| 290 |
|
\caption{Calculated free energies for several ice polymorphs with a |
| 291 |
|
variety of common water models. All calculations used a cutoff radius |
| 292 |
|
of 9 \AA\ and were performed at 200 K and $\sim$1 atm. Units are |
| 293 |
< |
kcal/mol. Calculated error of the final digits is in |
| 294 |
< |
parentheses. $^{*}$Ice $I_c$ rapidly converts to a liquid at 200 K |
| 295 |
< |
with the SSD/RF model.} |
| 293 |
> |
kcal/mol. Calculated error of the final digits is in parentheses.} |
| 294 |
|
|
| 295 |
|
\begin{tabular}{lcccc} |
| 296 |
|
\hline |
| 301 |
|
TIP5P & -11.85(3) & -11.86(2) & -11.96(2) & -12.29(2)\\ |
| 302 |
|
SPC/E & -12.67(2) & -12.96(2) & -13.25(3) & -13.55(2)\\ |
| 303 |
|
SSD/E & -11.27(2) & -11.19(4) & -12.09(2) & -12.54(2)\\ |
| 304 |
< |
SSD/RF & -11.51(2) & NA$^{*}$ & -12.08(3) & -12.29(2)\\ |
| 304 |
> |
SSD/RF & -11.51(2) & -11.47(2) & -12.08(3) & -12.29(2)\\ |
| 305 |
|
\end{tabular} |
| 306 |
|
\label{freeEnergy} |
| 307 |
|
\end{center} |
| 395 |
|
\begin{figure} |
| 396 |
|
\includegraphics[width=\linewidth]{cutoffChange.eps} |
| 397 |
|
\caption{Free energy as a function of cutoff radius for (A) SSD/E, (B) |
| 398 |
< |
TIP3P, and (C) SSD/RF. Data points omitted include SSD/E: $I_c$ 12 |
| 399 |
< |
\AA\, TIP3P: $I_c$ 12 \AA\ and B 12 \AA\, and SSD/RF: $I_c$ 9 |
| 400 |
< |
\AA . These crystals are unstable at 200 K and rapidly convert into |
| 401 |
< |
liquids. The connecting lines are qualitative visual aid.} |
| 398 |
> |
TIP3P, and (C) SSD/RF with a reaction field. Both SSD/E and TIP3P show |
| 399 |
> |
significant cutoff radius dependence of the free energy and appear to |
| 400 |
> |
converge when moving to cutoffs greater than 12 \AA. Use of a reaction |
| 401 |
> |
field with SSD/RF results in free energies that exhibit minimal cutoff |
| 402 |
> |
radius dependence.} |
| 403 |
|
\label{incCutoff} |
| 404 |
|
\end{figure} |
| 405 |
|
|
| 407 |
|
computationally efficient water models was done in order to evaluate |
| 408 |
|
the trend in free energy values when moving to systems that do not |
| 409 |
|
involve potential truncation. As seen in Fig. \ref{incCutoff}, the |
| 410 |
< |
free energy of all the ice polymorphs show a substantial dependence on |
| 411 |
< |
cutoff radius. In general, there is a narrowing of the free energy |
| 412 |
< |
differences while moving to greater cutoff radius. Interestingly, by |
| 413 |
< |
increasing the cutoff radius, the free energy gap was narrowed enough |
| 414 |
< |
in the SSD/E model that the liquid state is preferred under standard |
| 415 |
< |
simulation conditions (298 K and 1 atm). Thus, it is recommended that |
| 416 |
< |
simulations using this model choose interaction truncation radii |
| 417 |
< |
greater than 9 \AA\ . This narrowing trend is much more subtle in the |
| 418 |
< |
case of SSD/RF, indicating that the free energies calculated with a |
| 419 |
< |
reaction field present provide a more accurate picture of the free |
| 420 |
< |
energy landscape in the absence of potential truncation. |
| 410 |
> |
free energy of all the ice polymorphs for the SSD/E and TIP3P models |
| 411 |
> |
show a substantial dependence on cutoff radius. In general, there is a |
| 412 |
> |
narrowing of the free energy differences while moving to greater |
| 413 |
> |
cutoff radii. As the free energies for the polymorphs converge, the |
| 414 |
> |
stability advantage that Ice-{\it i} exhibits is reduced; however, it |
| 415 |
> |
remains the most stable polymorph for both of these models over the |
| 416 |
> |
depicted range for both models. This narrowing trend is not |
| 417 |
> |
significant in the case of SSD/RF, indicating that the free energies |
| 418 |
> |
calculated with a reaction field present provide, at minimal |
| 419 |
> |
computational cost, a more accurate picture of the free energy |
| 420 |
> |
landscape in the absence of potential truncation. Interestingly, |
| 421 |
> |
increasing the cutoff radius a mere 1.5 \AA\ with the SSD/E model |
| 422 |
> |
destabilizes the Ice-{\it i} polymorph enough that the liquid state is |
| 423 |
> |
preferred under standard simulation conditions (298 K and 1 |
| 424 |
> |
atm). Thus, it is recommended that simulations using this model choose |
| 425 |
> |
interaction truncation radii greater than 9 \AA. Considering this |
| 426 |
> |
stabilization provided by smaller cutoffs, it is not surprising that |
| 427 |
> |
crystallization into Ice-{\it i} was observed with SSD/E. The choice |
| 428 |
> |
of a 9 \AA\ cutoff in the previous simulations gives the Ice-{\it i} |
| 429 |
> |
polymorph a greater than 1 kcal/mol lower free energy than the ice |
| 430 |
> |
$I_\textrm{h}$ starting configurations. |
| 431 |
|
|
| 432 |
|
To further study the changes resulting to the inclusion of a |
| 433 |
|
long-range interaction correction, the effect of an Ewald summation |
