynamics simulations and the analytic framework of the extended jump model (EJM). The water reorientation is shown to occur through large- amplitude angular jumps due to the exchange of hydrogen (H)-bond acceptors, with a minor contribution from the diffusive H-bond frame reorientation between these exchanges. The robust character of this mechanism with respect to different water models is discussed. We fully characterize these jump events, including the distributions of trajectories around the average path. The average path values and the distributions of the jump time and the jump amplitude, the two key parameters in the Ivanov jump model component of the EJM, are determined. We also discuss the possibility of selectively exciting water molecules close to the jump event, of interest for ultrafast infrared experiments. In addition to a comparison of predicted reorientation times with experimental results, the reorientation time temperature dependence is discussed. A detailed description of the pathway free energetics for the water reorientation is presented; this is used to identify the jump rate-limiting step as the translational motion in which the initial H-bond of the reorientating water is elongated and the new H-bond acceptor water approaches. 1. Introduction Many of liquid water’s special and ubiquitous properties originate from its propensity to form very dynamic, labile hydrogen (H)-bond networks. 1-5 A major fashion in which this network constantly rearranges by breaking and forming H-bonds is through the reorientation of water molecules. This rearrange- ment also occurs when the water hydration pattern adapts to a changing solute, and water reorientation is at the heart of hydration dynamics. Thus, for chemical processes involving a charge redistribution in aqueous solution, a major response of the water solvent is the reorientation of individual water molecules. Examples in aqueous solution include S N 2 reactions 6 and proton transfer, 7,8 where the reaction coordinate for the latter involves water reorientation. 7,8 Similarly, the reaction coordinate governing proton transport 9-11 both in bulk water or in water wires within biological channels such as in gramicidin A involves the reorientation of water molecules; this is possibly the rate-limiting step, 10,12 but a detailed description remains elusive. 11 Water reorientation also determines the hydration layer lability around biological macromolecules such as proteins or DNA strands and thus conditions the biomolecule flexibility and function, such as the selective molecular recognition of ligands. 2,13,14 Several mechanisms describing the molecular reorientation of water have been suggested over the years. One such is the “flickering clusters” mechanism, 1 relying on the concept of cooperative H-bonds; when an H-bond disappears, an entire water cluster dissolves, allowing the water molecules to reorient before forming a new H-bond. Another suggestion is based on an analogy with the reorientation mechanism in ice, 1,15 involving the diffusion of Bjerrum orientational defects. However, not- withstanding occasional concerns about the degree of its validity, 1,2,16-19 by far the most widely employed mechanism to describe water reorientation is the Debye small-step diffusion model. 20 We have recently argued that the diffusive model is inad- equate and that, instead, water reorientation proceeds mainly through large-amplitude angular jumps involving H-bond partner exchange for the reorienting water molecule. 21 Indeed, the reorientation was described in terms of a chemical reaction involving the exchange of H-bond partners for the reorienting water. 21 In the present paper, we detail and significantly extend this previous work, aspects of which are emphasized in the following description of the remainder of this paper. We present in section 2 the molecular jump mechanism. We first very briefly review the shortcomings of the diffusive model and then extend our previous description based on an average path to include distributions of the jump angle and the waiting time for the jump. The distribution of the OH frequency and the probability to selectively excite a system close to the jump event, of interest in ultrafast infrared experiments, are also presented. Further, the sensitivity of the primary results to H-bond definitions and water potential is discussed. Section 3 turns to the detailed discussion of the analytic extended jump model, including an improved description of the model jump time. Calculated reorientation times at room temperature are compared with experimental results. In section 4, we provide for the first time a discussion of the reorientation time temper- ature dependence, a detailed description of the pathway free energetics for the water reorientation, and an identification of the rate-limiting step in the process. Section 5 provides some concluding remarks. * To whom correspondence should be addressed. E-mail: damien.laage@ ens.fr. † Ecole Normale Supérieure. ‡ CNRS UMR Pasteur. § University of Colorado. J. Phys. Chem. B 2008, 112, 14230–14242 14230 10.1021/jp805217u CCC: $40.75  2008 American Chemical Society Published on Web 10/23/2008