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\begin{document} |
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\title{On the structural and transport properties of the soft sticky |
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dipole (SSD) and related single point water models} |
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\author{Christopher J. Fennell and J. Daniel Gezelter\footnote{Corresponding author. \ Electronic mail: gezelter@nd.edu}} |
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\affiliation{Department of Chemistry and Biochemistry\\ University of Notre Dame\\ |
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\author{Christopher J. Fennell and J. Daniel |
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Gezelter\footnote{Corresponding author. \ Electronic mail: |
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gezelter@nd.edu} \\ Department of Chemistry and Biochemistry\\ University of Notre Dame\\ |
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Notre Dame, Indiana 46556} |
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\date{\today} |
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\maketitle |
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\doublespacing |
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\begin{abstract} |
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The density maximum and temperature dependence of the self-diffusion |
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family. |
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\end{abstract} |
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\maketitle |
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\newpage |
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%\narrowtext |
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%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% |
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% BODY OF TEXT |
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time steps is illustrated in figure |
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\ref{timestep}. |
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|
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%\begin{figure} |
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%\begin{center} |
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%\epsfxsize=6in |
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%\epsfbox{timeStep.epsi} |
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%\caption{Energy conservation using both quaternion-based integration and |
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%the {\sc dlm} method with increasing time step. The larger time step |
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%plots are shifted from the true energy baseline (that of $\Delta t$ = |
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%0.1~fs) for clarity.} |
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%\label{timestep} |
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%\end{center} |
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%\end{figure} |
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\begin{figure} |
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\begin{center} |
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\epsfxsize=6in |
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\epsfbox{timeStep.epsi} |
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\caption{Energy conservation using both quaternion-based integration and the |
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{\sc dlm} method with increasing time step. The larger time step plots |
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are shifted from the true energy baseline (that of $\Delta t$ = |
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0.1~fs) for clarity.} |
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\label{timestep} |
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\end{center} |
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\end{figure} |
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|
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In figure \ref{timestep}, the resulting energy drift at various time |
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steps for both the {\sc dlm} and quaternion integration schemes is |
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configurations showed similar results, with a liquid-phase density |
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maximum in this same region (between 255 and 260~K). |
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|
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%\begin{figure} |
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%\begin{center} |
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%\epsfxsize=6in |
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%\epsfbox{denseSSDnew.eps} |
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%\caption{Density versus temperature for TIP4P [Ref. \onlinecite{Jorgensen98b}], |
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% TIP3P [Ref. \onlinecite{Jorgensen98b}], SPC/E [Ref. \onlinecite{Clancy94}], SSD |
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% without Reaction Field, SSD, and experiment [Ref. \onlinecite{CRC80}]. The |
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% arrows indicate the change in densities observed when turning off the |
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% reaction field. The the lower than expected densities for the SSD |
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% model were what prompted the original reparameterization of SSD1 |
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% [Ref. \onlinecite{Ichiye03}].} |
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%\label{dense1} |
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%\end{center} |
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%\end{figure} |
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\begin{figure} |
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\begin{center} |
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\epsfxsize=6in |
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\epsfbox{denseSSDnew.eps} |
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\caption{ Density versus temperature for TIP4P [Ref. \citen{Jorgensen98b}], |
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TIP3P [Ref. \citen{Jorgensen98b}], SPC/E [Ref. \citen{Clancy94}], SSD |
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without Reaction Field, SSD, and experiment [Ref. \citen{CRC80}]. The |
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arrows indicate the change in densities observed when turning off the |
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reaction field. The the lower than expected densities for the SSD |
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model were what prompted the original reparameterization of SSD1 |
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[Ref. \citen{Ichiye03}].} |
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\label{dense1} |
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\end{center} |
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\end{figure} |
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|
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The density maximum for SSD compares quite favorably to other |
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simple water models. Figure \ref{dense1} also shows calculated |
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\ref{diffuse}, alongside experimental, SPC/E, and TIP5P |
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results.\cite{Gillen72,Holz00,Clancy94,Jorgensen01} |
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|
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%\begin{figure} |
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%\begin{center} |
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%\epsfxsize=6in |
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%\epsfbox{betterDiffuse.epsi} |
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%\caption{Average self-diffusion constant as a function of temperature for |
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%SSD, SPC/E [Ref. \onlinecite{Clancy94}], and TIP5P |
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%[Ref. \onlinecite{Jorgensen01}] compared with experimental data |
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%[Refs. \onlinecite{Gillen72} and \onlinecite{Holz00}]. Of the three water models |
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%shown, SSD has the least deviation from the experimental values. The |
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%rapidly increasing diffusion constants for TIP5P and SSD correspond to |
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%significant decreases in density at the higher temperatures.} |
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%\label{diffuse} |
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%\end{center} |
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%\end{figure} |
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\begin{figure} |
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\begin{center} |
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\epsfxsize=6in |
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\epsfbox{betterDiffuse.epsi} |
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\caption{ Average self-diffusion constant as a function of temperature for |
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SSD, SPC/E [Ref. \citen{Clancy94}], and TIP5P |
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[Ref. \citen{Jorgensen01}] compared with experimental data |
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[Refs. \citen{Gillen72} and \citen{Holz00}]. Of the three water models |
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shown, SSD has the least deviation from the experimental values. The |
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rapidly increasing diffusion constants for TIP5P and SSD correspond to |
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significant decreases in density at the higher temperatures.} |
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\label{diffuse} |
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\end{center} |
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\end{figure} |
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|
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The observed values for the diffusion constant point out one of the |
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strengths of the SSD model. Of the three models shown, the SSD model |
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transition occurs at 235~K. These melting transitions are |
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considerably lower than the experimental value. |
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|
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%\begin{figure} |
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%\begin{center} |
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%\epsfxsize=6in |
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%\epsfbox{corrDiag.eps} |
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%\caption{An illustration of angles involved in the correlations observed in Fig. \ref{contour}.} |
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%\label{corrAngle} |
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%\end{center} |
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%\end{figure} |
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\begin{figure} |
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\begin{center} |
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\epsfxsize=6in |
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\epsfbox{fullContours.eps} |
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\caption{ Contour plots of 2D angular pair correlation functions for |
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512 SSD molecules at 100~K (A \& B) and 300~K (C \& D). Dark areas |
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signify regions of enhanced density while light areas signify |
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depletion relative to the bulk density. White areas have pair |
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correlation values below 0.5 and black areas have values above 1.5.} |
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\label{contour} |
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\end{center} |
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\end{figure} |
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|
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%\begin{figure} |
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%\begin{center} |
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%\epsfxsize=6in |
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%\epsfbox{fullContours.eps} |
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%\caption{Contour plots of 2D angular pair correlation functions for |
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%512 SSD molecules at 100~K (A \& B) and 300~K (C \& D). Dark areas |
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%signify regions of enhanced density while light areas signify |
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%depletion relative to the bulk density. White areas have pair |
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%correlation values below 0.5 and black areas have values above 1.5.} |
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%\label{contour} |
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%\end{center} |
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%\end{figure} |
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\begin{figure} |
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\begin{center} |
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\epsfxsize=6in |
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\epsfbox{corrDiag.eps} |
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\caption{ An illustration of angles involved in the correlations observed in Fig. \ref{contour}.} |
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\label{corrAngle} |
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\end{center} |
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\end{figure} |
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|
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Additional analysis of the melting process was performed using |
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two-dimensional structure and dipole angle correlations. Expressions |
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|
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\begin{table} |
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\begin{center} |
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\caption{Parameters for the original and adjusted models} |
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\caption{ Parameters for the original and adjusted models} |
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\begin{tabular}{ l c c c c } |
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\hline \\[-3mm] |
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\ \ \ Parameters\ \ \ & \ \ \ SSD [Ref. \onlinecite{Ichiye96}] \ \ \ |
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& \ SSD1 [Ref. \onlinecite{Ichiye03}]\ \ & \ SSD/E\ \ & \ \ SSD/RF \\ |
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\ \ \ Parameters\ \ \ & \ \ \ SSD [Ref. \citen{Ichiye96}] \ \ \ |
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& \ SSD1 [Ref. \citen{Ichiye03}]\ \ & \ SSD/E\ \ & \ \ SSD/RF \\ |
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\hline \\[-3mm] |
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\ \ \ $\sigma$ (\AA) & 3.051 & 3.016 & 3.035 & 3.019\\ |
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\ \ \ $\epsilon$ (kcal/mol) & 0.152 & 0.152 & 0.152 & 0.152\\ |
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\end{center} |
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\end{table} |
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|
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%\begin{figure} |
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%\begin{center} |
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%\epsfxsize=5in |
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%\epsfbox{GofRCompare.epsi} |
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%\caption{Plots comparing experiment [Ref. \onlinecite{Head-Gordon00_1}] with |
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%SSD/E and SSD1 without reaction field (top), as well as |
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%SSD/RF and SSD1 with reaction field turned on |
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%(bottom). The insets show the respective first peaks in detail. Note |
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%how the changes in parameters have lowered and broadened the first |
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%peak of SSD/E and SSD/RF.} |
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%\label{grcompare} |
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%\end{center} |
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%\end{figure} |
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\begin{figure} |
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\begin{center} |
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\epsfxsize=5in |
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\epsfbox{GofRCompare.epsi} |
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\caption{ Plots comparing experiment [Ref. \citen{Head-Gordon00_1}] with |
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SSD/E and SSD1 without reaction field (top), as well as |
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SSD/RF and SSD1 with reaction field turned on |
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(bottom). The insets show the respective first peaks in detail. Note |
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how the changes in parameters have lowered and broadened the first |
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peak of SSD/E and SSD/RF.} |
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\label{grcompare} |
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\end{center} |
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\end{figure} |
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|
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%\begin{figure} |
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%\begin{center} |
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%\epsfxsize=6in |
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%\epsfbox{dualsticky_bw.eps} |
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%\caption{Positive and negative isosurfaces of the sticky potential for |
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%SSD1 (left) and SSD/E \& SSD/RF (right). Light areas |
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%correspond to the tetrahedral attractive component, and darker areas |
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%correspond to the dipolar repulsive component.} |
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%\label{isosurface} |
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%\end{center} |
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%\end{figure} |
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\begin{figure} |
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\begin{center} |
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\epsfxsize=6in |
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\epsfbox{dualsticky_bw.eps} |
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\caption{ Positive and negative isosurfaces of the sticky potential for |
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SSD1 (left) and SSD/E \& SSD/RF (right). Light areas |
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correspond to the tetrahedral attractive component, and darker areas |
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correspond to the dipolar repulsive component.} |
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\label{isosurface} |
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\end{center} |
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\end{figure} |
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|
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In the original paper detailing the development of SSD, Liu and Ichiye |
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placed particular emphasis on an accurate description of the first |
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simulations had the same thermalization, equilibration, and data |
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collection times as stated previously. |
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|
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%\begin{figure} |
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%\begin{center} |
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%\epsfxsize=6in |
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%\epsfbox{ssdeDense.epsi} |
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%\caption{Comparison of densities calculated with SSD/E to |
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%SSD1 without a reaction field, TIP3P [Ref. \onlinecite{Jorgensen98b}], |
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%TIP5P [Ref. \onlinecite{Jorgensen00}], SPC/E [Ref. \onlinecite{Clancy94}] and |
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%experiment [Ref. \onlinecite{CRC80}]. The window shows a expansion around |
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%300 K with error bars included to clarify this region of |
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%interest. Note that both SSD1 and SSD/E show good agreement with |
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%experiment when the long-range correction is neglected.} |
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%\label{ssdedense} |
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%\end{center} |
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%\end{figure} |
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\begin{figure} |
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\begin{center} |
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\epsfxsize=6in |
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\epsfbox{ssdeDense.epsi} |
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\caption{ Comparison of densities calculated with SSD/E to |
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SSD1 without a reaction field, TIP3P [Ref. \citen{Jorgensen98b}], |
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TIP5P [Ref. \citen{Jorgensen00}], SPC/E [Ref. \citen{Clancy94}] and |
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experiment [Ref. \citen{CRC80}]. The window shows a expansion around |
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300 K with error bars included to clarify this region of |
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interest. Note that both SSD1 and SSD/E show good agreement with |
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experiment when the long-range correction is neglected.} |
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\label{ssdedense} |
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\end{center} |
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\end{figure} |
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|
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Fig. \ref{ssdedense} shows the density profile for the SSD/E |
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model in comparison to SSD1 without a reaction field, other |
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melting transition for SSD/E was shown to occur at 235~K. The |
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same transition temperature observed with SSD and SSD1. |
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|
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%\begin{figure} |
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%\begin{center} |
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%\epsfxsize=6in |
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%\epsfbox{ssdrfDense.epsi} |
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%\caption{Comparison of densities calculated with SSD/RF to |
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%SSD1 with a reaction field, TIP3P [Ref. \onlinecite{Jorgensen98b}], |
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%TIP5P [Ref. \onlinecite{Jorgensen00}], SPC/E [Ref. \onlinecite{Clancy94}], and |
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%experiment [Ref. \onlinecite{CRC80}]. The inset shows the necessity of |
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%reparameterization when utilizing a reaction field long-ranged |
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%correction - SSD/RF provides significantly more accurate |
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%densities than SSD1 when performing room temperature |
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%simulations.} |
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%\label{ssdrfdense} |
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%\end{center} |
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%\end{figure} |
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\begin{figure} |
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\begin{center} |
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\epsfxsize=6in |
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\epsfbox{ssdrfDense.epsi} |
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\caption{ Comparison of densities calculated with SSD/RF to |
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SSD1 with a reaction field, TIP3P [Ref. \citen{Jorgensen98b}], |
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TIP5P [Ref. \citen{Jorgensen00}], SPC/E [Ref. \citen{Clancy94}], and |
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experiment [Ref. \citen{CRC80}]. The inset shows the necessity of |
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reparameterization when utilizing a reaction field long-ranged |
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correction - SSD/RF provides significantly more accurate |
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densities than SSD1 when performing room temperature |
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simulations.} |
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\label{ssdrfdense} |
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\end{center} |
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\end{figure} |
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|
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Including the reaction field long-range correction in the simulations |
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results in a more interesting comparison. A density profile including |
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maximum at 255~K, fairly close to the density maxima of 260~K and |
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265~K, shown by SSD and SSD1 respectively. |
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|
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%\begin{figure} |
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%\begin{center} |
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%\epsfxsize=6in |
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%\epsfbox{ssdeDiffuse.epsi} |
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%\caption{The diffusion constants calculated from SSD/E and |
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%SSD1 (both without a reaction field) along with experimental results |
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%[Refs. \onlinecite{Gillen72} and \onlinecite{Holz00}]. The NVE calculations were |
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%performed at the average densities observed in the 1 atm NPT |
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%simulations for the respective models. SSD/E is slightly more mobile |
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%than experiment at all of the temperatures, but it is closer to |
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%experiment at biologically relevant temperatures than SSD1 without a |
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%long-range correction.} |
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%\label{ssdediffuse} |
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%\end{center} |
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%\end{figure} |
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\begin{figure} |
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> |
\begin{center} |
| 800 |
> |
\epsfxsize=6in |
| 801 |
> |
\epsfbox{ssdeDiffuse.epsi} |
| 802 |
> |
\caption{ The diffusion constants calculated from SSD/E and |
| 803 |
> |
SSD1 (both without a reaction field) along with experimental results |
| 804 |
> |
[Refs. \citen{Gillen72} and \citen{Holz00}]. The NVE calculations were |
| 805 |
> |
performed at the average densities observed in the 1 atm NPT |
| 806 |
> |
simulations for the respective models. SSD/E is slightly more mobile |
| 807 |
> |
than experiment at all of the temperatures, but it is closer to |
| 808 |
> |
experiment at biologically relevant temperatures than SSD1 without a |
| 809 |
> |
long-range correction.} |
| 810 |
> |
\label{ssdediffuse} |
| 811 |
> |
\end{center} |
| 812 |
> |
\end{figure} |
| 813 |
|
|
| 814 |
|
The reparameterization of the SSD water model, both for use with and |
| 815 |
|
without an applied long-range correction, brought the densities up to |
| 836 |
|
of SSD/E relative to SSD1 under the most commonly simulated |
| 837 |
|
conditions. |
| 838 |
|
|
| 839 |
< |
%\begin{figure} |
| 840 |
< |
%\begin{center} |
| 841 |
< |
%\epsfxsize=6in |
| 842 |
< |
%\epsfbox{ssdrfDiffuse.epsi} |
| 843 |
< |
%\caption{The diffusion constants calculated from SSD/RF and |
| 844 |
< |
%SSD1 (both with an active reaction field) along with |
| 845 |
< |
%experimental results [Refs. \onlinecite{Gillen72} and \onlinecite{Holz00}]. The |
| 846 |
< |
%NVE calculations were performed at the average densities observed in |
| 847 |
< |
%the 1 atm NPT simulations for both of the models. SSD/RF |
| 848 |
< |
%simulates the diffusion of water throughout this temperature range |
| 849 |
< |
%very well. The rapidly increasing diffusion constants at high |
| 850 |
< |
%temperatures for both models can be attributed to lower calculated |
| 851 |
< |
%densities than those observed in experiment.} |
| 852 |
< |
%\label{ssdrfdiffuse} |
| 853 |
< |
%\end{center} |
| 854 |
< |
%\end{figure} |
| 839 |
> |
\begin{figure} |
| 840 |
> |
\begin{center} |
| 841 |
> |
\epsfxsize=6in |
| 842 |
> |
\epsfbox{ssdrfDiffuse.epsi} |
| 843 |
> |
\caption{ The diffusion constants calculated from SSD/RF and |
| 844 |
> |
SSD1 (both with an active reaction field) along with |
| 845 |
> |
experimental results [Refs. \citen{Gillen72} and \citen{Holz00}]. The |
| 846 |
> |
NVE calculations were performed at the average densities observed in |
| 847 |
> |
the 1 atm NPT simulations for both of the models. SSD/RF |
| 848 |
> |
simulates the diffusion of water throughout this temperature range |
| 849 |
> |
very well. The rapidly increasing diffusion constants at high |
| 850 |
> |
temperatures for both models can be attributed to lower calculated |
| 851 |
> |
densities than those observed in experiment.} |
| 852 |
> |
\label{ssdrfdiffuse} |
| 853 |
> |
\end{center} |
| 854 |
> |
\end{figure} |
| 855 |
|
|
| 856 |
|
In figure \ref{ssdrfdiffuse}, the diffusion constants for SSD/RF are |
| 857 |
|
compared to SSD1 with an active reaction field. Note that SSD/RF |
| 870 |
|
\begin{minipage}{\linewidth} |
| 871 |
|
\renewcommand{\thefootnote}{\thempfootnote} |
| 872 |
|
\begin{center} |
| 873 |
< |
\caption{Properties of the single-point water models compared with |
| 873 |
> |
\caption{ Properties of the single-point water models compared with |
| 874 |
|
experimental data at ambient conditions. Deviations of the of the |
| 875 |
|
averages are given in parentheses.} |
| 876 |
|
\begin{tabular}{ l c c c c c } |
| 883 |
|
\ \ $D$ ($10^{-5}$ cm$^2$/s) & 1.78(0.7) & 2.51(0.18) & 2.00(0.17) & 2.32(0.06) & 2.299\cite{Mills73} \\ |
| 884 |
|
\ \ Coordination Number ($n_C$) & 3.9 & 4.3 & 3.8 & 4.4 & |
| 885 |
|
4.7\footnote{Calculated by integrating $g_{\text{OO}}(r)$ in |
| 886 |
< |
Ref. \onlinecite{Head-Gordon00_1}} \\ |
| 886 |
> |
Ref. \citen{Head-Gordon00_1}} \\ |
| 887 |
|
\ \ H-bonds per particle ($n_H$) & 3.7 & 3.6 & 3.7 & 3.7 & |
| 888 |
|
3.5\footnote{Calculated by integrating $g_{\text{OH}}(r)$ in |
| 889 |
< |
Ref. \onlinecite{Soper86}} \\ |
| 890 |
< |
\ \ $\tau_1$ (ps) & 10.9(0.6) & 7.3(0.4) & 7.5(0.7) & 7.2(0.4) & 5.7\footnote{Calculated for 298 K from data in Ref. \onlinecite{Eisenberg69}} \\ |
| 889 |
> |
Ref. \citen{Soper86}} \\ |
| 890 |
> |
\ \ $\tau_1$ (ps) & 10.9(0.6) & 7.3(0.4) & 7.5(0.7) & 7.2(0.4) & 5.7\footnote{Calculated for 298 K from data in Ref. \citen{Eisenberg69}} \\ |
| 891 |
|
\ \ $\tau_2$ (ps) & 4.7(0.4) & 3.1(0.2) & 3.5(0.3) & 3.2(0.2) & 2.3\footnote{Calculated for 298 K from data in |
| 892 |
< |
Ref. \onlinecite{Krynicki66}} |
| 892 |
> |
Ref. \citen{Krynicki66}} |
| 893 |
|
\end{tabular} |
| 894 |
|
\label{liquidproperties} |
| 895 |
|
\end{center} |
| 938 |
|
averaged over five detailed NVE simulations performed at the ambient |
| 939 |
|
conditions for each of the respective models. It should be noted that |
| 940 |
|
the commonly cited value of 1.9 ps for $\tau_2$ was determined from |
| 941 |
< |
the NMR data in Ref. \onlinecite{Krynicki66} at a temperature near |
| 941 |
> |
the NMR data in Ref. \citen{Krynicki66} at a temperature near |
| 942 |
|
34$^\circ$C.\cite{Rahman71} Because of the strong temperature |
| 943 |
|
dependence of $\tau_2$, it is necessary to recalculate it at 298~K to |
| 944 |
|
make proper comparisons. The value shown in Table |
| 945 |
|
\ref{liquidproperties} was calculated from the same NMR data in the |
| 946 |
< |
fashion described in Ref. \onlinecite{Krynicki66}. Similarly, $\tau_1$ was |
| 947 |
< |
recomputed for 298~K from the data in Ref. \onlinecite{Eisenberg69}. |
| 946 |
> |
fashion described in Ref. \citen{Krynicki66}. Similarly, $\tau_1$ was |
| 947 |
> |
recomputed for 298~K from the data in Ref. \citen{Eisenberg69}. |
| 948 |
|
Again, SSD/E and SSD/RF show improved behavior over SSD1, both with |
| 949 |
|
and without an active reaction field. Turning on the reaction field |
| 950 |
|
leads to much improved time constants for SSD1; however, these results |
| 955 |
|
|
| 956 |
|
\subsection{Additional Observations} |
| 957 |
|
|
| 958 |
< |
%\begin{figure} |
| 959 |
< |
%\begin{center} |
| 960 |
< |
%\epsfxsize=6in |
| 961 |
< |
%\epsfbox{icei_bw.eps} |
| 962 |
< |
%\caption{The most stable crystal structure assumed by the SSD family |
| 963 |
< |
%of water models. We refer to this structure as Ice-{\it i} to |
| 964 |
< |
%indicate its origins in computer simulation. This image was taken of |
| 965 |
< |
%the (001) face of the crystal.} |
| 966 |
< |
%\label{weirdice} |
| 967 |
< |
%\end{center} |
| 968 |
< |
%\end{figure} |
| 958 |
> |
\begin{figure} |
| 959 |
> |
\begin{center} |
| 960 |
> |
\epsfxsize=6in |
| 961 |
> |
\epsfbox{icei_bw.eps} |
| 962 |
> |
\caption{ The most stable crystal structure assumed by the SSD family |
| 963 |
> |
of water models. We refer to this structure as Ice-{\it i} to |
| 964 |
> |
indicate its origins in computer simulation. This image was taken of |
| 965 |
> |
the (001) face of the crystal.} |
| 966 |
> |
\label{weirdice} |
| 967 |
> |
\end{center} |
| 968 |
> |
\end{figure} |
| 969 |
|
|
| 970 |
|
While performing a series of melting simulations on an early iteration |
| 971 |
|
of SSD/E not discussed in this paper, we observed |
| 1006 |
|
|
| 1007 |
|
\begin{table} |
| 1008 |
|
\begin{center} |
| 1009 |
< |
\caption{Enthalpies of Formation (in kcal / mol) of the three crystal |
| 1009 |
> |
\caption{ Enthalpies of Formation (in kcal / mol) of the three crystal |
| 1010 |
|
structures (at 1 K) exhibited by the SSD family of water models} |
| 1011 |
|
\begin{tabular}{ l c c c } |
| 1012 |
|
\hline \\[-3mm] |
| 1082 |
|
|
| 1083 |
|
\bibliographystyle{jcp} |
| 1084 |
|
\bibliography{nptSSD} |
| 1089 |
– |
|
| 1090 |
– |
\newpage |
| 1091 |
– |
|
| 1092 |
– |
\begin{list} |
| 1093 |
– |
{Figure \arabic{captions}: }{\usecounter{captions} |
| 1094 |
– |
\setlength{\rightmargin}{\leftmargin}} |
| 1095 |
– |
|
| 1096 |
– |
\item Energy conservation using both quaternion-based integration and |
| 1097 |
– |
the {\sc dlm} method with increasing time step. The larger time step |
| 1098 |
– |
plots are shifted from the true energy baseline (that of $\Delta t$ = |
| 1099 |
– |
0.1~fs) for clarity. |
| 1100 |
– |
|
| 1101 |
– |
\item Density versus temperature for TIP4P [Ref. \onlinecite{Jorgensen98b}], |
| 1102 |
– |
TIP3P [Ref. \onlinecite{Jorgensen98b}], SPC/E |
| 1103 |
– |
[Ref. \onlinecite{Clancy94}], SSD without Reaction Field, SSD, and |
| 1104 |
– |
experiment [Ref. \onlinecite{CRC80}]. The arrows indicate the change |
| 1105 |
– |
in densities observed when turning off the reaction field. The the |
| 1106 |
– |
lower than expected densities for the SSD model were what prompted the |
| 1107 |
– |
original reparameterization of SSD1 [Ref. \onlinecite{Ichiye03}]. |
| 1108 |
– |
|
| 1109 |
– |
\item Average self-diffusion constant as a function of temperature for |
| 1110 |
– |
SSD, SPC/E [Ref. \onlinecite{Clancy94}], and TIP5P |
| 1111 |
– |
[Ref. \onlinecite{Jorgensen01}] compared with experimental data |
| 1112 |
– |
[Refs. \onlinecite{Gillen72} and \onlinecite{Holz00}]. Of the three |
| 1113 |
– |
water models shown, SSD has the least deviation from the experimental |
| 1114 |
– |
values. The rapidly increasing diffusion constants for TIP5P and SSD |
| 1115 |
– |
correspond to significant decreases in density at the higher |
| 1116 |
– |
temperatures. |
| 1117 |
– |
|
| 1118 |
– |
\item An illustration of angles involved in the correlations observed in |
| 1119 |
– |
Fig. \ref{contour}. |
| 1120 |
– |
|
| 1121 |
– |
\item Contour plots of 2D angular pair correlation functions for |
| 1122 |
– |
512 SSD molecules at 100~K (A \& B) and 300~K (C \& D). Dark areas |
| 1123 |
– |
signify regions of enhanced density while light areas signify |
| 1124 |
– |
depletion relative to the bulk density. White areas have pair |
| 1125 |
– |
correlation values below 0.5 and black areas have values above 1.5. |
| 1126 |
– |
|
| 1127 |
– |
\item Plots comparing experiment [Ref. \onlinecite{Head-Gordon00_1}] with |
| 1128 |
– |
SSD/E and SSD1 without reaction field (top), as well as SSD/RF and |
| 1129 |
– |
SSD1 with reaction field turned on (bottom). The insets show the |
| 1130 |
– |
respective first peaks in detail. Note how the changes in parameters |
| 1131 |
– |
have lowered and broadened the first peak of SSD/E and SSD/RF. |
| 1132 |
– |
|
| 1133 |
– |
\item Positive and negative isosurfaces of the sticky potential for |
| 1134 |
– |
SSD1 (left) and SSD/E \& SSD/RF (right). Light areas |
| 1135 |
– |
correspond to the tetrahedral attractive component, and darker areas |
| 1136 |
– |
correspond to the dipolar repulsive component. |
| 1137 |
– |
|
| 1138 |
– |
\item Comparison of densities calculated with SSD/E to |
| 1139 |
– |
SSD1 without a reaction field, TIP3P [Ref. \onlinecite{Jorgensen98b}], |
| 1140 |
– |
TIP5P [Ref. \onlinecite{Jorgensen00}], SPC/E [Ref. \onlinecite{Clancy94}] and |
| 1141 |
– |
experiment [Ref. \onlinecite{CRC80}]. The window shows a expansion around |
| 1142 |
– |
300 K with error bars included to clarify this region of |
| 1143 |
– |
interest. Note that both SSD1 and SSD/E show good agreement with |
| 1144 |
– |
experiment when the long-range correction is neglected. |
| 1145 |
– |
|
| 1146 |
– |
\item Comparison of densities calculated with SSD/RF to |
| 1147 |
– |
SSD1 with a reaction field, TIP3P [Ref. \onlinecite{Jorgensen98b}], |
| 1148 |
– |
TIP5P [Ref. \onlinecite{Jorgensen00}], SPC/E [Ref. \onlinecite{Clancy94}], and |
| 1149 |
– |
experiment [Ref. \onlinecite{CRC80}]. The inset shows the necessity of |
| 1150 |
– |
reparameterization when utilizing a reaction field long-ranged |
| 1151 |
– |
correction - SSD/RF provides significantly more accurate |
| 1152 |
– |
densities than SSD1 when performing room temperature |
| 1153 |
– |
simulations. |
| 1154 |
– |
|
| 1155 |
– |
\item The diffusion constants calculated from SSD/E and |
| 1156 |
– |
SSD1 (both without a reaction field) along with experimental results |
| 1157 |
– |
[Refs. \onlinecite{Gillen72} and \onlinecite{Holz00}]. The NVE calculations were |
| 1158 |
– |
performed at the average densities observed in the 1 atm NPT |
| 1159 |
– |
simulations for the respective models. SSD/E is slightly more mobile |
| 1160 |
– |
than experiment at all of the temperatures, but it is closer to |
| 1161 |
– |
experiment at biologically relevant temperatures than SSD1 without a |
| 1162 |
– |
long-range correction. |
| 1163 |
– |
|
| 1164 |
– |
\item The diffusion constants calculated from SSD/RF and |
| 1165 |
– |
SSD1 (both with an active reaction field) along with |
| 1166 |
– |
experimental results [Refs. \onlinecite{Gillen72} and \onlinecite{Holz00}]. The |
| 1167 |
– |
NVE calculations were performed at the average densities observed in |
| 1168 |
– |
the 1 atm NPT simulations for both of the models. SSD/RF |
| 1169 |
– |
simulates the diffusion of water throughout this temperature range |
| 1170 |
– |
very well. The rapidly increasing diffusion constants at high |
| 1171 |
– |
temperatures for both models can be attributed to lower calculated |
| 1172 |
– |
densities than those observed in experiment. |
| 1173 |
– |
|
| 1174 |
– |
\item The most stable crystal structure assumed by the SSD family |
| 1175 |
– |
of water models. We refer to this structure as Ice-{\it i} to |
| 1176 |
– |
indicate its origins in computer simulation. This image was taken of |
| 1177 |
– |
the (001) face of the crystal. |
| 1178 |
– |
\end{list} |
| 1179 |
– |
|
| 1180 |
– |
\newpage |
| 1181 |
– |
|
| 1182 |
– |
\begin{figure} |
| 1183 |
– |
\begin{center} |
| 1184 |
– |
\epsfxsize=6in |
| 1185 |
– |
\epsfbox{timeStep.epsi} |
| 1186 |
– |
%\caption{Energy conservation using both quaternion-based integration and |
| 1187 |
– |
%the {\sc dlm} method with increasing time step. The larger time step |
| 1188 |
– |
%plots are shifted from the true energy baseline (that of $\Delta t$ = |
| 1189 |
– |
%0.1~fs) for clarity.} |
| 1190 |
– |
\label{timestep} |
| 1191 |
– |
\end{center} |
| 1192 |
– |
\end{figure} |
| 1193 |
– |
|
| 1194 |
– |
\newpage |
| 1195 |
– |
|
| 1196 |
– |
\begin{figure} |
| 1197 |
– |
\begin{center} |
| 1198 |
– |
\epsfxsize=6in |
| 1199 |
– |
\epsfbox{denseSSDnew.eps} |
| 1200 |
– |
%\caption{Density versus temperature for TIP4P [Ref. \onlinecite{Jorgensen98b}], |
| 1201 |
– |
% TIP3P [Ref. \onlinecite{Jorgensen98b}], SPC/E [Ref. \onlinecite{Clancy94}], SSD |
| 1202 |
– |
% without Reaction Field, SSD, and experiment [Ref. \onlinecite{CRC80}]. The |
| 1203 |
– |
% arrows indicate the change in densities observed when turning off the |
| 1204 |
– |
% reaction field. The the lower than expected densities for the SSD |
| 1205 |
– |
% model were what prompted the original reparameterization of SSD1 |
| 1206 |
– |
% [Ref. \onlinecite{Ichiye03}].} |
| 1207 |
– |
\label{dense1} |
| 1208 |
– |
\end{center} |
| 1209 |
– |
\end{figure} |
| 1085 |
|
|
| 1211 |
– |
\newpage |
| 1086 |
|
|
| 1213 |
– |
\begin{figure} |
| 1214 |
– |
\begin{center} |
| 1215 |
– |
\epsfxsize=6in |
| 1216 |
– |
\epsfbox{betterDiffuse.epsi} |
| 1217 |
– |
%\caption{Average self-diffusion constant as a function of temperature for |
| 1218 |
– |
%SSD, SPC/E [Ref. \onlinecite{Clancy94}], and TIP5P |
| 1219 |
– |
%[Ref. \onlinecite{Jorgensen01}] compared with experimental data |
| 1220 |
– |
%[Refs. \onlinecite{Gillen72} and \onlinecite{Holz00}]. Of the three water models |
| 1221 |
– |
%shown, SSD has the least deviation from the experimental values. The |
| 1222 |
– |
%rapidly increasing diffusion constants for TIP5P and SSD correspond to |
| 1223 |
– |
%significant decreases in density at the higher temperatures.} |
| 1224 |
– |
\label{diffuse} |
| 1225 |
– |
\end{center} |
| 1226 |
– |
\end{figure} |
| 1227 |
– |
|
| 1228 |
– |
\newpage |
| 1229 |
– |
|
| 1230 |
– |
\begin{figure} |
| 1231 |
– |
\begin{center} |
| 1232 |
– |
\epsfxsize=6in |
| 1233 |
– |
\epsfbox{corrDiag.eps} |
| 1234 |
– |
%\caption{An illustration of angles involved in the correlations observed in Fig. \ref{contour}.} |
| 1235 |
– |
\label{corrAngle} |
| 1236 |
– |
\end{center} |
| 1237 |
– |
\end{figure} |
| 1238 |
– |
|
| 1239 |
– |
\newpage |
| 1240 |
– |
|
| 1241 |
– |
\begin{figure} |
| 1242 |
– |
\begin{center} |
| 1243 |
– |
\epsfxsize=6in |
| 1244 |
– |
\epsfbox{fullContours.eps} |
| 1245 |
– |
%\caption{Contour plots of 2D angular pair correlation functions for |
| 1246 |
– |
%512 SSD molecules at 100~K (A \& B) and 300~K (C \& D). Dark areas |
| 1247 |
– |
%signify regions of enhanced density while light areas signify |
| 1248 |
– |
%depletion relative to the bulk density. White areas have pair |
| 1249 |
– |
%correlation values below 0.5 and black areas have values above 1.5.} |
| 1250 |
– |
\label{contour} |
| 1251 |
– |
\end{center} |
| 1252 |
– |
\end{figure} |
| 1253 |
– |
|
| 1254 |
– |
\newpage |
| 1255 |
– |
|
| 1256 |
– |
\begin{figure} |
| 1257 |
– |
\begin{center} |
| 1258 |
– |
\epsfxsize=6in |
| 1259 |
– |
\epsfbox{GofRCompare.epsi} |
| 1260 |
– |
%\caption{Plots comparing experiment [Ref. \onlinecite{Head-Gordon00_1}] with |
| 1261 |
– |
%SSD/E and SSD1 without reaction field (top), as well as |
| 1262 |
– |
%SSD/RF and SSD1 with reaction field turned on |
| 1263 |
– |
%(bottom). The insets show the respective first peaks in detail. Note |
| 1264 |
– |
%how the changes in parameters have lowered and broadened the first |
| 1265 |
– |
%peak of SSD/E and SSD/RF.} |
| 1266 |
– |
\label{grcompare} |
| 1267 |
– |
\end{center} |
| 1268 |
– |
\end{figure} |
| 1269 |
– |
|
| 1270 |
– |
\newpage |
| 1271 |
– |
|
| 1272 |
– |
\begin{figure} |
| 1273 |
– |
\begin{center} |
| 1274 |
– |
\epsfxsize=7in |
| 1275 |
– |
\epsfbox{dualsticky_bw.eps} |
| 1276 |
– |
%\caption{Positive and negative isosurfaces of the sticky potential for |
| 1277 |
– |
%SSD1 (left) and SSD/E \& SSD/RF (right). Light areas |
| 1278 |
– |
%correspond to the tetrahedral attractive component, and darker areas |
| 1279 |
– |
%correspond to the dipolar repulsive component.} |
| 1280 |
– |
\label{isosurface} |
| 1281 |
– |
\end{center} |
| 1282 |
– |
\end{figure} |
| 1283 |
– |
|
| 1284 |
– |
\newpage |
| 1285 |
– |
|
| 1286 |
– |
\begin{figure} |
| 1287 |
– |
\begin{center} |
| 1288 |
– |
\epsfxsize=6in |
| 1289 |
– |
\epsfbox{ssdeDense.epsi} |
| 1290 |
– |
%\caption{Comparison of densities calculated with SSD/E to |
| 1291 |
– |
%SSD1 without a reaction field, TIP3P [Ref. \onlinecite{Jorgensen98b}], |
| 1292 |
– |
%TIP5P [Ref. \onlinecite{Jorgensen00}], SPC/E [Ref. \onlinecite{Clancy94}] and |
| 1293 |
– |
%experiment [Ref. \onlinecite{CRC80}]. The window shows a expansion around |
| 1294 |
– |
%300 K with error bars included to clarify this region of |
| 1295 |
– |
%interest. Note that both SSD1 and SSD/E show good agreement with |
| 1296 |
– |
%experiment when the long-range correction is neglected.} |
| 1297 |
– |
\label{ssdedense} |
| 1298 |
– |
\end{center} |
| 1299 |
– |
\end{figure} |
| 1300 |
– |
|
| 1301 |
– |
\newpage |
| 1302 |
– |
|
| 1303 |
– |
\begin{figure} |
| 1304 |
– |
\begin{center} |
| 1305 |
– |
\epsfxsize=6in |
| 1306 |
– |
\epsfbox{ssdrfDense.epsi} |
| 1307 |
– |
%\caption{Comparison of densities calculated with SSD/RF to |
| 1308 |
– |
%SSD1 with a reaction field, TIP3P [Ref. \onlinecite{Jorgensen98b}], |
| 1309 |
– |
%TIP5P [Ref. \onlinecite{Jorgensen00}], SPC/E [Ref. \onlinecite{Clancy94}], and |
| 1310 |
– |
%experiment [Ref. \onlinecite{CRC80}]. The inset shows the necessity of |
| 1311 |
– |
%reparameterization when utilizing a reaction field long-ranged |
| 1312 |
– |
%correction - SSD/RF provides significantly more accurate |
| 1313 |
– |
%densities than SSD1 when performing room temperature |
| 1314 |
– |
%simulations.} |
| 1315 |
– |
\label{ssdrfdense} |
| 1316 |
– |
\end{center} |
| 1317 |
– |
\end{figure} |
| 1318 |
– |
|
| 1319 |
– |
\newpage |
| 1320 |
– |
|
| 1321 |
– |
\begin{figure} |
| 1322 |
– |
\begin{center} |
| 1323 |
– |
\epsfxsize=6in |
| 1324 |
– |
\epsfbox{ssdeDiffuse.epsi} |
| 1325 |
– |
%\caption{The diffusion constants calculated from SSD/E and |
| 1326 |
– |
%SSD1 (both without a reaction field) along with experimental results |
| 1327 |
– |
%[Refs. \onlinecite{Gillen72} and \onlinecite{Holz00}]. The NVE calculations were |
| 1328 |
– |
%performed at the average densities observed in the 1 atm NPT |
| 1329 |
– |
%simulations for the respective models. SSD/E is slightly more mobile |
| 1330 |
– |
%than experiment at all of the temperatures, but it is closer to |
| 1331 |
– |
%experiment at biologically relevant temperatures than SSD1 without a |
| 1332 |
– |
%long-range correction.} |
| 1333 |
– |
\label{ssdediffuse} |
| 1334 |
– |
\end{center} |
| 1335 |
– |
\end{figure} |
| 1336 |
– |
|
| 1337 |
– |
\newpage |
| 1338 |
– |
|
| 1339 |
– |
\begin{figure} |
| 1340 |
– |
\begin{center} |
| 1341 |
– |
\epsfxsize=6in |
| 1342 |
– |
\epsfbox{ssdrfDiffuse.epsi} |
| 1343 |
– |
%\caption{The diffusion constants calculated from SSD/RF and |
| 1344 |
– |
%SSD1 (both with an active reaction field) along with |
| 1345 |
– |
%experimental results [Refs. \onlinecite{Gillen72} and \onlinecite{Holz00}]. The |
| 1346 |
– |
%NVE calculations were performed at the average densities observed in |
| 1347 |
– |
%the 1 atm NPT simulations for both of the models. SSD/RF |
| 1348 |
– |
%simulates the diffusion of water throughout this temperature range |
| 1349 |
– |
%very well. The rapidly increasing diffusion constants at high |
| 1350 |
– |
%temperatures for both models can be attributed to lower calculated |
| 1351 |
– |
%densities than those observed in experiment.} |
| 1352 |
– |
\label{ssdrfdiffuse} |
| 1353 |
– |
\end{center} |
| 1354 |
– |
\end{figure} |
| 1355 |
– |
|
| 1356 |
– |
\newpage |
| 1357 |
– |
|
| 1358 |
– |
\begin{figure} |
| 1359 |
– |
\begin{center} |
| 1360 |
– |
\epsfxsize=6in |
| 1361 |
– |
\epsfbox{icei_bw.eps} |
| 1362 |
– |
%\caption{The most stable crystal structure assumed by the SSD family |
| 1363 |
– |
%of water models. We refer to this structure as Ice-{\it i} to |
| 1364 |
– |
%indicate its origins in computer simulation. This image was taken of |
| 1365 |
– |
%the (001) face of the crystal.} |
| 1366 |
– |
\label{weirdice} |
| 1367 |
– |
\end{center} |
| 1368 |
– |
\end{figure} |
| 1369 |
– |
|
| 1087 |
|
\end{document} |
