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|
|
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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 |
297 |
< |
of 9 \AA\ and were performed at 200 K and $\sim$1 atm. Units are |
297 |
> |
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.} |
299 |
|
|
300 |
< |
\begin{tabular}{lcccc} |
300 |
> |
\begin{tabular}{lccccc} |
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|
\hline |
302 |
< |
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 |
304 |
< |
TIP3P & -11.41(2) & -11.23(3) & -11.82(3) & -12.30(3)\\ |
305 |
< |
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) & -\\ |
305 |
> |
TIP4P & -11.84(3) & -12.04(2) & -12.08(3) & - & -12.33(3)\\ |
306 |
> |
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) & -\\ |
309 |
> |
SSD/RF & -11.51(2) & -11.47(2) & -12.08(3) & -12.29(2) & -\\ |
310 |
|
\end{tabular} |
311 |
|
\label{freeEnergy} |
312 |
|
\end{center} |
405 |
|
long-range correction show noticable free energy dependence on the |
406 |
|
cutoff radius and show some degree of converge at large cutoff radii. |
407 |
|
Inclusion of a long-range correction reduces the cutoff radius |
408 |
< |
dependence of the free energy for all the models. Data for ice I$_c$ |
409 |
< |
with TIP3P using both 12 and 13.5 \AA\ cutoffs were omitted because |
410 |
< |
the crystal was prone to distortion and melting at 200 K. Ice-{\it |
411 |
< |
i}$^\prime$ is the form of Ice-{\it i} used in the SPC/E simulations.} |
408 |
> |
dependence of the free energy for all the models. Error for the |
409 |
> |
larger cutoff points is equivalent to that observed at 9.0 \AA\ (see |
410 |
> |
Table \ref{freeEnergy}). Data for ice I$_c$ with TIP3P using both 12 |
411 |
> |
and 13.5 \AA\ cutoffs were omitted because the crystal was prone to |
412 |
> |
distortion and melting at 200 K. Ice-{\it i}$^\prime$ is the form of |
413 |
> |
Ice-{\it i} used in the SPC/E simulations.} |
414 |
|
\label{incCutoff} |
415 |
|
\end{figure} |
416 |
|
|
459 |
|
studied assumes the role of the preferred polymorph under different |
460 |
|
cutoff conditions. The inclusion of the Ewald correction flattens and |
461 |
|
narrows the sequences of free energies so much that they often overlap |
462 |
< |
within error (see Table \ref{spcecut}), indicating that other |
463 |
< |
conditions, such as cell volume in microcanonical simulations, can |
464 |
< |
influence the chosen polymorph upon crystallization. All of these |
465 |
< |
results support the finding that the Ice-{\it i} polymorph is a stable |
466 |
< |
crystal structure that should be considered when studying the phase |
465 |
< |
behavior of water models. |
462 |
> |
within error, indicating that other conditions, such as cell volume in |
463 |
> |
microcanonical simulations, can influence the chosen polymorph upon |
464 |
> |
crystallization. All of these results support the finding that the |
465 |
> |
Ice-{\it i} polymorph is a stable crystal structure that should be |
466 |
> |
considered when studying the phase behavior of water models. |
467 |
|
|
467 |
– |
\begin{table*} |
468 |
– |
\begin{minipage}{\linewidth} |
469 |
– |
\begin{center} |
470 |
– |
|
471 |
– |
\caption{The free energy versus cutoff radius for the studied ice |
472 |
– |
polymorphs using SPC/E after the inclusion of the PME long-range |
473 |
– |
interaction correction. Units are kcal/mol.} |
474 |
– |
|
475 |
– |
\begin{tabular}{ccccc} |
476 |
– |
\hline |
477 |
– |
Cutoff (\AA) & $I_h$ & $I_c$ & B & Ice-{\it i} \\ |
478 |
– |
\hline |
479 |
– |
9.0 & -12.98(2) & -13.00(2) & -12.97(3) & -13.02(2) \\ |
480 |
– |
10.5 & -13.13(3) & -13.09(4) & -13.17(3) & -13.11(2) \\ |
481 |
– |
12.0 & -13.06(2) & -13.09(2) & -13.15(4) & -13.12(2) \\ |
482 |
– |
13.5 & -13.02(2) & -13.02(2) & -13.08(2) & -13.07(2) \\ |
483 |
– |
15.0 & -13.11(4) & -12.97(2) & -13.09(2) & -12.95(2) \\ |
484 |
– |
\end{tabular} |
485 |
– |
\label{spcecut} |
486 |
– |
\end{center} |
487 |
– |
\end{minipage} |
488 |
– |
\end{table*} |
489 |
– |
|
468 |
|
\section{Conclusions} |
469 |
|
|
470 |
|
The free energy for proton ordered variants of hexagonal and cubic ice |