--- trunk/ssdePaper/nptSSD.tex	2003/09/19 19:29:24	777
+++ trunk/ssdePaper/nptSSD.tex	2003/11/06 23:00:00	856
@@ -36,12 +36,12 @@ for the SSD water model, both with and without the use
 \begin{abstract}
 NVE and NPT molecular dynamics simulations were performed in order to
 investigate the density maximum and temperature dependent transport
-for the SSD water model, both with and without the use of reaction
-field. The constant pressure simulations of the melting of both $I_h$
-and $I_c$ ice showed a density maximum near 260 K. In most cases, the
-calculated densities were significantly lower than the densities
-calculated in simulations of other water models. Analysis of particle
-diffusion showed SSD to capture the transport properties of
+for SSD and related water models, both with and without the use of
+reaction field. The constant pressure simulations of the melting of
+both $I_h$ and $I_c$ ice showed a density maximum near 260 K. In most
+cases, the calculated densities were significantly lower than the
+densities calculated in simulations of other water models. Analysis of
+particle diffusion showed SSD to capture the transport properties of
 experimental very well in both the normal and super-cooled liquid
 regimes. In order to correct the density behavior, SSD was
 reparameterized for use both with and without a long-range interaction
@@ -308,24 +308,26 @@ constant pressure and temperature dynamics. This invol
 \section{Results and discussion}
 
 Melting studies were performed on the randomized ice crystals using
-constant pressure and temperature dynamics. This involved an initial
-randomization of velocities about the starting temperature of 25 K for
-varying amounts of time. The systems were all equilibrated for 100 ps
-prior to a 200 ps data collection run at each temperature setting,
-ranging from 25 to 400 K, with a maximum degree increment of 25 K. For
-regions of interest along this stepwise progression, the temperature
-increment was decreased from 25 K to 10 and then 5 K. The above
-equilibration and production times were sufficient in that the system
-volume fluctuations dampened out in all but the very cold simulations
-(below 225 K). In order to further improve statistics, an ensemble
-average was accumulated from five separate simulation progressions,
-each starting from a different ice crystal.
+constant pressure and temperature dynamics. By performing melting
+simulations, the melting transition can be determined by monitoring
+the heat capacity, in addition to determining the density maximum,
+provided that the density maximum occurs in the liquid and not the
+supercooled regimes. An ensemble average from five separate melting
+simulations was acquired, each starting from different ice crystals
+generated as described previously. All simulations were equilibrated
+for 100 ps prior to a 200 ps data collection run at each temperature
+setting, ranging from 25 to 400 K, with a maximum degree increment of
+25 K. For regions of interest along this stepwise progression, the
+temperature increment was decreased from 25 K to 10 and then 5 K. The
+above equilibration and production times were sufficient in that the
+system volume fluctuations dampened out in all but the very cold
+simulations (below 225 K).
 
 \subsection{Density Behavior}
 In the initial average density versus temperature plot, the density
-maximum clearly appears between 255 and 265 K. The calculated
-densities within this range were nearly indistinguishable, as can be
-seen in the zoom of this region of interest, shown in figure
+maximum appears between 255 and 265 K. The calculated densities within
+this range were nearly indistinguishable, as can be seen in the zoom
+of this region of interest, shown in figure
 \ref{dense1}. The greater certainty of the average value at 260 K makes 
 a good argument for the actual density maximum residing at this
 midpoint value. Figure \ref{dense1} was constructed using ice $I_h$
@@ -341,8 +343,11 @@ TIP3P\cite{Jorgensen98b}, SPC/E\cite{Clancy94}, SSD wi
 \begin{figure}
 \includegraphics[width=65mm,angle=-90]{dense2.eps}
 \caption{Density versus temperature for TIP4P\cite{Jorgensen98b}, 
-TIP3P\cite{Jorgensen98b}, SPC/E\cite{Clancy94}, SSD without Reaction
-Field, SSD, and Experiment\cite{CRC80}. }
+ TIP3P\cite{Jorgensen98b}, SPC/E\cite{Clancy94}, SSD without Reaction
+ Field, SSD, and Experiment\cite{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.\cite{Ichiye03}}
 \label{dense2}
 \end{figure}
 
@@ -570,37 +575,38 @@ soft sticky dipole reaction field (SSD/RF).
 
 \begin{table}
 \caption{Parameters for the original and adjusted models}
-\begin{tabular}{ l  c  c  c } 
+\begin{tabular}{ l  c  c  c  c } 
 \hline \\[-3mm]
-\ Parameters & \ \ \  SSD$^\dagger$\ \ \ \  & \ SSD/E\ \  & \ SSD/RF\ \ \\
+\ \ \ Parameters\ \ \  & \ \ \ SSD$^\dagger$ \ \ \ & \ SSD1$^\ddagger$\ \  & \ SSD/E\ \  & \ SSD/RF \\
 \hline \\[-3mm]
-\ \ \ $\sigma$ (\AA)  & 3.051 & 3.035 & 3.019\\
-\ \ \ $\epsilon$ (kcal/mol)\ \ & 0.152 & 0.152 & 0.152\\
-\ \ \ $\mu$ (D) & 2.35 & 2.418 & 2.480\\
-\ \ \ $\nu_0$ (kcal/mol)\ \ & 3.7284 & 3.90 & 3.90\\
-\ \ \ $r_l$ (\AA) & 2.75 & 2.40 & 2.40\\
-\ \ \ $r_u$ (\AA) & 3.35 & 3.80 & 3.80\\
-\ \ \ $\nu_0^\prime$ (kcal/mol)\ \ & 3.7284 & 3.90 & 3.90\\
-\ \ \ $r_l^\prime$ (\AA) & 2.75 & 2.75 & 2.75\\
-\ \ \ $r_u^\prime$ (\AA) & 4.00 & 3.35 & 3.35\\
+\ \ \ $\sigma$ (\AA)  & 3.051 & 3.016 & 3.035 & 3.019\\
+\ \ \ $\epsilon$ (kcal/mol) & 0.152 & 0.152 & 0.152 & 0.152\\
+\ \ \ $\mu$ (D) & 2.35 & 2.35 & 2.42 & 2.48\\
+\ \ \ $\nu_0$ (kcal/mol) & 3.7284 & 3.6613 & 3.90 & 3.90\\
+\ \ \ $r_l$ (\AA) & 2.75 & 2.75 & 2.40 & 2.40\\
+\ \ \ $r_u$ (\AA) & 3.35 & 3.35 & 3.80 & 3.80\\
+\ \ \ $\nu_0^\prime$ (kcal/mol) & 3.7284 & 3.6613 & 3.90 & 3.90\\
+\ \ \ $r_l^\prime$ (\AA) & 2.75 & 2.75 & 2.75 & 2.75\\
+\ \ \ $r_u^\prime$ (\AA) & 4.00 & 4.00 & 3.35 & 3.35\\
 \\[-2mm]$^\dagger$ ref. \onlinecite{Ichiye96}
+\\$^\ddagger$ ref. \onlinecite{Ichiye03}
 \end{tabular}
 \label{params}
 \end{table}
 
 \begin{figure} 
-\includegraphics[width=85mm]{gofrCompare.epsi} 
+\includegraphics[width=85mm]{GofRCompare.epsi} 
 \caption{Plots comparing experiment\cite{Head-Gordon00_1} with SSD/E 
-and SSD without reaction field (top), as well as SSD/RF and SSD with
+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. Solid Line - experiment, dashed line - SSD/E
-and SSD/RF, and dotted line - SSD (with and without reaction field).}
+and SSD/RF, and dotted line - SSD1 (with and without reaction field).}
 \label{grcompare} 
 \end{figure} 
 
 \begin{figure} 
 \includegraphics[width=85mm]{dualsticky.ps} 
-\caption{Isosurfaces of the sticky potential for SSD (left) and SSD/E \& 
+\caption{Isosurfaces of the sticky potential for SSD1 (left) and SSD/E \& 
 SSD/RF (right). Light areas correspond to the tetrahedral attractive
 part, and the darker areas correspond to the dipolar repulsive part.}
 \label{isosurface} 
@@ -677,12 +683,13 @@ stated earlier in this paper.
 stated earlier in this paper.
 
 \begin{figure} 
-\includegraphics[width=85mm]{ssdecompare.epsi} 
+\includegraphics[width=62mm, angle=-90]{ssdeDense.epsi} 
 \caption{Comparison of densities calculated with SSD/E to SSD without a 
-reaction field, TIP4P\cite{Jorgensen98b}, TIP3P\cite{Jorgensen98b},
-SPC/E\cite{Clancy94}, and Experiment\cite{CRC80}. The upper plot
-includes error bars, and the calculated results from the other
-references were removed for clarity.}
+reaction field, TIP3P\cite{Jorgensen98b}, TIP5P\cite{Jorgensen00},
+SPC/E\cite{Clancy94}, and Experiment\cite{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{figure} 
 
@@ -708,12 +715,13 @@ justify the modifications taken.
 justify the modifications taken.
 
 \begin{figure} 
-\includegraphics[width=85mm]{ssdrfcompare.epsi} 
+\includegraphics[width=62mm, angle=-90]{ssdrfDense.epsi} 
 \caption{Comparison of densities calculated with SSD/RF to SSD with a 
-reaction field, TIP4P\cite{Jorgensen98b}, TIP3P\cite{Jorgensen98b},
-SPC/E\cite{Clancy94}, and Experiment\cite{CRC80}. The upper plot
-includes error bars, and the calculated results from the other
-references were removed for clarity.}
+reaction field, TIP3P\cite{Jorgensen98b}, TIP5P\cite{Jorgensen00},
+SPC/E\cite{Clancy94}, and Experiment\cite{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{figure} 
 
@@ -751,25 +759,29 @@ lower densities with increasing temperature as rapidly
 lower densities with increasing temperature as rapidly.
 
 \begin{figure} 
-\includegraphics[width=85mm]{ssdediffuse.epsi} 
-\caption{Plots of the diffusion constants calculated from SSD/E and SSD,
- both without a reaction field along with experimental results from
- Gillen \emph{et al.}\cite{Gillen72} and Mills\cite{Mills73}. The
- upper plot is at densities calculated from the NPT simulations at a
- pressure of 1 atm, while the lower plot is at the experimentally
- calculated densities.}
-\label{ssdediffuse} 
+\includegraphics[width=65mm, angle=-90]{ssdrfDiffuse.epsi} 
+\caption{Plots of the diffusion constants calculated from SSD/RF and SSD1,
+ both with an active reaction field, along with experimental results
+ from Gillen \emph{et al.}\cite{Gillen72} and Mills\cite{Mills73}. The
+ NVE calculations were performed at the average densities observed in
+ the 1 atm NPT simulations for both of the models. Note how accurately
+ SSD/RF simulates the diffusion of water throughout this temperature
+ range. The more rapidly increasing diffusion constants at high
+ temperatures for both models is attributed to the significantly lower
+ densities than observed in experiment.}
+\label{ssdrfdiffuse} 
 \end{figure} 
 
 \begin{figure} 
-\includegraphics[width=85mm]{ssdrfdiffuse.epsi} 
-\caption{Plots of the diffusion constants calculated from SSD/RF and SSD,
- both with an active reaction field along with experimental results
+\includegraphics[width=65mm, angle=-90]{ssdeDiffuse.epsi} 
+\caption{Plots of the diffusion constants calculated from SSD/E and SSD1,
+ both without a reaction field, along with experimental results are
  from Gillen \emph{et al.}\cite{Gillen72} and Mills\cite{Mills73}. The
- upper plot is at densities calculated from the NPT simulations at a
- pressure of 1 atm, while the lower plot is at the experimentally
- calculated densities.}
-\label{ssdrfdiffuse} 
+ NVE calculations were performed at the average densities observed in
+ the 1 atm NPT simulations for the respective models. SSD/E is
+ slightly more fluid than experiment at all of the temperatures, but
+ it is closer than SSD1 without a long-range correction.}
+\label{ssdediffuse} 
 \end{figure} 
 
 In figure \ref{ssdrfdiffuse}, the diffusion constants for SSD/RF are
