--- trunk/ssdePaper/nptSSD.tex 2004/02/06 19:15:44 1033 +++ trunk/ssdePaper/nptSSD.tex 2004/02/09 14:42:27 1040 @@ -1,38 +1,37 @@ %\documentclass[prb,aps,times,twocolumn,tabularx]{revtex4} -\documentclass[preprint,aps]{revtex4} -%\documentclass[11pt]{article} -%\usepackage{endfloat} +%\documentclass[preprint,aps,endfloat]{revtex4} +\documentclass[11pt]{article} +\usepackage{endfloat} \usepackage{amsmath} \usepackage{epsf} \usepackage{berkeley} \usepackage{setspace} \usepackage{tabularx} \usepackage{graphicx} -%\usepackage[ref]{overcite} -%\usepackage{curves} -%\pagestyle{plain} -%\pagenumbering{arabic} -%\oddsidemargin 0.0cm \evensidemargin 0.0cm -%\topmargin -21pt \headsep 10pt -%\textheight 9.0in \textwidth 6.5in -%\brokenpenalty=10000 -%\renewcommand{\baselinestretch}{1.2} +\usepackage[ref]{overcite} +\pagestyle{plain} +\pagenumbering{arabic} +\oddsidemargin 0.0cm \evensidemargin 0.0cm +\topmargin -21pt \headsep 10pt +\textheight 9.0in \textwidth 6.5in +\brokenpenalty=10000 + %\renewcommand\citemid{\ } % no comma in optional reference note -\newcounter{captions} -\newcounter{figs} \begin{document} \title{On the structural and transport properties of the soft sticky dipole (SSD) and related single point water models} -\author{Christopher J. Fennell and J. Daniel Gezelter\footnote{Corresponding author. \ Electronic mail: gezelter@nd.edu}} - -\affiliation{Department of Chemistry and Biochemistry\\ University of Notre Dame\\ +\author{Christopher J. Fennell and J. Daniel +Gezelter\footnote{Corresponding author. \ Electronic mail: +gezelter@nd.edu} \\ Department of Chemistry and Biochemistry\\ University of Notre Dame\\ Notre Dame, Indiana 46556} \date{\today} +\maketitle +\doublespacing \begin{abstract} The density maximum and temperature dependence of the self-diffusion @@ -47,7 +46,7 @@ experimental water very well in both the normal and su calculated densities which were were significantly lower than experimental densities. Analysis of self-diffusion constants shows that the original SSD model captures the transport properties of -experimental water very well in both the normal and super-cooled +experimental water very well in both the normal and supercooled liquid regimes. We also present our reparameterized versions of SSD for use both with the reaction field or without any long-range electrostatic corrections. These are called the SSD/RF and SSD/E @@ -60,13 +59,10 @@ family. family. \end{abstract} -\maketitle - \newpage %\narrowtext - %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% % BODY OF TEXT %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% @@ -287,17 +283,17 @@ time steps is illustrated in figure time steps is illustrated in figure \ref{timestep}. -%\begin{figure} -%\begin{center} -%\epsfxsize=6in -%\epsfbox{timeStep.epsi} -%\caption{Energy conservation using both quaternion-based integration and -%the {\sc dlm} method with increasing time step. The larger time step -%plots are shifted from the true energy baseline (that of $\Delta t$ = -%0.1~fs) for clarity.} -%\label{timestep} -%\end{center} -%\end{figure} +\begin{figure} +\begin{center} +\epsfxsize=6in +\epsfbox{timeStep.epsi} +\caption{Energy conservation using both quaternion-based integration and the +{\sc dlm} method with increasing time step. The larger time step plots +are shifted from the true energy baseline (that of $\Delta t$ = +0.1~fs) for clarity.} +\label{timestep} +\end{center} +\end{figure} In figure \ref{timestep}, the resulting energy drift at various time steps for both the {\sc dlm} and quaternion integration schemes is @@ -372,20 +368,20 @@ maximum in this same region (between 255 and 260~K). configurations showed similar results, with a liquid-phase density maximum in this same region (between 255 and 260~K). -%\begin{figure} -%\begin{center} -%\epsfxsize=6in -%\epsfbox{denseSSDnew.eps} -%\caption{Density versus temperature for TIP4P [Ref. \onlinecite{Jorgensen98b}], -% TIP3P [Ref. \onlinecite{Jorgensen98b}], SPC/E [Ref. \onlinecite{Clancy94}], SSD -% without Reaction Field, SSD, and experiment [Ref. \onlinecite{CRC80}]. The -% arrows indicate the change in densities observed when turning off the -% reaction field. The the lower than expected densities for the SSD -% model were what prompted the original reparameterization of SSD1 -% [Ref. \onlinecite{Ichiye03}].} -%\label{dense1} -%\end{center} -%\end{figure} +\begin{figure} +\begin{center} +\epsfxsize=6in +\epsfbox{denseSSDnew.eps} +\caption{ Density versus temperature for TIP4P [Ref. \citen{Jorgensen98b}], + TIP3P [Ref. \citen{Jorgensen98b}], SPC/E [Ref. \citen{Clancy94}], SSD + without Reaction Field, SSD, and experiment [Ref. \citen{CRC80}]. The + arrows indicate the change in densities observed when turning off the + reaction field. The the lower than expected densities for the SSD + model were what prompted the original reparameterization of SSD1 + [Ref. \citen{Ichiye03}].} +\label{dense1} +\end{center} +\end{figure} The density maximum for SSD compares quite favorably to other simple water models. Figure \ref{dense1} also shows calculated @@ -456,20 +452,20 @@ results.\cite{Gillen72,Holz00,Clancy94,Jorgensen01} \ref{diffuse}, alongside experimental, SPC/E, and TIP5P results.\cite{Gillen72,Holz00,Clancy94,Jorgensen01} -%\begin{figure} -%\begin{center} -%\epsfxsize=6in -%\epsfbox{betterDiffuse.epsi} -%\caption{Average self-diffusion constant as a function of temperature for -%SSD, SPC/E [Ref. \onlinecite{Clancy94}], and TIP5P -%[Ref. \onlinecite{Jorgensen01}] compared with experimental data -%[Refs. \onlinecite{Gillen72} and \onlinecite{Holz00}]. Of the three water models -%shown, SSD has the least deviation from the experimental values. The -%rapidly increasing diffusion constants for TIP5P and SSD correspond to -%significant decreases in density at the higher temperatures.} -%\label{diffuse} -%\end{center} -%\end{figure} +\begin{figure} +\begin{center} +\epsfxsize=6in +\epsfbox{betterDiffuse.epsi} +\caption{ Average self-diffusion constant as a function of temperature for +SSD, SPC/E [Ref. \citen{Clancy94}], and TIP5P +[Ref. \citen{Jorgensen01}] compared with experimental data +[Refs. \citen{Gillen72} and \citen{Holz00}]. Of the three water models +shown, SSD has the least deviation from the experimental values. The +rapidly increasing diffusion constants for TIP5P and SSD correspond to +significant decreases in density at the higher temperatures.} +\label{diffuse} +\end{center} +\end{figure} The observed values for the diffusion constant point out one of the strengths of the SSD model. Of the three models shown, the SSD model @@ -499,27 +495,27 @@ considerably lower than the experimental value. transition occurs at 235~K. These melting transitions are considerably lower than the experimental value. -%\begin{figure} -%\begin{center} -%\epsfxsize=6in -%\epsfbox{corrDiag.eps} -%\caption{An illustration of angles involved in the correlations observed in Fig. \ref{contour}.} -%\label{corrAngle} -%\end{center} -%\end{figure} +\begin{figure} +\begin{center} +\epsfxsize=6in +\epsfbox{fullContours.eps} +\caption{ Contour plots of 2D angular pair correlation functions for +512 SSD molecules at 100~K (A \& B) and 300~K (C \& D). Dark areas +signify regions of enhanced density while light areas signify +depletion relative to the bulk density. White areas have pair +correlation values below 0.5 and black areas have values above 1.5.} +\label{contour} +\end{center} +\end{figure} -%\begin{figure} -%\begin{center} -%\epsfxsize=6in -%\epsfbox{fullContours.eps} -%\caption{Contour plots of 2D angular pair correlation functions for -%512 SSD molecules at 100~K (A \& B) and 300~K (C \& D). Dark areas -%signify regions of enhanced density while light areas signify -%depletion relative to the bulk density. White areas have pair -%correlation values below 0.5 and black areas have values above 1.5.} -%\label{contour} -%\end{center} -%\end{figure} +\begin{figure} +\begin{center} +\epsfxsize=6in +\epsfbox{corrDiag.eps} +\caption{ An illustration of angles involved in the correlations observed in Fig. \ref{contour}.} +\label{corrAngle} +\end{center} +\end{figure} Additional analysis of the melting process was performed using two-dimensional structure and dipole angle correlations. Expressions @@ -612,11 +608,11 @@ the liquid structure in simulations without a long-ran \begin{table} \begin{center} -\caption{Parameters for the original and adjusted models} +\caption{ Parameters for the original and adjusted models} \begin{tabular}{ l c c c c } \hline \\[-3mm] -\ \ \ Parameters\ \ \ & \ \ \ SSD [Ref. \onlinecite{Ichiye96}] \ \ \ -& \ SSD1 [Ref. \onlinecite{Ichiye03}]\ \ & \ SSD/E\ \ & \ \ SSD/RF \\ +\ \ \ Parameters\ \ \ & \ \ \ SSD [Ref. \citen{Ichiye96}] \ \ \ +& \ SSD1 [Ref. \citen{Ichiye03}]\ \ & \ SSD/E\ \ & \ \ SSD/RF \\ \hline \\[-3mm] \ \ \ $\sigma$ (\AA) & 3.051 & 3.016 & 3.035 & 3.019\\ \ \ \ $\epsilon$ (kcal/mol) & 0.152 & 0.152 & 0.152 & 0.152\\ @@ -632,31 +628,31 @@ the liquid structure in simulations without a long-ran \end{center} \end{table} -%\begin{figure} -%\begin{center} -%\epsfxsize=5in -%\epsfbox{GofRCompare.epsi} -%\caption{Plots comparing experiment [Ref. \onlinecite{Head-Gordon00_1}] with -%SSD/E and SSD1 without reaction field (top), as well as -%SSD/RF and SSD1 with reaction field turned on -%(bottom). The insets show the respective first peaks in detail. Note -%how the changes in parameters have lowered and broadened the first -%peak of SSD/E and SSD/RF.} -%\label{grcompare} -%\end{center} -%\end{figure} +\begin{figure} +\begin{center} +\epsfxsize=5in +\epsfbox{GofRCompare.epsi} +\caption{ Plots comparing experiment [Ref. \citen{Head-Gordon00_1}] with +SSD/E and SSD1 without reaction field (top), as well as +SSD/RF and SSD1 with reaction field turned on +(bottom). The insets show the respective first peaks in detail. Note +how the changes in parameters have lowered and broadened the first +peak of SSD/E and SSD/RF.} +\label{grcompare} +\end{center} +\end{figure} -%\begin{figure} -%\begin{center} -%\epsfxsize=6in -%\epsfbox{dualsticky_bw.eps} -%\caption{Positive and negative isosurfaces of the sticky potential for -%SSD1 (left) and SSD/E \& SSD/RF (right). Light areas -%correspond to the tetrahedral attractive component, and darker areas -%correspond to the dipolar repulsive component.} -%\label{isosurface} -%\end{center} -%\end{figure} +\begin{figure} +\begin{center} +\epsfxsize=6in +\epsfbox{dualsticky_bw.eps} +\caption{ Positive and negative isosurfaces of the sticky potential for +SSD1 (left) and SSD/E \& SSD/RF (right). Light areas +correspond to the tetrahedral attractive component, and darker areas +correspond to the dipolar repulsive component.} +\label{isosurface} +\end{center} +\end{figure} In the original paper detailing the development of SSD, Liu and Ichiye placed particular emphasis on an accurate description of the first @@ -728,22 +724,22 @@ collection times as stated previously. simulations had the same thermalization, equilibration, and data collection times as stated previously. -%\begin{figure} -%\begin{center} -%\epsfxsize=6in -%\epsfbox{ssdeDense.epsi} -%\caption{Comparison of densities calculated with SSD/E to -%SSD1 without a reaction field, TIP3P [Ref. \onlinecite{Jorgensen98b}], -%TIP5P [Ref. \onlinecite{Jorgensen00}], SPC/E [Ref. \onlinecite{Clancy94}] and -%experiment [Ref. \onlinecite{CRC80}]. The window shows a expansion around -%300 K with error bars included to clarify this region of -%interest. Note that both SSD1 and SSD/E show good agreement with -%experiment when the long-range correction is neglected.} -%\label{ssdedense} -%\end{center} -%\end{figure} +\begin{figure} +\begin{center} +\epsfxsize=6in +\epsfbox{ssdeDense.epsi} +\caption{ Comparison of densities calculated with SSD/E to +SSD1 without a reaction field, TIP3P [Ref. \citen{Jorgensen98b}], +TIP5P [Ref. \citen{Jorgensen00}], SPC/E [Ref. \citen{Clancy94}] and +experiment [Ref. \citen{CRC80}]. The window shows a expansion around +300 K with error bars included to clarify this region of +interest. Note that both SSD1 and SSD/E show good agreement with +experiment when the long-range correction is neglected.} +\label{ssdedense} +\end{center} +\end{figure} -Fig. \ref{ssdedense} shows the density profile for the SSD/E +Figure \ref{ssdedense} shows the density profile for the SSD/E model in comparison to SSD1 without a reaction field, other common water models, and experimental results. The calculated densities for both SSD/E and SSD1 have increased @@ -756,7 +752,7 @@ improved the structuring of the liquid (as seen in fig better than the SSD value of 0.967$\pm$0.003 g/cm$^3$. The changes to the dipole moment and sticky switching functions have improved the structuring of the liquid (as seen in figure -\ref{grcompare}, but they have shifted the density maximum to much +\ref{grcompare}), but they have shifted the density maximum to much lower temperatures. This comes about via an increase in the liquid disorder through the weakening of the sticky potential and strengthening of the dipolar character. However, this increasing @@ -765,21 +761,21 @@ same transition temperature observed with SSD and SSD1 melting transition for SSD/E was shown to occur at 235~K. The same transition temperature observed with SSD and SSD1. -%\begin{figure} -%\begin{center} -%\epsfxsize=6in -%\epsfbox{ssdrfDense.epsi} -%\caption{Comparison of densities calculated with SSD/RF to -%SSD1 with a reaction field, TIP3P [Ref. \onlinecite{Jorgensen98b}], -%TIP5P [Ref. \onlinecite{Jorgensen00}], SPC/E [Ref. \onlinecite{Clancy94}], and -%experiment [Ref. \onlinecite{CRC80}]. The inset shows the necessity of -%reparameterization when utilizing a reaction field long-ranged -%correction - SSD/RF provides significantly more accurate -%densities than SSD1 when performing room temperature -%simulations.} -%\label{ssdrfdense} -%\end{center} -%\end{figure} +\begin{figure} +\begin{center} +\epsfxsize=6in +\epsfbox{ssdrfDense.epsi} +\caption{ Comparison of densities calculated with SSD/RF to +SSD1 with a reaction field, TIP3P [Ref. \citen{Jorgensen98b}], +TIP5P [Ref. \citen{Jorgensen00}], SPC/E [Ref. \citen{Clancy94}], and +experiment [Ref. \citen{CRC80}]. The inset shows the necessity of +reparameterization when utilizing a reaction field long-ranged +correction - SSD/RF provides significantly more accurate +densities than SSD1 when performing room temperature +simulations.} +\label{ssdrfdense} +\end{center} +\end{figure} Including the reaction field long-range correction in the simulations results in a more interesting comparison. A density profile including @@ -799,21 +795,21 @@ maximum at 255~K, fairly close to the density maxima o maximum at 255~K, fairly close to the density maxima of 260~K and 265~K, shown by SSD and SSD1 respectively. -%\begin{figure} -%\begin{center} -%\epsfxsize=6in -%\epsfbox{ssdeDiffuse.epsi} -%\caption{The diffusion constants calculated from SSD/E and -%SSD1 (both without a reaction field) along with experimental results -%[Refs. \onlinecite{Gillen72} and \onlinecite{Holz00}]. The NVE calculations were -%performed at the average densities observed in the 1 atm NPT -%simulations for the respective models. SSD/E is slightly more mobile -%than experiment at all of the temperatures, but it is closer to -%experiment at biologically relevant temperatures than SSD1 without a -%long-range correction.} -%\label{ssdediffuse} -%\end{center} -%\end{figure} +\begin{figure} +\begin{center} +\epsfxsize=6in +\epsfbox{ssdeDiffuse.epsi} +\caption{ The diffusion constants calculated from SSD/E and +SSD1 (both without a reaction field) along with experimental results +[Refs. \citen{Gillen72} and \citen{Holz00}]. The NVE calculations were +performed at the average densities observed in the 1 atm NPT +simulations for the respective models. SSD/E is slightly more mobile +than experiment at all of the temperatures, but it is closer to +experiment at biologically relevant temperatures than SSD1 without a +long-range correction.} +\label{ssdediffuse} +\end{center} +\end{figure} The reparameterization of the SSD water model, both for use with and without an applied long-range correction, brought the densities up to @@ -840,22 +836,22 @@ conditions. of SSD/E relative to SSD1 under the most commonly simulated conditions. -%\begin{figure} -%\begin{center} -%\epsfxsize=6in -%\epsfbox{ssdrfDiffuse.epsi} -%\caption{The diffusion constants calculated from SSD/RF and -%SSD1 (both with an active reaction field) along with -%experimental results [Refs. \onlinecite{Gillen72} and \onlinecite{Holz00}]. The -%NVE calculations were performed at the average densities observed in -%the 1 atm NPT simulations for both of the models. SSD/RF -%simulates the diffusion of water throughout this temperature range -%very well. The rapidly increasing diffusion constants at high -%temperatures for both models can be attributed to lower calculated -%densities than those observed in experiment.} -%\label{ssdrfdiffuse} -%\end{center} -%\end{figure} +\begin{figure} +\begin{center} +\epsfxsize=6in +\epsfbox{ssdrfDiffuse.epsi} +\caption{ The diffusion constants calculated from SSD/RF and +SSD1 (both with an active reaction field) along with +experimental results [Refs. \citen{Gillen72} and \citen{Holz00}]. The +NVE calculations were performed at the average densities observed in +the 1 atm NPT simulations for both of the models. SSD/RF +simulates the diffusion of water throughout this temperature range +very well. The rapidly increasing diffusion constants at high +temperatures for both models can be attributed to lower calculated +densities than those observed in experiment.} +\label{ssdrfdiffuse} +\end{center} +\end{figure} In figure \ref{ssdrfdiffuse}, the diffusion constants for SSD/RF are compared to SSD1 with an active reaction field. Note that SSD/RF @@ -874,7 +870,7 @@ reparameterization when using an altered long-range co \begin{minipage}{\linewidth} \renewcommand{\thefootnote}{\thempfootnote} \begin{center} -\caption{Properties of the single-point water models compared with +\caption{ Properties of the single-point water models compared with experimental data at ambient conditions. Deviations of the of the averages are given in parentheses.} \begin{tabular}{ l c c c c c } @@ -887,13 +883,13 @@ Ref. \onlinecite{Head-Gordon00_1}} \\ \ \ $D$ ($10^{-5}$ cm$^2$/s) & 1.78(0.7) & 2.51(0.18) & 2.00(0.17) & 2.32(0.06) & 2.299\cite{Mills73} \\ \ \ Coordination Number ($n_C$) & 3.9 & 4.3 & 3.8 & 4.4 & 4.7\footnote{Calculated by integrating $g_{\text{OO}}(r)$ in -Ref. \onlinecite{Head-Gordon00_1}} \\ +Ref. \citen{Head-Gordon00_1}} \\ \ \ H-bonds per particle ($n_H$) & 3.7 & 3.6 & 3.7 & 3.7 & 3.5\footnote{Calculated by integrating $g_{\text{OH}}(r)$ in -Ref. \onlinecite{Soper86}} \\ -\ \ $\tau_1$ (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}} \\ +Ref. \citen{Soper86}} \\ +\ \ $\tau_1$ (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}} \\ \ \ $\tau_2$ (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 -Ref. \onlinecite{Krynicki66}} +Ref. \citen{Krynicki66}} \end{tabular} \label{liquidproperties} \end{center} @@ -942,13 +938,13 @@ the NMR data in Ref. \onlinecite{Krynicki66} at a temp averaged over five detailed NVE simulations performed at the ambient conditions for each of the respective models. It should be noted that the commonly cited value of 1.9 ps for $\tau_2$ was determined from -the NMR data in Ref. \onlinecite{Krynicki66} at a temperature near +the NMR data in Ref. \citen{Krynicki66} at a temperature near 34$^\circ$C.\cite{Rahman71} Because of the strong temperature dependence of $\tau_2$, it is necessary to recalculate it at 298~K to make proper comparisons. The value shown in Table \ref{liquidproperties} was calculated from the same NMR data in the -fashion described in Ref. \onlinecite{Krynicki66}. Similarly, $\tau_1$ was -recomputed for 298~K from the data in Ref. \onlinecite{Eisenberg69}. +fashion described in Ref. \citen{Krynicki66}. Similarly, $\tau_1$ was +recomputed for 298~K from the data in Ref. \citen{Eisenberg69}. Again, SSD/E and SSD/RF show improved behavior over SSD1, both with and without an active reaction field. Turning on the reaction field leads to much improved time constants for SSD1; however, these results @@ -959,17 +955,17 @@ can be attributed to the use of the Ewald sum.\cite{Ic \subsection{Additional Observations} -%\begin{figure} -%\begin{center} -%\epsfxsize=6in -%\epsfbox{icei_bw.eps} -%\caption{The most stable crystal structure assumed by the SSD family -%of water models. We refer to this structure as Ice-{\it i} to -%indicate its origins in computer simulation. This image was taken of -%the (001) face of the crystal.} -%\label{weirdice} -%\end{center} -%\end{figure} +\begin{figure} +\begin{center} +\epsfxsize=6in +\epsfbox{icei_bw.eps} +\caption{ The most stable crystal structure assumed by the SSD family +of water models. We refer to this structure as Ice-{\it i} to +indicate its origins in computer simulation. This image was taken of +the (001) face of the crystal.} +\label{weirdice} +\end{center} +\end{figure} While performing a series of melting simulations on an early iteration of SSD/E not discussed in this paper, we observed @@ -1010,7 +1006,7 @@ family, Ice-{\it i} had the lowest calculated enthalpy \begin{table} \begin{center} -\caption{Enthalpies of Formation (in kcal / mol) of the three crystal +\caption{ Enthalpies of Formation (in kcal / mol) of the three crystal structures (at 1 K) exhibited by the SSD family of water models} \begin{tabular}{ l c c c } \hline \\[-3mm] @@ -1086,285 +1082,6 @@ DMR-0079647. \bibliographystyle{jcp} \bibliography{nptSSD} - -\newpage - -\begin{list} - {Figure \arabic{captions}: }{\usecounter{captions} - \setlength{\rightmargin}{\leftmargin}} - -\item Energy conservation using both quaternion-based integration and -the {\sc dlm} method with increasing time step. The larger time step -plots are shifted from the true energy baseline (that of $\Delta t$ = -0.1~fs) for clarity. - -\item Density versus temperature for TIP4P [Ref. \onlinecite{Jorgensen98b}], -TIP3P [Ref. \onlinecite{Jorgensen98b}], SPC/E -[Ref. \onlinecite{Clancy94}], SSD without Reaction Field, SSD, and -experiment [Ref. \onlinecite{CRC80}]. The arrows indicate the change -in densities observed when turning off the reaction field. The the -lower than expected densities for the SSD model were what prompted the -original reparameterization of SSD1 [Ref. \onlinecite{Ichiye03}]. - -\item Average self-diffusion constant as a function of temperature for -SSD, SPC/E [Ref. \onlinecite{Clancy94}], and TIP5P -[Ref. \onlinecite{Jorgensen01}] compared with experimental data -[Refs. \onlinecite{Gillen72} and \onlinecite{Holz00}]. Of the three -water models shown, SSD has the least deviation from the experimental -values. The rapidly increasing diffusion constants for TIP5P and SSD -correspond to significant decreases in density at the higher -temperatures. - -\item An illustration of angles involved in the correlations observed in -Fig. \ref{contour}. - -\item Contour plots of 2D angular pair correlation functions for -512 SSD molecules at 100~K (A \& B) and 300~K (C \& D). Dark areas -signify regions of enhanced density while light areas signify -depletion relative to the bulk density. White areas have pair -correlation values below 0.5 and black areas have values above 1.5. -\item Plots comparing experiment [Ref. \onlinecite{Head-Gordon00_1}] with -SSD/E and SSD1 without reaction field (top), as well as SSD/RF and -SSD1 with reaction field turned on (bottom). The insets show the -respective first peaks in detail. Note how the changes in parameters -have lowered and broadened the first peak of SSD/E and SSD/RF. -\item Positive and negative isosurfaces of the sticky potential for -SSD1 (left) and SSD/E \& SSD/RF (right). Light areas -correspond to the tetrahedral attractive component, and darker areas -correspond to the dipolar repulsive component. - -\item Comparison of densities calculated with SSD/E to -SSD1 without a reaction field, TIP3P [Ref. \onlinecite{Jorgensen98b}], -TIP5P [Ref. \onlinecite{Jorgensen00}], SPC/E [Ref. \onlinecite{Clancy94}] and -experiment [Ref. \onlinecite{CRC80}]. The window shows a expansion around -300 K with error bars included to clarify this region of -interest. Note that both SSD1 and SSD/E show good agreement with -experiment when the long-range correction is neglected. - -\item Comparison of densities calculated with SSD/RF to -SSD1 with a reaction field, TIP3P [Ref. \onlinecite{Jorgensen98b}], -TIP5P [Ref. \onlinecite{Jorgensen00}], SPC/E [Ref. \onlinecite{Clancy94}], and -experiment [Ref. \onlinecite{CRC80}]. The inset shows the necessity of -reparameterization when utilizing a reaction field long-ranged -correction - SSD/RF provides significantly more accurate -densities than SSD1 when performing room temperature -simulations. - -\item The diffusion constants calculated from SSD/E and -SSD1 (both without a reaction field) along with experimental results -[Refs. \onlinecite{Gillen72} and \onlinecite{Holz00}]. The NVE calculations were -performed at the average densities observed in the 1 atm NPT -simulations for the respective models. SSD/E is slightly more mobile -than experiment at all of the temperatures, but it is closer to -experiment at biologically relevant temperatures than SSD1 without a -long-range correction. - -\item The diffusion constants calculated from SSD/RF and -SSD1 (both with an active reaction field) along with -experimental results [Refs. \onlinecite{Gillen72} and \onlinecite{Holz00}]. The -NVE calculations were performed at the average densities observed in -the 1 atm NPT simulations for both of the models. SSD/RF -simulates the diffusion of water throughout this temperature range -very well. The rapidly increasing diffusion constants at high -temperatures for both models can be attributed to lower calculated -densities than those observed in experiment. - -\item The most stable crystal structure assumed by the SSD family -of water models. We refer to this structure as Ice-{\it i} to -indicate its origins in computer simulation. This image was taken of -the (001) face of the crystal. -\end{list} - -\newpage - -\begin{figure} -\begin{center} -\epsfxsize=6in -\epsfbox{timeStep.epsi} -%\caption{Energy conservation using both quaternion-based integration and -%the {\sc dlm} method with increasing time step. The larger time step -%plots are shifted from the true energy baseline (that of $\Delta t$ = -%0.1~fs) for clarity.} -\label{timestep} -\end{center} -\end{figure} - -\newpage - -\begin{figure} -\begin{center} -\epsfxsize=6in -\epsfbox{denseSSDnew.eps} -%\caption{Density versus temperature for TIP4P [Ref. \onlinecite{Jorgensen98b}], -% TIP3P [Ref. \onlinecite{Jorgensen98b}], SPC/E [Ref. \onlinecite{Clancy94}], SSD -% without Reaction Field, SSD, and experiment [Ref. \onlinecite{CRC80}]. The -% arrows indicate the change in densities observed when turning off the -% reaction field. The the lower than expected densities for the SSD -% model were what prompted the original reparameterization of SSD1 -% [Ref. \onlinecite{Ichiye03}].} -\label{dense1} -\end{center} -\end{figure} - -\newpage - -\begin{figure} -\begin{center} -\epsfxsize=6in -\epsfbox{betterDiffuse.epsi} -%\caption{Average self-diffusion constant as a function of temperature for -%SSD, SPC/E [Ref. \onlinecite{Clancy94}], and TIP5P -%[Ref. \onlinecite{Jorgensen01}] compared with experimental data -%[Refs. \onlinecite{Gillen72} and \onlinecite{Holz00}]. Of the three water models -%shown, SSD has the least deviation from the experimental values. The -%rapidly increasing diffusion constants for TIP5P and SSD correspond to -%significant decreases in density at the higher temperatures.} -\label{diffuse} -\end{center} -\end{figure} - -\newpage - -\begin{figure} -\begin{center} -\epsfxsize=6in -\epsfbox{corrDiag.eps} -%\caption{An illustration of angles involved in the correlations observed in Fig. \ref{contour}.} -\label{corrAngle} -\end{center} -\end{figure} - -\newpage - -\begin{figure} -\begin{center} -\epsfxsize=6in -\epsfbox{fullContours.eps} -%\caption{Contour plots of 2D angular pair correlation functions for -%512 SSD molecules at 100~K (A \& B) and 300~K (C \& D). Dark areas -%signify regions of enhanced density while light areas signify -%depletion relative to the bulk density. White areas have pair -%correlation values below 0.5 and black areas have values above 1.5.} -\label{contour} -\end{center} -\end{figure} - -\newpage - -\begin{figure} -\begin{center} -\epsfxsize=6in -\epsfbox{GofRCompare.epsi} -%\caption{Plots comparing experiment [Ref. \onlinecite{Head-Gordon00_1}] with -%SSD/E and SSD1 without reaction field (top), as well as -%SSD/RF and SSD1 with reaction field turned on -%(bottom). The insets show the respective first peaks in detail. Note -%how the changes in parameters have lowered and broadened the first -%peak of SSD/E and SSD/RF.} -\label{grcompare} -\end{center} -\end{figure} - -\newpage - -\begin{figure} -\begin{center} -\epsfxsize=7in -\epsfbox{dualsticky_bw.eps} -%\caption{Positive and negative isosurfaces of the sticky potential for -%SSD1 (left) and SSD/E \& SSD/RF (right). Light areas -%correspond to the tetrahedral attractive component, and darker areas -%correspond to the dipolar repulsive component.} -\label{isosurface} -\end{center} -\end{figure} - -\newpage - -\begin{figure} -\begin{center} -\epsfxsize=6in -\epsfbox{ssdeDense.epsi} -%\caption{Comparison of densities calculated with SSD/E to -%SSD1 without a reaction field, TIP3P [Ref. \onlinecite{Jorgensen98b}], -%TIP5P [Ref. \onlinecite{Jorgensen00}], SPC/E [Ref. \onlinecite{Clancy94}] and -%experiment [Ref. \onlinecite{CRC80}]. The window shows a expansion around -%300 K with error bars included to clarify this region of -%interest. Note that both SSD1 and SSD/E show good agreement with -%experiment when the long-range correction is neglected.} -\label{ssdedense} -\end{center} -\end{figure} - -\newpage - -\begin{figure} -\begin{center} -\epsfxsize=6in -\epsfbox{ssdrfDense.epsi} -%\caption{Comparison of densities calculated with SSD/RF to -%SSD1 with a reaction field, TIP3P [Ref. \onlinecite{Jorgensen98b}], -%TIP5P [Ref. \onlinecite{Jorgensen00}], SPC/E [Ref. \onlinecite{Clancy94}], and -%experiment [Ref. \onlinecite{CRC80}]. The inset shows the necessity of -%reparameterization when utilizing a reaction field long-ranged -%correction - SSD/RF provides significantly more accurate -%densities than SSD1 when performing room temperature -%simulations.} -\label{ssdrfdense} -\end{center} -\end{figure} - -\newpage - - \begin{figure} -\begin{center} -\epsfxsize=6in -\epsfbox{ssdeDiffuse.epsi} -%\caption{The diffusion constants calculated from SSD/E and -%SSD1 (both without a reaction field) along with experimental results -%[Refs. \onlinecite{Gillen72} and \onlinecite{Holz00}]. The NVE calculations were -%performed at the average densities observed in the 1 atm NPT -%simulations for the respective models. SSD/E is slightly more mobile -%than experiment at all of the temperatures, but it is closer to -%experiment at biologically relevant temperatures than SSD1 without a -%long-range correction.} -\label{ssdediffuse} -\end{center} -\end{figure} - -\newpage - -\begin{figure} -\begin{center} -\epsfxsize=6in -\epsfbox{ssdrfDiffuse.epsi} -%\caption{The diffusion constants calculated from SSD/RF and -%SSD1 (both with an active reaction field) along with -%experimental results [Refs. \onlinecite{Gillen72} and \onlinecite{Holz00}]. The -%NVE calculations were performed at the average densities observed in -%the 1 atm NPT simulations for both of the models. SSD/RF -%simulates the diffusion of water throughout this temperature range -%very well. The rapidly increasing diffusion constants at high -%temperatures for both models can be attributed to lower calculated -%densities than those observed in experiment.} -\label{ssdrfdiffuse} -\end{center} -\end{figure} - -\newpage - -\begin{figure} -\begin{center} -\epsfxsize=6in -\epsfbox{icei_bw.eps} -%\caption{The most stable crystal structure assumed by the SSD family -%of water models. We refer to this structure as Ice-{\it i} to -%indicate its origins in computer simulation. This image was taken of -%the (001) face of the crystal.} -\label{weirdice} -\end{center} -\end{figure} - \end{document}