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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 |
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of 9 \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 |
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parentheses. $^{*}$Ice $I_c$ rapidly converts to a liquid at 200 K |
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< |
with the SSD/RF model.} |
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kcal/mol. Calculated error of the final digits is in parentheses.} |
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|
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\begin{tabular}{lcccc} |
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\hline |
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|
TIP5P & -11.85(3) & -11.86(2) & -11.96(2) & -12.29(2)\\ |
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SPC/E & -12.67(2) & -12.96(2) & -13.25(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) & NA$^{*}$ & -12.08(3) & -12.29(2)\\ |
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> |
SSD/RF & -11.51(2) & -11.47(2) & -12.08(3) & -12.29(2)\\ |
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|
\end{tabular} |
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\label{freeEnergy} |
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\end{center} |
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\begin{figure} |
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\includegraphics[width=\linewidth]{cutoffChange.eps} |
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\caption{Free energy as a function of cutoff radius for (A) SSD/E, (B) |
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TIP3P, and (C) SSD/RF. Data points omitted include SSD/E: $I_c$ 12 |
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\AA\, TIP3P: $I_c$ 12 \AA\ and B 12 \AA\, and SSD/RF: $I_c$ 9 |
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< |
\AA . These crystals are unstable at 200 K and rapidly convert into |
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liquids. The connecting lines are qualitative visual aid.} |
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TIP3P, and (C) SSD/RF with a reaction field. Both SSD/E and TIP3P show |
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> |
significant cutoff radius dependence of the free energy and appear to |
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> |
converge when moving to cutoffs greater than 12 \AA. Use of a reaction |
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> |
field with SSD/RF results in free energies that exhibit minimal cutoff |
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> |
radius dependence.} |
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\label{incCutoff} |
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\end{figure} |
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|
|
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|
computationally efficient water models was done in order to evaluate |
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the trend in free energy values when moving to systems that do not |
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involve potential truncation. As seen in Fig. \ref{incCutoff}, the |
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free energy of all the ice polymorphs show a substantial dependence on |
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< |
cutoff radius. In general, there is a narrowing of the free energy |
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< |
differences while moving to greater cutoff radius. Interestingly, by |
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< |
increasing the cutoff radius, the free energy gap was narrowed enough |
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< |
in the SSD/E model that the liquid state is preferred under standard |
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< |
simulation conditions (298 K and 1 atm). Thus, it is recommended that |
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< |
simulations using this model choose interaction truncation radii |
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< |
greater than 9 \AA\ . This narrowing trend is much more subtle in the |
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case of SSD/RF, indicating that the free energies calculated with a |
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< |
reaction field present provide a more accurate picture of the free |
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< |
energy landscape in the absence of potential truncation. |
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> |
free energy of all the ice polymorphs for the SSD/E and TIP3P models |
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> |
show a substantial dependence on cutoff radius. In general, there is a |
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> |
narrowing of the free energy differences while moving to greater |
413 |
> |
cutoff radii. As the free energies for the polymorphs converge, the |
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> |
stability advantage that Ice-{\it i} exhibits is reduced; however, it |
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> |
remains the most stable polymorph for both of these models over the |
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> |
depicted range for both models. This narrowing trend is not |
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> |
significant in the case of SSD/RF, indicating that the free energies |
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> |
calculated with a reaction field present provide, at minimal |
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> |
computational cost, a more accurate picture of the free energy |
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> |
landscape in the absence of potential truncation. Interestingly, |
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> |
increasing the cutoff radius a mere 1.5 \AA\ with the SSD/E model |
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> |
destabilizes the Ice-{\it i} polymorph enough that the liquid state is |
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> |
preferred under standard simulation conditions (298 K and 1 |
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> |
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 |
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> |
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 |
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> |
$I_\textrm{h}$ starting configurations. |
431 |
|
|
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|
To further study the changes resulting to the inclusion of a |
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|
long-range interaction correction, the effect of an Ewald summation |