| 263 |
|
\caption{Calculated free energies for several ice polymorphs with a |
| 264 |
|
variety of common water models. All calculations used a cutoff radius |
| 265 |
|
of 9 \AA\ and were performed at 200 K and $\sim$1 atm. Units are |
| 266 |
< |
kcal/mol. *Ice $I_c$ is unstable at 200 K using SSD/RF.} |
| 266 |
> |
kcal/mol. Calculated error of the final digits is in parentheses. *Ice |
| 267 |
> |
$I_c$ rapidly converts to a liquid at 200 K with the SSD/RF model.} |
| 268 |
|
\begin{tabular}{ l c c c c } |
| 269 |
|
\hline |
| 270 |
< |
\ \quad \ Water Model\ \ & \ \quad \ \ \ \ $I_h$ \ \ & \ \quad \ \ \ \ $I_c$ \ \ & \ \quad \ \ \ \ B \ \ & \ \quad \ \ \ Ice-{\it i} \ \quad \ \\ |
| 270 |
> |
Water Model & $I_h$ & $I_c$ & B & Ice-{\it i}\\ |
| 271 |
|
\hline |
| 272 |
< |
\ \quad \ TIP3P & \ \quad \ -11.41 & \ \quad \ -11.23 & \ \quad \ -11.82 & \quad -12.30\\ |
| 273 |
< |
\ \quad \ TIP4P & \ \quad \ -11.84 & \ \quad \ -12.04 & \ \quad \ -12.08 & \quad -12.33\\ |
| 274 |
< |
\ \quad \ TIP5P & \ \quad \ -11.85 & \ \quad \ -11.86 & \ \quad \ -11.96 & \quad -12.29\\ |
| 275 |
< |
\ \quad \ SPC/E & \ \quad \ -12.67 & \ \quad \ -12.96 & \ \quad \ -13.25 & \quad -13.55\\ |
| 276 |
< |
\ \quad \ SSD/E & \ \quad \ -11.27 & \ \quad \ -11.19 & \ \quad \ -12.09 & \quad -12.54\\ |
| 277 |
< |
\ \quad \ SSD/RF & \ \quad \ -11.51 & \ \quad \ NA* & \ \quad \ -12.08 & \quad -12.29\\ |
| 272 |
> |
TIP3P & -11.41(4) & -11.23(6) & -11.82(5) & -12.30(5)\\ |
| 273 |
> |
TIP4P & -11.84(5) & -12.04(4) & -12.08(6) & -12.33(6)\\ |
| 274 |
> |
TIP5P & -11.85(5) & -11.86(4) & -11.96(4) & -12.29(4)\\ |
| 275 |
> |
SPC/E & -12.67(3) & -12.96(3) & -13.25(5) & -13.55(3)\\ |
| 276 |
> |
SSD/E & -11.27(3) & -11.19(8) & -12.09(4) & -12.54(4)\\ |
| 277 |
> |
SSD/RF & -11.51(4) & NA* & -12.08(5) & -12.29(4)\\ |
| 278 |
|
\end{tabular} |
| 279 |
|
\label{freeEnergy} |
| 280 |
|
\end{center} |
| 322 |
|
\renewcommand{\thefootnote}{\thempfootnote} |
| 323 |
|
\begin{center} |
| 324 |
|
\caption{Melting ($T_m$), boiling ($T_b$), and sublimation ($T_s$) |
| 325 |
< |
temperatures of several common water models compared with experiment.} |
| 325 |
> |
temperatures at 1 atm for several common water models compared with |
| 326 |
> |
experiment. The $T_m$ and $T_s$ values from simulation correspond to a |
| 327 |
> |
transition between Ice-{\it i} (or Ice-{\it i}$^\prime$) and the |
| 328 |
> |
liquid or gas state.} |
| 329 |
|
\begin{tabular}{ l c c c c c c c } |
| 330 |
|
\hline |
| 331 |
< |
\ \ Equilibria Point\ \ & \ \ \ \ \ TIP3P \ \ & \ \ \ \ \ TIP4P \ \ & \ \quad \ \ \ \ TIP5P \ \ & \ \ \ \ \ SPC/E \ \ & \ \ \ \ \ SSD/E \ \ & \ \ \ \ \ SSD/RF \ \ & \ \ \ \ \ Exp. \ \ \\ |
| 331 |
> |
Equilibria Point & TIP3P & TIP4P & TIP5P & SPC/E & SSD/E & SSD/RF & Exp.\\ |
| 332 |
|
\hline |
| 333 |
< |
\ \ $T_m$ (K) & \ \ 269 & \ \ 265 & \ \ 271 & 297 & \ \ - & \ \ 278 & \ \ 273\\ |
| 334 |
< |
\ \ $T_b$ (K) & \ \ 357 & \ \ 354 & \ \ 337 & 396 & \ \ - & \ \ 349 & \ \ 373\\ |
| 335 |
< |
\ \ $T_s$ (K) & \ \ - & \ \ - & \ \ - & - & \ \ 355 & \ \ - & \ \ -\\ |
| 333 |
> |
$T_m$ (K) & 269(8) & 266(10) & 271(7) & 296(5) & - & 278(7) & 273\\ |
| 334 |
> |
$T_b$ (K) & 357(2) & 354(3) & 337(3) & 396(4) & - & 348(3) & 373\\ |
| 335 |
> |
$T_s$ (K) & - & - & - & - & 355(3) & - & -\\ |
| 336 |
|
\end{tabular} |
| 337 |
|
\label{meltandboil} |
| 338 |
|
\end{center} |
| 348 |
|
studies in the literature. Earlier free energy studies of ice $I$ |
| 349 |
|
using TIP4P predict a $T_m$ ranging from 214 to 238 K (differences |
| 350 |
|
being attributed to choice of interaction truncation and different |
| 351 |
< |
ordered and disordered molecular arrangements). If the presence of ice |
| 352 |
< |
B and Ice-{\it i} were omitted, a $T_m$ value around 210 K would be |
| 351 |
> |
ordered and disordered molecular |
| 352 |
> |
arrangements).\cite{Vlot99,Gao00,Sanz04} If the presence of ice B and |
| 353 |
> |
Ice-{\it i} were omitted, a $T_m$ value around 210 K would be |
| 354 |
|
predicted from this work. However, the $T_m$ from Ice-{\it i} is |
| 355 |
|
calculated at 265 K, significantly higher in temperature than the |
| 356 |
|
previous studies. Also of interest in these results is that SSD/E does |
| 369 |
|
\caption{Free energy as a function of cutoff radius for (A) SSD/E, (B) |
| 370 |
|
TIP3P, and (C) SSD/RF. Data points omitted include SSD/E: $I_c$ 12 |
| 371 |
|
\AA\, TIP3P: $I_c$ 12 \AA\ and B 12 \AA\, and SSD/RF: $I_c$ 9 |
| 372 |
< |
\AA\. These crystals are unstable at 200 K and rapidly convert into a |
| 373 |
< |
liquid. The connecting lines are qualitative visual aid.} |
| 372 |
> |
\AA . These crystals are unstable at 200 K and rapidly convert into |
| 373 |
> |
liquids. The connecting lines are qualitative visual aid.} |
| 374 |
|
\label{incCutoff} |
| 375 |
|
\end{figure} |
| 376 |
|
|
| 422 |
|
\hline |
| 423 |
|
\ \ Water Model \ \ & \ \ \ \ \ $I_h$ \ \ & \ \ \ \ \ $I_c$ \ \ & \ \quad \ \ \ \ B \ \ & \ \ \ \ \ Ice-{\it i} \ \ \\ |
| 424 |
|
\hline |
| 425 |
< |
\ \ TIP3P & \ \ -11.53 & \ \ -11.24 & \ \ -11.51 & \ \ -11.67\\ |
| 426 |
< |
\ \ SPC/E & \ \ -12.77 & \ \ -12.92 & \ \ -12.96 & \ \ -13.02\\ |
| 425 |
> |
TIP3P & -11.53(4) & -11.24(6) & -11.51(5) & -11.67(5)\\ |
| 426 |
> |
SPC/E & -12.77(3) & -12.92(3) & -12.96(5) & -13.02(3)\\ |
| 427 |
|
\end{tabular} |
| 428 |
|
\label{pmeShift} |
| 429 |
|
\end{center} |
