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