--- trunk/iceiPaper/iceiPaper.tex	2004/09/21 20:12:13	1487
+++ trunk/iceiPaper/iceiPaper.tex	2004/10/07 20:39:44	1542
@@ -147,7 +147,7 @@ location peak in the radial distibution function.
 normally square tetramer into a rhombus with alternating approximately
 85 and 95 degree angles.  The degree of this distortion is model
 dependent and significant enough to split the tetramer diagonal
-location peak in the radial distibution function.
+location peak in the radial distribution function.
 
 \section{Methods}
 
@@ -285,23 +285,23 @@ values.
 
 \begin{table*}
 \begin{minipage}{\linewidth}
-\renewcommand{\thefootnote}{\thempfootnote}
-\begin{center}
+\begin{center}
+
 \caption{Calculated free energies for several ice polymorphs with a 
 variety of common water models. All calculations used a cutoff radius
 of 9 \AA\ and were performed at 200 K and $\sim$1 atm. Units are
-kcal/mol. Calculated error of the final digits is in parentheses. *Ice
-$I_c$ rapidly converts to a liquid at 200 K with the SSD/RF model.}
-\begin{tabular}{ l  c  c  c  c }
+kcal/mol. Calculated error of the final digits is in parentheses.}
+
+\begin{tabular}{lcccc}
 \hline 
 Water Model & $I_h$ & $I_c$ & B & Ice-{\it i}\\
 \hline 
 TIP3P & -11.41(2) & -11.23(3) & -11.82(3) & -12.30(3)\\
 TIP4P & -11.84(3) & -12.04(2) & -12.08(3) & -12.33(3)\\
 TIP5P & -11.85(3) & -11.86(2) & -11.96(2) & -12.29(2)\\
-SPC/E & -12.67(2) & -12.96(2) & -13.25(3) & -13.55(2)\\
+SPC/E & -12.87(2) & -13.05(2) & -13.26(3) & -13.55(2)\\
 SSD/E & -11.27(2) & -11.19(4) & -12.09(2) & -12.54(2)\\
-SSD/RF & -11.51(2) & NA* & -12.08(3) & -12.29(2)\\
+SSD/RF & -11.51(2) & -11.47(2) & -12.08(3) & -12.29(2)\\
 \end{tabular}
 \label{freeEnergy}
 \end{center}
@@ -346,16 +346,17 @@ conservative charge based models.}
 
 \begin{table*}
 \begin{minipage}{\linewidth}
-\renewcommand{\thefootnote}{\thempfootnote}
 \begin{center}
+
 \caption{Melting ($T_m$), boiling ($T_b$), and sublimation ($T_s$) 
 temperatures at 1 atm for several common water models compared with
 experiment. The $T_m$ and $T_s$ values from simulation correspond to a
 transition between Ice-{\it i} (or Ice-{\it i}$^\prime$) and the
 liquid or gas state.}
-\begin{tabular}{ l  c  c  c  c  c  c  c }
+
+\begin{tabular}{lccccccc}
 \hline 
-Equilibria Point & TIP3P & TIP4P & TIP5P & SPC/E & SSD/E & SSD/RF & Exp.\\
+Equilibrium Point & TIP3P & TIP4P & TIP5P & SPC/E & SSD/E & SSD/RF & Exp.\\
 \hline 
 $T_m$ (K)  & 269(4) & 266(5) & 271(4) & 296(3) & - & 278(4) & 273\\
 $T_b$ (K)  & 357(2) & 354(2) & 337(2) & 396(2) & - & 348(2) & 373\\
@@ -394,10 +395,11 @@ TIP3P, and (C) SSD/RF. Data points omitted include SSD
 \begin{figure}
 \includegraphics[width=\linewidth]{cutoffChange.eps}
 \caption{Free energy as a function of cutoff radius for (A) SSD/E, (B) 
-TIP3P, and (C) SSD/RF. Data points omitted include SSD/E: $I_c$ 12
-\AA\, TIP3P: $I_c$ 12 \AA\ and B 12 \AA\, and SSD/RF: $I_c$ 9
-\AA . These crystals are unstable at 200 K and rapidly convert into
-liquids. The connecting lines are qualitative visual aid.}
+TIP3P, and (C) SSD/RF with a reaction field. Both SSD/E and TIP3P show
+significant cutoff radius dependence of the free energy and appear to
+converge when moving to cutoffs greater than 12 \AA. Use of a reaction
+field with SSD/RF results in free energies that exhibit minimal cutoff
+radius dependence.}
 \label{incCutoff}
 \end{figure}
 
@@ -405,52 +407,64 @@ free energy of all the ice polymorphs show a substanti
 computationally efficient water models was done in order to evaluate
 the trend in free energy values when moving to systems that do not
 involve potential truncation. As seen in Fig. \ref{incCutoff}, the
-free energy of all the ice polymorphs show a substantial dependence on
-cutoff radius. In general, there is a narrowing of the free energy
-differences while moving to greater cutoff radius. Interestingly, by
-increasing the cutoff radius, the free energy gap was narrowed enough
-in the SSD/E model that the liquid state is preferred under standard
-simulation conditions (298 K and 1 atm). Thus, it is recommended that
-simulations using this model choose interaction truncation radii
-greater than 9 \AA\ . This narrowing trend is much more subtle in the
-case of SSD/RF, indicating that the free energies calculated with a
-reaction field present provide a more accurate picture of the free
-energy landscape in the absence of potential truncation.
+free energy of all the ice polymorphs for the SSD/E and TIP3P models
+show a substantial dependence on cutoff radius. In general, there is a
+narrowing of the free energy differences while moving to greater
+cutoff radii.  As the free energies for the polymorphs converge, the
+stability advantage that Ice-{\it i} exhibits is reduced; however, it
+remains the most stable polymorph for both of these models over the
+depicted range for both models. This narrowing trend is not
+significant in the case of SSD/RF, indicating that the free energies
+calculated with a reaction field present provide, at minimal
+computational cost, a more accurate picture of the free energy
+landscape in the absence of potential truncation.  Interestingly,
+increasing the cutoff radius a mere 1.5 \AA\ with the SSD/E model
+destabilizes the Ice-{\it i} polymorph enough that the liquid state is
+preferred under standard simulation conditions (298 K and 1
+atm). Thus, it is recommended that simulations using this model choose
+interaction truncation radii greater than 9 \AA. Considering this
+stabilization provided by smaller cutoffs, it is not surprising that
+crystallization into Ice-{\it i} was observed with SSD/E.  The choice
+of a 9 \AA\ cutoff in the previous simulations gives the Ice-{\it i}
+polymorph a greater than 1 kcal/mol lower free energy than the ice
+$I_\textrm{h}$ starting configurations.
 
 To further study the changes resulting to the inclusion of a
 long-range interaction correction, the effect of an Ewald summation
 was estimated by applying the potential energy difference do to its
-inclusion in systems in the presence and absence of the
-correction. This was accomplished by calculation of the potential
-energy of identical crystals both with and without PME. The free
-energies for the investigated polymorphs using the TIP3P and SPC/E
-water models are shown in Table \ref{pmeShift}. The same trend pointed
-out through increase of cutoff radius is observed in these PME
-results. Ice-{\it i} is the preferred polymorph at ambient conditions
-for both the TIP3P and SPC/E water models; however, the narrowing of
-the free energy differences between the various solid forms is
+inclusion in systems in the presence and absence of the correction.
+This was accomplished by calculation of the potential energy of
+identical crystals both with and without PME.  The free energies for
+the investigated polymorphs using the TIP3P and SPC/E water models are
+shown in Table \ref{pmeShift}.  The same trend pointed out through
+increase of cutoff radius is observed in these PME results. Ice-{\it
+i} is the preferred polymorph at ambient conditions for both the TIP3P
+and SPC/E water models; however, the narrowing of the free energy
+differences between the various solid forms with the SPC/E model is
 significant enough that it becomes less clear that it is the most
-stable polymorph with the SPC/E model.  The free energies of Ice-{\it
-i} and ice B nearly overlap within error, with ice $I_c$ just outside
-as well, indicating that Ice-{\it i} might be metastable with respect
-to ice B and possibly ice $I_c$ with SPC/E. However, these results do
-not significantly alter the finding that the Ice-{\it i} polymorph is
-a stable crystal structure that should be considered when studying the
+stable polymorph.  The free energies of Ice-{\it i} and $I_\textrm{c}$
+overlap within error, while ice B and $I_\textrm{h}$ are just outside
+at t slightly higher free energy.  This indicates that with SPC/E,
+Ice-{\it i} might be metastable with all the studied polymorphs,
+particularly ice $I_\textrm{c}$. However, these results do not
+significantly alter the finding that the Ice-{\it i} polymorph is a
+stable crystal structure that should be considered when studying the
 phase behavior of water models.
 
 \begin{table*}
 \begin{minipage}{\linewidth}
-\renewcommand{\thefootnote}{\thempfootnote}
 \begin{center}
+
 \caption{The free energy of the studied ice polymorphs after applying 
 the energy difference attributed to the inclusion of the PME
 long-range interaction correction. Units are kcal/mol.}
-\begin{tabular}{ l  c  c  c  c }
+
+\begin{tabular}{ccccc}
 \hline 
-\ \ Water Model \ \ & \ \ \ \ \ $I_h$ \ \ & \ \ \ \ \ $I_c$ \ \ & \ \quad \ \ \ \ B \ \ & \ \ \ \ \ Ice-{\it i} \ \ \\
+Water Model &  $I_h$ & $I_c$ &  B & Ice-{\it i} \\
 \hline 
-TIP3P  & -11.53(2) & -11.24(3) & -11.51(3) & -11.67(3)\\
-SPC/E  & -12.77(2) & -12.92(2) & -12.96(3) & -13.02(2)\\
+TIP3P  & -11.53(2) & -11.24(3) & -11.51(3) & -11.67(3) \\
+SPC/E  & -12.97(2) & -13.00(2) & -12.96(3) & -13.02(2) \\
 \end{tabular}
 \label{pmeShift}
 \end{center}
