1 AbstractThe effect of the Berendsen thermostat on the dynamical properties of bulk SPC/E water is tested by generating power spectra associated with fluctuations in various observables. The Berendsen thermostat is found to be very effective in preserving temporal correlations in fluctuations of tagged particle quantities over a very wide range of frequencies. Even correlations in fluctuations of global properties, such as the total potential energy, are well-preserved for time periods shorter than the thermostat time constant.Deviations in dynamical behaviour from the microcanonical limit do not, however, always decrease smoothly with increasing values of the thermostat time constant but may be somewhat larger for some intermediate values of τ B , specially in the supercooled regime, which are similar to time scales for slow relaxation processes in bulk water. 2The ideal ensemble to extract dynamical information from a molecular dynamics simulation is the microcanonical (NVE) ensemble [1,2]. Since the total energy is conserved in this ensemble, the Newtonian equations of motion can be assumed to represent the natural evolution of the system, subject to the accuracy of using classical mechanics to describe the atomic dynamics. The constant energy (E) and volume (V) conditions do not, however, correspond to the most common experimental conditions and therefore it is often desirable to implement MD simulations in the canonical (NVT) and isothermal-isobaric (NPT) ensembles. An additional reason for preferring the NVT ensemble is that when long run lengths are required, as in the case of studies of slow dynamics in liquids or glasses, there may be significant energy drift in the NVE ensemble.Two types of approaches have been developed to adapt MD simulations to the canonical ensemble: (i) extended Lagrangian methods, such as NoseHoover thermostats and (ii) resampling or rescaling of velocities, as in the case of the Andersen and Berendsen thermostats. The extended Lagrangian methods will generate the true canonical distribution of velocities. The rescaling approaches will only ensure that the average kinetic energy of the system corresponds to the expected value at the desired temperature but have the advantage that they can be combined very simply with the Verlet algorithm. In both approaches, the degree of perturbation of the real time evolution of the system can be adjusted by manipulating various thermostat parameters.The Berendsen thermostat represents a proportional scaling of the velocities per time step in the algorithm with the scaling factor being givenwhere ∆t is the time step, τ B is the time constant of the Berendsen thermostat , T 0 is the desired temperature and T is the instantaneous temperature Fluctutations in global properties were strongly affected when τ B was less than 0.1ps implying that analysis of fluctuations cannot be used to determine observable properties. Single-particle properties, including dynamical quantities such as the diffusivity and orientational correlation times, were found t...

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The temperature-dependent changes in the hydrogen-bond network of SPC/E water have been examined using power spectral analysis of fluctuations in tagged-molecule potential energies and local tetrahedral order parameters. The clear signatures of multiple time-scale or 1/f R behavior in the power spectra are shown to depend sensitively on the strength of hydrogen bonding. The analysis focuses on three specific power spectral features: the frequency of crossover to white noise behavior, the exponent in the 1/f R regime, and the librational peak. The exponent of the tagged-particle potential-energy fluctuations is shown to be strongly correlated with the diffusivity in the temperature range of 230 to 300 K. This correlation is strongest in the temperaturedensity regimes where the mechanism for diffusion is likely to be dominated by translational-rotational coupling, suggesting that the value of the exponent is a measure of the efficiency of the coupling of librational modes with network vibrations. The temperature dependence of all power spectral features was found to be strongest along the 0.9-g cm -3 isochore, which corresponds closely to the density of minimum diffusivity for the temperature range studied here. The static distributions of the tagged-particle quantities were examined to determine the degree of heterogeneity of the local molecular environment and its relationship with power spectral features. † Part of the special issue "Frank H. Stillinger Festschrift".

To understand the modifications of the hydrogen bond network of water by ionic solutes, power spectra as well as static distributions of the potential energies of tagged solvent molecules and solute ions have been computed from molecular dynamics simulations of aqueous NaCl solutions. The key power spectral features of interest are the presence of high-frequency peaks due to localized vibrational modes, the existence of a multiple time scale or 1/falpha frequency regime characteristic of networked liquids, and the frequency of crossover from 1/falpha type behavior to white noise. Hydrophilic solutes, such as the sodium cation and the chloride anion, are shown to mirror the multiple time scale behavior of the hydrogen bond network fluctuations, unlike hydrophobic solutes which display essentially white noise spectra. While the power spectra associated with tagged H2O molecules are not very sensitive to concentration in the intermediate frequency 1/falpha regime, the crossover to white noise is shifted to lower frequencies on going from pure solvent to aqueous alkali halide solutions. This suggests that new and relatively slow time scales enter the picture, possibly associated with processes such as migration of water molecules from the hydration shell to the bulk or conversion of contact ion pairs into solvent-separated ion pairs which translate into variations in equilibrium transport properties of salt solutions with concentration. For anions, cations, and solvent molecules, the trends in the alpha exponents of the multiple time scale region and the self-diffusivities are found to be strongly correlated.

Power spectra for various tagged particle quantities in bulk extended simple point charge model water [H. J. C. Berendsen, J. R. Grigera, and T. P. Straatsma, J. Phys. Chem. 91, 6269 (1987)] are shown to have a regime with 1f(alpha) dependence on frequency f with alpha lying between 1 and 1.5 if the dynamical changes in the particular observable are sensitive to the multiple time-scale behavior of the hydrogen-bond network. The variations in mobility associated with the diffusional anomaly are mirrored in the scaling exponent alpha associated with this multiple time-scale behavior, suggesting that monitoring of 1f(alpha) behavior is a simple and direct method for linking phenomena on three distinctive length and time scales: the local molecular environment, hydrogen-bond network reorganizations, and the diffusivity. Our results indicate that experimental studies of supercooled water to probe the density dependence of 1f(alpha) spectral features, or equivalent stretched exponential behavior in time-correlation functions, will be of interest.