--- trunk/fennellDissertation/iceChapter.tex	2006/08/29 23:34:48	2981
+++ trunk/fennellDissertation/iceChapter.tex	2006/08/30 22:14:37	2986
@@ -8,12 +8,12 @@ available, it is only natural to compare the models un
 These models have been used to investigate important physical
 phenomena like phase transitions and the hydrophobic
 effect.\cite{Yamada02,Marrink94,Gallagher03} With the choice of models
-available, it is only natural to compare the models under interesting
+available, it is only natural to compare them under interesting
 thermodynamic conditions in an attempt to clarify the limitations of
-each of the models.\cite{Jorgensen83,Jorgensen98b,Baez94,Mahoney01}
-Two important property to quantify are the Gibbs and Helmholtz free
-energies, particularly for the solid forms of water, as these predict
-the thermodynamic stability of the various phases. Water has a
+each.\cite{Jorgensen83,Jorgensen98b,Baez94,Mahoney01} Two important
+property to quantify are the Gibbs and Helmholtz free energies,
+particularly for the solid forms of water, as these predict the
+thermodynamic stability of the various phases. Water has a
 particularly rich phase diagram and takes on a number of different and
 stable crystalline structures as the temperature and pressure are
 varied. This complexity makes it a challenging task to investigate the
@@ -279,9 +279,9 @@ TIP3P & -11.41(2) & -11.23(3) & -11.82(3) & -12.30(3) 
 \cmidrule(l){7-8} 
 & \multicolumn{5}{c}{(kcal mol$^{-1}$)} & \multicolumn{2}{c}{(K)}\\
 \midrule
-TIP3P & -11.41(2) & -11.23(3) & -11.82(3) & -12.30(3) & - & 269(7) & 357(4)\\
-TIP4P & -11.84(3) & -12.04(2) & -12.08(3) & - & -12.33(3) & 262(6) & 354(4)\\
 TIP5P & -11.85(3) & -11.86(2) & -11.96(2) & - & -12.29(2) & 266(7) & 337(4)\\
+TIP4P & -11.84(3) & -12.04(2) & -12.08(3) & - & -12.33(3) & 262(6) & 354(4)\\
+TIP3P & -11.41(2) & -11.23(3) & -11.82(3) & -12.30(3) & - & 269(7) & 357(4)\\
 SPC/E & -12.87(2) & -13.05(2) & -13.26(3) & - & -13.55(2) & 299(6) & 396(4)\\
 SSD/E & -11.27(2) & -11.19(4) & -12.09(2) & -12.54(2) & - & *355(4) & -\\
 SSD/RF & -11.96(2) & -11.60(2) & -12.53(3) & -12.79(2) & - & 278(7) & 382(4)\\
@@ -403,7 +403,40 @@ influence the polymorph expressed upon crystallization
 
 \section{Expanded Results Using Damped Shifted Force Electrostatics}
 
+In chapter \ref{chap:electrostatics}, we discussed in detail a
+pairwise method for handling electrostatics (shifted force, {\sc sf})
+that can be used as a simple and efficient replacement for the Ewald
+summation. Answering the question of the free energies of these ice
+polymorphs with varying water models would be an interesting
+application of this technique. To this end, we set up thermodynamic
+integrations of all of the previously discussed ice polymorphs using
+the {\sc sf} technique with a cutoff radius of 12~\AA\ and an $\alpha$
+of 0.2125~\AA . These calculations were performed on TIP5P-E and
+TIP4P-Ew (variants of the root models optimized for the Ewald
+summation) as well as SPC/E, SSD/RF, and TRED (see section
+\ref{sec:tredWater}).
 
+\begin{table}
+\centering
+\caption{HELMHOLTZ FREE ENERGIES OF ICE POLYMORPHS USING THE DAMPED
+SHIFTED FORCE CORRECTION}
+\begin{tabular}{ lccccc }
+\toprule
+\toprule
+Model & I$_\textrm{h}$ & I$_\textrm{c}$ & B & Ice-$i$ & Ice-$i^\prime$ \\
+\cmidrule(lr){2-6}
+& \multicolumn{5}{c}{(kcal mol$^{-1}$)} \\
+\midrule 
+TIP5P-E & -10.76(4) & -10.72(4) & & - & -10.68(4) \\
+TIP4P-Ew & & -11.77(3) & & - & -11.60(3) \\
+SPC/E & -12.98(3) & -11.60(3) & & - & -12.93(3) \\
+SSD/RF & -11.81(4) & -11.65(3) & & -12.41(4) & - \\
+TRED & -12.58(3) & -12.44(3) & & -13.09(4) & - \\
+\end{tabular}
+\label{tab:dampedFreeEnergy}
+\end{table}
+
+
 \section{Conclusions}
 
 In this work, thermodynamic integration was used to determine the
