| 83 |
|
considered energetic stabilization and neglected entropic |
| 84 |
|
contributions to the overall free energy. To address this issue, we |
| 85 |
|
have calculated the absolute free energy of this crystal using |
| 86 |
< |
thermodynamic integration and compared to the free energies of ice |
| 86 |
> |
thermodynamic integration and compared it to the free energies of ice |
| 87 |
|
I$_\textrm{c}$ and ice I$_\textrm{h}$ (the common low-density ice |
| 88 |
|
polymorphs) and ice B (a higher density, but very stable crystal |
| 89 |
|
structure observed by B\'{a}ez and Clancy in free energy studies of |
| 454 |
|
SPC/E & -12.99(3) & -13.00(3) & -13.03(3) & - & -12.99(3) \\ |
| 455 |
|
SSD/RF & -11.83(3) & -11.66(4) & -12.32(3) & -12.39(3) & - \\ |
| 456 |
|
TRED & -12.61(3) & -12.43(3) & -12.89(3) & -13.12(3) & - \\ |
| 457 |
+ |
\bottomrule |
| 458 |
|
\end{tabular} |
| 459 |
|
\label{tab:dampedFreeEnergy} |
| 460 |
|
\end{table} |
| 512 |
|
Ice-$i$ was still observed to be a stable polymorph for all of the |
| 513 |
|
studied water models. |
| 514 |
|
|
| 515 |
< |
So what is the preferred solid polymorph for simulated water? As |
| 516 |
< |
indicated above, the answer appears to be dependent both on the |
| 517 |
< |
conditions and the model used. In the case of short cutoffs without a |
| 518 |
< |
long-range interaction correction, Ice-$i$ and Ice-$i^\prime$ have |
| 519 |
< |
the lowest free energy of the studied polymorphs with all the models. |
| 520 |
< |
Ideally, crystallization of each model under constant pressure |
| 521 |
< |
conditions, as was done with SSD/E, would aid in the identification of |
| 522 |
< |
their respective preferred structures. This work, however, helps |
| 523 |
< |
illustrate how studies involving one specific model can lead to |
| 523 |
< |
insight about important behavior of others. |
| 515 |
> |
So what is the preferred solid polymorph for simulated water? The |
| 516 |
> |
answer appears to be dependent both on the conditions and the model |
| 517 |
> |
used. In the case of short cutoffs without a long-range interaction |
| 518 |
> |
correction, Ice-$i$ and Ice-$i^\prime$ have the lowest free energy of |
| 519 |
> |
the studied polymorphs with all the models. Ideally, crystallization |
| 520 |
> |
of each model under constant pressure conditions, as was done with |
| 521 |
> |
SSD/E, would aid in identifying their respective preferred structures. |
| 522 |
> |
This work, however, helps illustrate how studies involving one |
| 523 |
> |
specific model can lead to insight about important behavior of others. |
| 524 |
|
|
| 525 |
|
We also note that none of the water models used in this study are |
| 526 |
|
polarizable or flexible models. It is entirely possible that the |
| 534 |
|
computational cost increase that comes with including polarizability |
| 535 |
|
is an issue. |
| 536 |
|
|
| 537 |
< |
Finally, due to the stability of Ice-$i$ in the investigated |
| 538 |
< |
simulation conditions, a question arises as to possible experimental |
| 539 |
< |
observation of this polymorph. The rather extensive past and current |
| 540 |
< |
experimental investigation of water in the low pressure regime makes |
| 541 |
< |
us hesitant to ascribe any relevance to this work outside of the |
| 542 |
< |
simulation community. It is for this reason that we chose a name for |
| 543 |
< |
this polymorph which involves an imaginary quantity. That said, there |
| 544 |
< |
are certain experimental conditions that would provide the most ideal |
| 545 |
< |
situation for possible observation. These include the negative |
| 546 |
< |
pressure or stretched solid regime, small clusters in vacuum |
| 547 |
< |
deposition environments, and in clathrate structures involving small |
| 548 |
< |
non-polar molecules. For the purpose of comparison with experimental |
| 549 |
< |
results, we have calculated the oxygen-oxygen pair correlation |
| 550 |
< |
function, $g_\textrm{OO}(r)$, and the structure factor, $S(\vec{q})$ |
| 551 |
< |
for the two Ice-$i$ variants (along with example ice I$_\textrm{h}$ |
| 552 |
< |
and I$_\textrm{c}$ plots) at 77~K, and they are shown in figures |
| 553 |
< |
\ref{fig:gofr} and \ref{fig:sofq}. It is interesting to note that the |
| 554 |
< |
structure factors for Ice-$i^\prime$ and ice I$_\textrm{c}$ are quite |
| 555 |
< |
similar. The primary differences are small peaks at 1.125, 2.29, and |
| 556 |
< |
2.53~\AA$^{-1}$, so particular attention to these regions would be |
| 557 |
< |
needed to distinguish Ice-$i^\prime$ from ice I$_\textrm{c}$. |
| 537 |
> |
Finally, the stability of Ice-$i$ in these simulations raises the |
| 538 |
> |
possibility of experimental observation. The extensive body of |
| 539 |
> |
research on water in the low pressure regime makes us hesitant to |
| 540 |
> |
ascribe any relevance to this work outside the simulation community. |
| 541 |
> |
It is for this reason that we chose a name for this polymorph |
| 542 |
> |
involving an imaginary quantity. That said, there are certain |
| 543 |
> |
conditions that would be ideal for experimental observation of |
| 544 |
> |
Ice-$i$. These include the negative pressure or stretched solid |
| 545 |
> |
regime, clusters deposited in vacuum environments, and clathrate |
| 546 |
> |
structures involving small non-polar molecules. For the purpose of |
| 547 |
> |
comparison with future experimental results, we calculated the |
| 548 |
> |
oxygen-oxygen pair correlation function, $g_\textrm{OO}(r)$, and the |
| 549 |
> |
structure factor, $S(\vec{q})$ for the two Ice-$i$ variants (along |
| 550 |
> |
with ice I$_\textrm{h}$ and I$_\textrm{c}$) at 77~K (figures |
| 551 |
> |
\ref{fig:gofr} and \ref{fig:sofq}). It is interesting to note that |
| 552 |
> |
the structure factors for Ice-$i^\prime$ and ice I$_\textrm{c}$ are |
| 553 |
> |
quite similar. The primary differences are small peaks at 1.125, |
| 554 |
> |
2.29, and 2.53~\AA$^{-1}$, so particular attention to these regions |
| 555 |
> |
would be needed to distinguish Ice-$i^\prime$ from ice I$_\textrm{c}$. |
| 556 |
|
|
| 557 |
|
\begin{figure} |
| 558 |
|
\includegraphics[width=\linewidth]{./figures/iceGofr.pdf} |
