Multiple Time-Scale Behavior of the Hydrogen-Bond Network in Water

Abstract

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".

Model-based fit procedure for power-law-like spectra

“…At very low frequency the spectrum is rather steep: a simple fit of the low-frequency data shows a 1/f 2 behavior, and thus we can surmise that this is just the high-frequency tail of a simple relaxation with a very low relaxation constant (this accounts for 2 fit parameters: amplitude and relaxation rate). At higher frequency the slope is smaller and Mudi and Chakravarty estimate a spectral index slightly higher than 1 [16]: since there is no hint of a downward bend, I exclude the full spectral shape (18) and also the reduced form (22), and I choose (19) instead, i.e. I include the possibility of a low-frequency flattening, made invisible by the high-frequency tail of the simple relaxation (this adds three more parameters to the fit: an amplitude, a minimum relaxation rate, and a spectral index β).…”

“…Using (15), (16) or (17) improves the fit stability but means that the final description of the relaxation rate distribution is incomplete. We have already given a simple argument that shows that a nonuniform distribution of relaxation processes like g λ ∝ λ −β between the maximum and minimum relaxation rates λ min , λ max , produces a spectral density with an intermediate 1/f 1+β region: an exact integration yields the spectral density…”

“…I have tested the simple model-derived spectral densities described in section 3 on data kindly provided by C. Chakravarty and A. Mudi [15]: the original spectral data are shown in figure 10 and correspond to the 230 K curve in figure 1a of reference [16] (see also [17,18,19] for full simulation details). At very low frequency the spectrum is rather steep: a simple fit of the low-frequency data shows a 1/f 2 behavior, and thus we can surmise that this is just the high-frequency tail of a simple relaxation with a very low relaxation constant (this accounts for 2 fit parameters: amplitude and relaxation rate).…”

“…11. Fit to the spectral data from [16] shown in figure 10 (thick black curve). The data are shown in light gray in the background; the dotted curves a, b, c, and d represent respectively the first, second, third and fourth term of the model (27).…”

Effect of Ionic Solutes on the Hydrogen Bond Network Dynamics of Water: Power Spectral Analysis of Aqueous NaCl Solutions

“…[6][7][8][9] To do this, temperature-and densitydependent changes in the hydrogen bond network of SPC/E water were characterized using power spectral analysis of fluctuations in tagged molecule configurational energies and local tetrahedral order. The analysis focused in particular on the multiple time scale regime which is characterized by a 1/f R dependence of the power spectrum on the frequency f with R lying between 0.5 and 1.5.…”