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\begin{document} |
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\title{Ice-{\it i}: a simulation-predicted ice polymorph which is more |
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stable than Ice $I_h$ for point-charge and point-dipole water models} |
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\title{Free Energy Analysis of Simulated Ice Polymorphs Using Simple |
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Dipolar and Charge Based Water Models} |
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\author{Christopher J. Fennell and J. Daniel Gezelter \\ |
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Department of Chemistry and Biochemistry\\ University of Notre Dame\\ |
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\begin{figure} |
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\includegraphics[width=\linewidth]{orderedIcei.eps} |
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\caption{Image of a proton ordered crystal of Ice-{\it i} looking |
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down the (001) crystal face. The rows of water tetramers surrounded by |
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octagonal pores leads to a crystal structure that is significantly |
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down the (001) crystal face. The rows of water tetramers surrounded |
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by octagonal pores leads to a crystal structure that is significantly |
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less dense than ice $I_h$.} |
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\label{protOrder} |
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\end{figure} |
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\caption{Possible orientational motions for a restrained molecule. |
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$\theta$ angles correspond to displacement from the body-frame {\it |
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z}-axis, while $\omega$ angles correspond to rotation about the |
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body-frame {\it z}-axis. $K_\theta$ and $K_\omega$ are spring |
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body-frame {\it z}-axis. $K_\theta$ and $K_\omega$ are spring |
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constants for the harmonic springs restraining motion in the $\theta$ |
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and $\omega$ directions.} |
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\label{waterSpring} |
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\begin{center} |
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\caption{Calculated free energies for several ice polymorphs with a |
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variety of common water models. All calculations used a cutoff radius |
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of 9 \AA\ and were performed at 200 K and $\sim$1 atm. Units are |
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kcal/mol. Calculated error of the final digits is in parentheses.} |
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variety of common water models. All calculations used a cutoff radius |
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of 9.0 \AA\ and were performed at 200 K and $\sim$1 atm. Units are |
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kcal/mol. Calculated error of the final digits is in parentheses.} |
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\begin{tabular}{lcccc} |
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\begin{tabular}{lccccc} |
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\hline |
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Water Model & $I_h$ & $I_c$ & B & Ice-{\it i}\\ |
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Water Model & $I_h$ & $I_c$ & B & Ice-{\it i} & Ice-{\it i}$^\prime$\\ |
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\hline |
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TIP3P & -11.41(2) & -11.23(3) & -11.82(3) & -12.30(3)\\ |
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TIP4P & -11.84(3) & -12.04(2) & -12.08(3) & -12.33(3)\\ |
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TIP5P & -11.85(3) & -11.86(2) & -11.96(2) & -12.29(2)\\ |
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SPC/E & -12.87(2) & -13.05(2) & -13.26(3) & -13.55(2)\\ |
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SSD/E & -11.27(2) & -11.19(4) & -12.09(2) & -12.54(2)\\ |
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SSD/RF & -11.51(2) & -11.47(2) & -12.08(3) & -12.29(2)\\ |
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TIP3P & -11.41(2) & -11.23(3) & -11.82(3) & -12.30(3) & -\\ |
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TIP4P & -11.84(3) & -12.04(2) & -12.08(3) & - & -12.33(3)\\ |
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TIP5P & -11.85(3) & -11.86(2) & -11.96(2) & - & -12.29(2)\\ |
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SPC/E & -12.87(2) & -13.05(2) & -13.26(3) & - & -13.55(2)\\ |
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SSD/E & -11.27(2) & -11.19(4) & -12.09(2) & -12.54(2) & -\\ |
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SSD/RF & -11.51(2) & -11.47(2) & -12.08(3) & -12.29(2) & -\\ |
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\end{tabular} |
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\label{freeEnergy} |
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\end{center} |
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long-range correction show noticable free energy dependence on the |
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cutoff radius and show some degree of converge at large cutoff radii. |
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Inclusion of a long-range correction reduces the cutoff radius |
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dependence of the free energy for all the models. Data for ice I$_c$ |
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with TIP3P using 12 and 13.5 \AA\ cutoff radii were omitted being that |
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the crystal was prone to distortion and melting at 200 K.} |
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dependence of the free energy for all the models. Error for the |
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larger cutoff points is equivalent to that observed at 9.0 \AA\ (see |
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Table \ref{freeEnergy}). Data for ice I$_c$ with TIP3P using both 12 |
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and 13.5 \AA\ cutoffs were omitted because the crystal was prone to |
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distortion and melting at 200 K. Ice-{\it i}$^\prime$ is the form of |
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Ice-{\it i} used in the SPC/E simulations.} |
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\label{incCutoff} |
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\end{figure} |
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Ice-{\it i} polymorph is a stable crystal structure that should be |
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considered when studying the phase behavior of water models. |
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\begin{table*} |
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\begin{minipage}{\linewidth} |
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\begin{center} |
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|
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\caption{The free energy versus cutoff radius for the studied ice |
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polymorphs using SPC/E after the inclusion of the PME long-range |
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interaction correction. Units are kcal/mol.} |
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|
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\begin{tabular}{ccccc} |
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\hline |
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Cutoff (\AA) & $I_h$ & $I_c$ & B & Ice-{\it i} \\ |
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\hline |
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9.0 & -12.98(2) & -13.00(2) & -12.97(3) & -13.02(2) \\ |
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10.5 & -13.13(3) & -13.09(4) & -13.17(3) & -13.11(2) \\ |
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12.0 & -13.06(2) & -13.09(2) & -13.15(4) & -13.12(2) \\ |
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13.5 & -13.02(2) & -13.02(2) & -13.08(2) & -13.07(2) \\ |
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15.0 & -13.11(4) & -12.97(2) & -13.09(2) & -12.95(2) \\ |
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\end{tabular} |
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\label{pmeShift} |
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\end{center} |
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\end{minipage} |
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\end{table*} |
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\section{Conclusions} |
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The free energy for proton ordered variants of hexagonal and cubic ice |
