| 45 |
|
known low-pressure ice structures under all of these water models. |
| 46 |
|
Additionally, potential truncation was shown to have an effect on the |
| 47 |
|
calculated free energies, and can result in altered free energy |
| 48 |
< |
landscapes. Structure factor for the new crystal were generated and |
| 49 |
< |
we await experimental confirmation of the existence of this new |
| 50 |
< |
polymorph. |
| 48 |
> |
landscapes. Structure factor predictions for the new crystal were |
| 49 |
> |
generated and we await experimental confirmation of the existence of |
| 50 |
> |
this new polymorph. |
| 51 |
|
\end{abstract} |
| 52 |
|
|
| 53 |
|
%\narrowtext |
| 105 |
|
|
| 106 |
|
\begin{figure} |
| 107 |
|
\includegraphics[width=\linewidth]{unitCell.eps} |
| 108 |
< |
\caption{Unit cells for (A) Ice-{\it i} and (B) Ice-$i^\prime$, the |
| 109 |
< |
elongated variant of Ice-{\it i}. The spheres represent the |
| 108 |
> |
\caption{Unit cells for (A) Ice-{\it i} and (B) Ice-{\it i}$^\prime$, |
| 109 |
> |
the elongated variant of Ice-{\it i}. The spheres represent the |
| 110 |
|
center-of-mass locations of the water molecules. The $a$ to $c$ |
| 111 |
|
ratios for Ice-{\it i} and Ice-{\it i}$^\prime$ are given by |
| 112 |
|
$a:2.1214c$ and $a:1.7850c$ respectively.} |
| 138 |
|
from which Ice-{\it i} was crystallized (SSD/E) in addition to several |
| 139 |
|
common water models (TIP3P, TIP4P, TIP5P, and SPC/E) and a reaction |
| 140 |
|
field parametrized single point dipole water model (SSD/RF). It should |
| 141 |
< |
be noted that a second version of Ice-{\it i} (Ice-$i^\prime$) was |
| 142 |
< |
used in calculations involving SPC/E, TIP4P, and TIP5P. The unit cell |
| 143 |
< |
of this crystal (Fig. \ref{iceiCell}B) is similar to the Ice-{\it i} |
| 144 |
< |
unit it is extended in the direction of the (001) face and compressed |
| 145 |
< |
along the other two faces. |
| 141 |
> |
be noted that a second version of Ice-{\it i} (Ice-{\it i}$^\prime$) |
| 142 |
> |
was used in calculations involving SPC/E, TIP4P, and TIP5P. The unit |
| 143 |
> |
cell of this crystal (Fig. \ref{iceiCell}B) is similar to the Ice-{\it |
| 144 |
> |
i} unit it is extended in the direction of the (001) face and |
| 145 |
> |
compressed along the other two faces. There is typically a small |
| 146 |
> |
distortion of proton ordered Ice-{\it i}$^\prime$ that converts the |
| 147 |
> |
normally square tetramer into a rhombus with alternating approximately |
| 148 |
> |
85 and 95 degree angles. The degree of this distortion is model |
| 149 |
> |
dependent and significant enough to split the tetramer diagonal |
| 150 |
> |
location peak in the radial distribution function. |
| 151 |
|
|
| 152 |
|
\section{Methods} |
| 153 |
|
|
| 285 |
|
|
| 286 |
|
\begin{table*} |
| 287 |
|
\begin{minipage}{\linewidth} |
| 283 |
– |
\renewcommand{\thefootnote}{\thempfootnote} |
| 288 |
|
\begin{center} |
| 289 |
+ |
|
| 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 parentheses. *Ice |
| 294 |
< |
$I_c$ rapidly converts to a liquid at 200 K with the SSD/RF model.} |
| 295 |
< |
\begin{tabular}{ l c c c c } |
| 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.} |
| 296 |
> |
|
| 297 |
> |
\begin{tabular}{lcccc} |
| 298 |
|
\hline |
| 299 |
|
Water Model & $I_h$ & $I_c$ & B & Ice-{\it i}\\ |
| 300 |
|
\hline |
| 303 |
|
TIP5P & -11.85(3) & -11.86(2) & -11.96(2) & -12.29(2)\\ |
| 304 |
|
SPC/E & -12.67(2) & -12.96(2) & -13.25(3) & -13.55(2)\\ |
| 305 |
|
SSD/E & -11.27(2) & -11.19(4) & -12.09(2) & -12.54(2)\\ |
| 306 |
< |
SSD/RF & -11.51(2) & NA* & -12.08(3) & -12.29(2)\\ |
| 306 |
> |
SSD/RF & -11.51(2) & NA$^{*}$ & -12.08(3) & -12.29(2)\\ |
| 307 |
|
\end{tabular} |
| 308 |
|
\label{freeEnergy} |
| 309 |
|
\end{center} |
| 348 |
|
|
| 349 |
|
\begin{table*} |
| 350 |
|
\begin{minipage}{\linewidth} |
| 344 |
– |
\renewcommand{\thefootnote}{\thempfootnote} |
| 351 |
|
\begin{center} |
| 352 |
+ |
|
| 353 |
|
\caption{Melting ($T_m$), boiling ($T_b$), and sublimation ($T_s$) |
| 354 |
|
temperatures at 1 atm for several common water models compared with |
| 355 |
|
experiment. The $T_m$ and $T_s$ values from simulation correspond to a |
| 356 |
|
transition between Ice-{\it i} (or Ice-{\it i}$^\prime$) and the |
| 357 |
|
liquid or gas state.} |
| 358 |
< |
\begin{tabular}{ l c c c c c c c } |
| 358 |
> |
|
| 359 |
> |
\begin{tabular}{lccccccc} |
| 360 |
|
\hline |
| 361 |
< |
Equilibria Point & TIP3P & TIP4P & TIP5P & SPC/E & SSD/E & SSD/RF & Exp.\\ |
| 361 |
> |
Equilibrium Point & TIP3P & TIP4P & TIP5P & SPC/E & SSD/E & SSD/RF & Exp.\\ |
| 362 |
|
\hline |
| 363 |
|
$T_m$ (K) & 269(4) & 266(5) & 271(4) & 296(3) & - & 278(4) & 273\\ |
| 364 |
|
$T_b$ (K) & 357(2) & 354(2) & 337(2) & 396(2) & - & 348(2) & 373\\ |
| 443 |
|
|
| 444 |
|
\begin{table*} |
| 445 |
|
\begin{minipage}{\linewidth} |
| 438 |
– |
\renewcommand{\thefootnote}{\thempfootnote} |
| 446 |
|
\begin{center} |
| 447 |
+ |
|
| 448 |
|
\caption{The free energy of the studied ice polymorphs after applying |
| 449 |
|
the energy difference attributed to the inclusion of the PME |
| 450 |
|
long-range interaction correction. Units are kcal/mol.} |
| 451 |
< |
\begin{tabular}{ l c c c c } |
| 451 |
> |
|
| 452 |
> |
\begin{tabular}{ccccc} |
| 453 |
|
\hline |
| 454 |
< |
\ \ Water Model \ \ & \ \ \ \ \ $I_h$ \ \ & \ \ \ \ \ $I_c$ \ \ & \ \quad \ \ \ \ B \ \ & \ \ \ \ \ Ice-{\it i} \ \ \\ |
| 454 |
> |
Water Model & $I_h$ & $I_c$ & B & Ice-{\it i} \\ |
| 455 |
|
\hline |
| 456 |
< |
TIP3P & -11.53(2) & -11.24(3) & -11.51(3) & -11.67(3)\\ |
| 457 |
< |
SPC/E & -12.77(2) & -12.92(2) & -12.96(3) & -13.02(2)\\ |
| 456 |
> |
TIP3P & -11.53(2) & -11.24(3) & -11.51(3) & -11.67(3) \\ |
| 457 |
> |
SPC/E & -12.77(2) & -12.92(2) & -12.96(3) & -13.02(2) \\ |
| 458 |
|
\end{tabular} |
| 459 |
|
\label{pmeShift} |
| 460 |
|
\end{center} |
| 493 |
|
deposition environments, and in clathrate structures involving small |
| 494 |
|
non-polar molecules. Figs. \ref{fig:gofr} and \ref{fig:sofq} contain |
| 495 |
|
our predictions for both the pair distribution function ($g_{OO}(r)$) |
| 496 |
< |
and the structure factor ($S(\vec{q})$ for ice $I_c$ and for ice-{\it |
| 497 |
< |
i} at a temperature of 77K. In our initial comparison of the |
| 498 |
< |
predicted S(q) for Ice-{\it i} and experimental studies of amorphous |
| 499 |
< |
solid water, it is possible that some of the ``spurious'' peaks that |
| 500 |
< |
could not be assigned in an early report on high-density amorphous |
| 501 |
< |
(HDA) ice could correspond to peaks labeled in this |
| 502 |
< |
S(q).\cite{Bizid87} It should be noted that there is typically poor |
| 503 |
< |
agreement on crystal densities between simulation and experiment, so |
| 495 |
< |
such peak comparisons should be made with caution. We will leave it |
| 496 |
< |
to our experimental colleagues to make the final determination on |
| 497 |
< |
whether this ice polymorph is named appropriately (i.e. with an |
| 498 |
< |
imaginary number) or if it can be promoted to Ice-0. |
| 496 |
> |
and the structure factor ($S(\vec{q})$ for ice $I_h$, $I_c$, and for |
| 497 |
> |
ice-{\it i} at a temperature of 77K. In studies of the high and low |
| 498 |
> |
density forms of amorphous ice, ``spurious'' diffraction peaks have |
| 499 |
> |
been observed experimentally.\cite{Bizid87} It is possible that a |
| 500 |
> |
variant of Ice-{\it i} could explain some of this behavior; however, |
| 501 |
> |
we will leave it to our experimental colleagues to make the final |
| 502 |
> |
determination on whether this ice polymorph is named appropriately |
| 503 |
> |
(i.e. with an imaginary number) or if it can be promoted to Ice-0. |
| 504 |
|
|
| 505 |
|
\begin{figure} |
| 506 |
|
\includegraphics[width=\linewidth]{iceGofr.eps} |
| 507 |
< |
\caption{Radial distribution functions of Ice-{\it i} and ice $I_c$ |
| 508 |
< |
calculated from from simulations of the SSD/RF water model at 77 K.} |
| 507 |
> |
\caption{Radial distribution functions of ice $I_h$, $I_c$, |
| 508 |
> |
Ice-{\it i}, and Ice-{\it i}$^\prime$ calculated from from simulations |
| 509 |
> |
of the SSD/RF water model at 77 K.} |
| 510 |
|
\label{fig:gofr} |
| 511 |
|
\end{figure} |
| 512 |
|
|
| 513 |
|
\begin{figure} |
| 514 |
|
\includegraphics[width=\linewidth]{sofq.eps} |
| 515 |
< |
\caption{Predicted structure factors for Ice-{\it i} and ice $I_c$ at |
| 516 |
< |
77 K. The raw structure factors have been convoluted with a gaussian |
| 517 |
< |
instrument function (0.075 \AA$^{-1}$ width) to compensate for the |
| 518 |
< |
trunction effects in our finite size simulations. The labeled peaks |
| 519 |
< |
compared favorably with ``spurious'' peaks observed in experimental |
| 514 |
< |
studies of amorphous solid water.\cite{Bizid87}} |
| 515 |
> |
\caption{Predicted structure factors for ice $I_h$, $I_c$, Ice-{\it i}, |
| 516 |
> |
and Ice-{\it i}$^\prime$ at 77 K. The raw structure factors have |
| 517 |
> |
been convoluted with a gaussian instrument function (0.075 \AA$^{-1}$ |
| 518 |
> |
width) to compensate for the trunction effects in our finite size |
| 519 |
> |
simulations.} |
| 520 |
|
\label{fig:sofq} |
| 521 |
|
\end{figure} |
| 522 |
|
|
