| 294 |
|
|
| 295 |
|
\caption{Calculated free energies for several ice polymorphs with a |
| 296 |
|
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 |
| 298 |
|
kcal/mol. Calculated error of the final digits is in parentheses.} |
| 299 |
|
|
| 300 |
< |
\begin{tabular}{lcccc} |
| 300 |
> |
\begin{tabular}{lccccc} |
| 301 |
|
\hline |
| 302 |
< |
Water Model & $I_h$ & $I_c$ & B & Ice-{\it i}\\ |
| 302 |
> |
Water Model & $I_h$ & $I_c$ & B & Ice-{\it i} & Ice-{\it i}$^\prime$\\ |
| 303 |
|
\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)\\ |
| 306 |
< |
TIP5P & -11.85(3) & -11.86(2) & -11.96(2) & -12.29(2)\\ |
| 307 |
< |
SPC/E & -12.87(2) & -13.05(2) & -13.26(3) & -13.55(2)\\ |
| 308 |
< |
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)\\ |
| 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)\\ |
| 306 |
> |
TIP5P & -11.85(3) & -11.86(2) & -11.96(2) & - & -12.29(2)\\ |
| 307 |
> |
SPC/E & -12.87(2) & -13.05(2) & -13.26(3) & - & -13.55(2)\\ |
| 308 |
> |
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 |
