| 35 |
|
SSD/E water models.\cite{Baez95a} Liquid state free energies at 300 |
| 36 |
|
and 400 K for all of these water models were also determined using |
| 37 |
|
this same technique, in order to determine melting points and to |
| 38 |
< |
generate phase diagrams. All simulations were carried out at |
| 38 |
> |
generate phase diagrams. System sizes were 648 or 1728 molecules for |
| 39 |
> |
ice B, 1024 or 1280 molecules for ice $I_h$, 1000 molecules for ice |
| 40 |
> |
$I_c$, and 1024 molecules for Ice-{\it i} and the liquid state |
| 41 |
> |
simulations. The larger crystal sizes were necessary for simulations |
| 42 |
> |
involving larger cutoff values. All simulations were carried out at |
| 43 |
|
densities which correspond to a pressure of approximately 1 atm at |
| 44 |
|
their respective temperatures. |
| 45 |
|
|
| 138 |
|
and absence of PME was applied to the previous results in order to |
| 139 |
|
predict changes to the free energy landscape. |
| 140 |
|
|
| 141 |
+ |
Additionally, $g_{OO}(r)$ and $S(\vec{q})$ plots were generated for |
| 142 |
+ |
the two Ice-{\it i} variants (along with example ice $I_h$ and $I_c$ |
| 143 |
+ |
plots) at 77K, and they are shown in figures \ref{fig:gofr} and |
| 144 |
+ |
\ref{fig:sofq}. The $S(\vec{q})$ is related to a three dimensional |
| 145 |
+ |
Fourier transform of the radial distribution function, which |
| 146 |
+ |
simplifies to the following expression: |
| 147 |
+ |
|
| 148 |
+ |
\begin{equation} |
| 149 |
+ |
S(q) = 1 + 4\pi\rho\int_{0}^{\infty} r^2 \frac{\sin kr}{kr}g_{OO}(r)dr, |
| 150 |
+ |
\label{sofqEq} |
| 151 |
+ |
\end{equation} |
| 152 |
+ |
|
| 153 |
+ |
where $\rho$ is the number density. To obtain a good estimation of |
| 154 |
+ |
$S(\vec{q})$, $g_{OO}(r)$ needs to extend to large $r$ values. Thus, |
| 155 |
+ |
simulations to obtain these plots were run on crystals eight times the |
| 156 |
+ |
size of those used in the thermodynamic integrations. |
| 157 |
+ |
|
| 158 |
+ |
\begin{figure} |
| 159 |
+ |
\includegraphics[width=\linewidth]{iceGofr.eps} |
| 160 |
+ |
\caption{Radial distribution functions of ice $I_h$, $I_c$, and |
| 161 |
+ |
Ice-{\it i} calculated from from simulations of the SSD/RF water model |
| 162 |
+ |
at 77 K. The Ice-{\it i} distribution function was obtained from |
| 163 |
+ |
simulations composed of TIP4P water.} |
| 164 |
+ |
\label{fig:gofr} |
| 165 |
+ |
\end{figure} |
| 166 |
+ |
|
| 167 |
+ |
\begin{figure} |
| 168 |
+ |
\includegraphics[width=\linewidth]{sofq.eps} |
| 169 |
+ |
\caption{Predicted structure factors for ice $I_h$, $I_c$, Ice-{\it i}, |
| 170 |
+ |
and Ice-{\it i}$^\prime$ at 77 K. The raw structure factors have |
| 171 |
+ |
been convoluted with a gaussian instrument function (0.075 \AA$^{-1}$ |
| 172 |
+ |
width) to compensate for the trunction effects in our finite size |
| 173 |
+ |
simulations.} |
| 174 |
+ |
\label{fig:sofq} |
| 175 |
+ |
\end{figure} |
| 176 |
+ |
|
| 177 |
+ |
|
| 178 |
|
\newpage |
| 179 |
|
|
| 180 |
|
\bibliographystyle{jcp} |
