Hydrogen-bond dynamics for the extended simple point-charge model of water

tions. We analyze the dynamics using energetic and geometric definitions of a hydrogen bond, and employ two analysis methods: ~i! a history-dependent correlation function, related to the distribution of bond lifetimes, and ~ii! a history-independent correlation function. For method ~i! we find an approximately Arrhenius temperature dependence of the bond lifetime, and find that the distribution of bond lifetimes is extremely sensitive to the choice of bond definition. For method ~ii! we find—independent of bond definition—that the dynamics are consistent with the predictions of the mode-coupling theory, suggesting that the slow dynamics of hydrogen bonds can be explained in the same framework as standard transport quantities. Our results allow us to clarify the significance of the choice of both bond definition and analysis technique. PACS number~s!: 61.43.Fs, 61.20.Ne The anomalous properties of water are believed to be connected to the influence of the microscopic behavior of hydrogen bonding on both dynamic and thermodynamic properties of bulk water @1‐4#. Both experimental @5‐11# and theoretical @12‐22# studies have focused on understanding various aspects of the hydrogen bond, including network connectivity and relaxation time, bond lifetime, and other properties. On supercooling, relaxation times typically display a powerlaw behavior with an apparent divergence at a temperature T s’228 K, that has gained much attention. Molecular dynamics ~MD! studies, while limited by the accuracy of the model, are particularly useful for investigating the anomalous behavior in the supercooled regime since nucleation does not occur on the time scale of MD simulations. Furthermore, MD provides immediate access to hydrogen-bond information, which expedites investigation of the bond dynamics. As a result, several studies previously focused on bond dynamics using MD. Here we investigate the temperature dependence of the hydrogen-bond dynamics using the extended simple point charge ~SPC/E! model of water @23#. A brief report of some of our results recently appeared @24#, and here we provide a more complete account. We study the bond dynamics using two possible definitions of a hydrogen bond, and consider two analysis methods first proposed by Stillinger @25#: ~i! correlations in a time series of bonds which are continuously intact, and thus dependent on the history of bond breaking; and ~ii! correlations independent of the history of bondbreaking events. For analysis method ~i!, we find that the average bond lifetime t HB, measured by the first breaking time, displays an Arrhenius temperature dependence, as expected from experiments @5,6#. For analysis method ~ii!, we find a nonexponential relaxation of the bond correlations and power-law behavior of correlation time t R that can be interpreted using mode-coupling theory ~MCT! for the dynamics of supercooled liquids @26#. Previously, the transport properties were shown to be well described by MCT @27,28#, suggesting that the bond dynamics may be understood in the same theoretical framework as transport properties. Moreover, the possible relationship between the MCT predictions and the observed power-law behavior of water’s dynamics quantities was previously discussed @27‐29#. Simulations very close to the MCT transition temperature T c , show the expected breakdown of the MCT predictions. Furthermore, the dynamic behavior in this region has also been shown to correlate with the properties of the potential energy surface @30#—which may aid in