--- trunk/iceiPaper/iceiPaper.tex 2005/01/07 18:42:41 1908 +++ trunk/iceiPaper/iceiPaper.tex 2005/01/07 20:57:50 1909 @@ -1,9 +1,10 @@ %\documentclass[prb,aps,twocolumn,tabularx]{revtex4} -\documentclass[11pt]{article} +\documentclass[12pt]{article} \usepackage{endfloat} \usepackage{amsmath} \usepackage{epsf} -\usepackage{berkeley} +\usepackage{times} +\usepackage{mathptm} \usepackage{setspace} \usepackage{tabularx} \usepackage{graphicx} @@ -191,13 +192,14 @@ ice crystal at 200 K. For these studies, $K_\mathrm{r of and rotation around the principle axis of the molecule respectively. These spring constants are typically calculated from the mean-square displacements of water molecules in an unrestrained -ice crystal at 200 K. For these studies, $K_\mathrm{r} = 4.29$ kcal -mol$^{-1}$, $K_\theta\ = 13.88$ kcal mol$^{-1}$, and $K_\omega\ = -17.75$ kcal mol$^{-1}$. It is clear from Fig. \ref{waterSpring} that -the values of $\theta$ range from $0$ to $\pi$, while $\omega$ ranges -from $-\pi$ to $\pi$. The partition function for a molecular crystal -restrained in this fashion can be evaluated analytically, and the -Helmholtz Free Energy ({\it A}) is given by +ice crystal at 200 K. For these studies, $K_\mathrm{v} = 4.29$ kcal +mol$^{-1}$ \AA$^{-2}$, $K_\theta\ = 13.88$ kcal mol$^{-1}$ rad$^{-2}$, +and $K_\omega\ = 17.75$ kcal mol$^{-1}$ rad$^{-2}$. It is clear from +Fig. \ref{waterSpring} that the values of $\theta$ range from $0$ to +$\pi$, while $\omega$ ranges from $-\pi$ to $\pi$. The partition +function for a molecular crystal restrained in this fashion can be +evaluated analytically, and the Helmholtz Free Energy ({\it A}) is +given by \begin{eqnarray} A = E_m\ -\ kT\ln \left (\frac{kT}{h\nu}\right )^3&-&kT\ln \left [\pi^\frac{1}{2}\left (\frac{8\pi^2I_\mathrm{A}kT}{h^2}\right @@ -390,14 +392,14 @@ In this report, thermodynamic integration was used to \section{Conclusions} -In this report, thermodynamic integration was used to determine the -absolute free energies of several ice polymorphs. Of the studied -crystal forms, Ice-{\it i} was observed to be the stable crystalline -state for {\it all} the water models when using a 9.0 \AA\ -intermolecular interaction cutoff. Through investigation of possible -interaction truncation methods, the free energy was shown to be -partially dependent on simulation conditions; however, Ice-{\it i} was -still observered to be a stable polymorph of the studied water models. +In this work, thermodynamic integration was used to determine the +absolute free energies of several ice polymorphs. The new polymorph, +Ice-{\it i} was observed to be the stable crystalline state for {\it +all} the water models when using a 9.0 \AA\ cutoff. However, the free +energy partially depends on simulation conditions (particularly on the +choice of long range correction method). Regardless, Ice-{\it i} was +still observered to be a stable polymorph for all of the studied water +models. So what is the preferred solid polymorph for simulated water? As indicated above, the answer appears to be dependent both on the @@ -408,10 +410,7 @@ lead to insight about important behavior of others. I pressure conditions, as was done with SSD/E, would aid in the identification of their respective preferred structures. This work, however, helps illustrate how studies involving one specific model can -lead to insight about important behavior of others. In general, the -above results support 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. +lead to insight about important behavior of others. We also note that none of the water models used in this study are polarizable or flexible models. It is entirely possible that the @@ -431,11 +430,16 @@ non-polar molecules. For experimental comparison purp situation for possible observation. These include the negative pressure or stretched solid regime, small clusters in vacuum deposition environments, and in clathrate structures involving small -non-polar molecules. For experimental comparison purposes, example -$g_{OO}(r)$ and $S(\vec{q})$ plots were generated for the two Ice-{\it -i} variants (along with example ice $I_h$ and $I_c$ plots) at 77K, and -they are shown in figures \ref{fig:gofr} and \ref{fig:sofq} -respectively. +non-polar molecules. For the purpose of comparison with experimental +results, we have calculated the oxygen-oxygen pair correlation +function, $g_{OO}(r)$, and the structure factor, $S(\vec{q})$ for the +two Ice-{\it i} variants (along with example ice $I_h$ and $I_c$ +plots) at 77K, and they are shown in figures \ref{fig:gofr} and +\ref{fig:sofq} respectively. It is interesting to note that the +structure factors for Ice-{\it i}$^\prime$ and Ice-I$_c$ are quite similar. +The primary differences are small peaks at 1.125, 2.29, and 2.53 +\AA${-1}$, so particular attention to these regions would be needed +to identify the new {\it i}$^\prime$ variant from the I$_{c}$ variant. \begin{figure} \centering @@ -466,7 +470,7 @@ Bunch-of-Boxes (B.o.B) computer cluster (NSF grant DMR \newpage -\bibliographystyle{jcp} +\bibliographystyle{achemso} \bibliography{iceiPaper}