276 |
|
$I_h$, was investigated initially, but was found to be not as stable |
277 |
|
as proton disordered or antiferroelectric variants of ice $I_h$. The |
278 |
|
proton ordered variant of ice $I_h$ used here is a simple |
279 |
< |
antiferroelectric version that has an 8 molecule unit |
280 |
< |
cell.\cite{Davidson84} The crystals contained 648 or 1728 molecules |
281 |
< |
for ice B, 1024 or 1280 molecules for ice $I_h$, 1000 molecules for |
282 |
< |
ice $I_c$, or 1024 molecules for Ice-{\it i}. The larger crystal sizes |
283 |
< |
were necessary for simulations involving larger cutoff values. |
279 |
> |
antiferroelectric version that we divised, and it has an 8 molecule |
280 |
> |
unit cell similar to other predicted antiferroelectric $I_h$ |
281 |
> |
crystals.\cite{Davidson84} The crystals contained 648 or 1728 |
282 |
> |
molecules for ice B, 1024 or 1280 molecules for ice $I_h$, 1000 |
283 |
> |
molecules for ice $I_c$, or 1024 molecules for Ice-{\it i}. The larger |
284 |
> |
crystal sizes were necessary for simulations involving larger cutoff |
285 |
> |
values. |
286 |
|
|
287 |
|
\begin{table*} |
288 |
|
\begin{minipage}{\linewidth} |
297 |
|
\hline |
298 |
|
Water Model & $I_h$ & $I_c$ & B & Ice-{\it i}\\ |
299 |
|
\hline |
300 |
< |
TIP3P & -11.41(4) & -11.23(6) & -11.82(5) & -12.30(5)\\ |
301 |
< |
TIP4P & -11.84(5) & -12.04(4) & -12.08(6) & -12.33(6)\\ |
302 |
< |
TIP5P & -11.85(5) & -11.86(4) & -11.96(4) & -12.29(4)\\ |
303 |
< |
SPC/E & -12.67(3) & -12.96(3) & -13.25(5) & -13.55(3)\\ |
304 |
< |
SSD/E & -11.27(3) & -11.19(8) & -12.09(4) & -12.54(4)\\ |
305 |
< |
SSD/RF & -11.51(4) & NA* & -12.08(5) & -12.29(4)\\ |
300 |
> |
TIP3P & -11.41(2) & -11.23(3) & -11.82(3) & -12.30(3)\\ |
301 |
> |
TIP4P & -11.84(3) & -12.04(2) & -12.08(3) & -12.33(3)\\ |
302 |
> |
TIP5P & -11.85(3) & -11.86(2) & -11.96(2) & -12.29(2)\\ |
303 |
> |
SPC/E & -12.67(2) & -12.96(2) & -13.25(3) & -13.55(2)\\ |
304 |
> |
SSD/E & -11.27(2) & -11.19(4) & -12.09(2) & -12.54(2)\\ |
305 |
> |
SSD/RF & -11.51(2) & NA* & -12.08(3) & -12.29(2)\\ |
306 |
|
\end{tabular} |
307 |
|
\label{freeEnergy} |
308 |
|
\end{center} |
358 |
|
\hline |
359 |
|
Equilibria Point & TIP3P & TIP4P & TIP5P & SPC/E & SSD/E & SSD/RF & Exp.\\ |
360 |
|
\hline |
361 |
< |
$T_m$ (K) & 269(8) & 266(10) & 271(7) & 296(5) & - & 278(7) & 273\\ |
362 |
< |
$T_b$ (K) & 357(2) & 354(3) & 337(3) & 396(4) & - & 348(3) & 373\\ |
363 |
< |
$T_s$ (K) & - & - & - & - & 355(3) & - & -\\ |
361 |
> |
$T_m$ (K) & 269(4) & 266(5) & 271(4) & 296(3) & - & 278(4) & 273\\ |
362 |
> |
$T_b$ (K) & 357(2) & 354(2) & 337(2) & 396(2) & - & 348(2) & 373\\ |
363 |
> |
$T_s$ (K) & - & - & - & - & 355(2) & - & -\\ |
364 |
|
\end{tabular} |
365 |
|
\label{meltandboil} |
366 |
|
\end{center} |
431 |
|
for both the TIP3P and SPC/E water models; however, the narrowing of |
432 |
|
the free energy differences between the various solid forms is |
433 |
|
significant enough that it becomes less clear that it is the most |
434 |
< |
stable polymorph. The free energies of Ice-{\it i} and ice B overlap |
435 |
< |
within error, with ice $I_c$ just outside, indicating that Ice-{\it i} |
436 |
< |
might be metastable with respect to ice B and possibly ice $I_c$ in |
437 |
< |
the SPC/E water model. However, these results do not significantly |
438 |
< |
alter the finding that the Ice-{\it i} polymorph is a stable crystal |
439 |
< |
structure that should be considered when studying the phase behavior |
440 |
< |
of water models. |
434 |
> |
stable polymorph in the SPC/E. The free energies of Ice-{\it i} and |
435 |
> |
ice B nearly overlap within error, with ice $I_c$ just outside as |
436 |
> |
well, indicating that Ice-{\it i} might be metastable with respect to |
437 |
> |
ice B and possibly ice $I_c$ in the SPC/E water model. However, these |
438 |
> |
results do not significantly alter the finding that the Ice-{\it i} |
439 |
> |
polymorph is a stable crystal structure that should be considered when |
440 |
> |
studying the phase behavior of water models. |
441 |
|
|
442 |
|
\begin{table*} |
443 |
|
\begin{minipage}{\linewidth} |
450 |
|
\hline |
451 |
|
\ \ Water Model \ \ & \ \ \ \ \ $I_h$ \ \ & \ \ \ \ \ $I_c$ \ \ & \ \quad \ \ \ \ B \ \ & \ \ \ \ \ Ice-{\it i} \ \ \\ |
452 |
|
\hline |
453 |
< |
TIP3P & -11.53(4) & -11.24(6) & -11.51(5) & -11.67(5)\\ |
454 |
< |
SPC/E & -12.77(3) & -12.92(3) & -12.96(5) & -13.02(3)\\ |
453 |
> |
TIP3P & -11.53(2) & -11.24(3) & -11.51(3) & -11.67(3)\\ |
454 |
> |
SPC/E & -12.77(2) & -12.92(2) & -12.96(3) & -13.02(2)\\ |
455 |
|
\end{tabular} |
456 |
|
\label{pmeShift} |
457 |
|
\end{center} |