| 8 |
|
These models have been used to investigate important physical |
| 9 |
|
phenomena like phase transitions and the hydrophobic |
| 10 |
|
effect.\cite{Yamada02,Marrink94,Gallagher03} With the choice of models |
| 11 |
< |
available, it is only natural to compare the models under interesting |
| 11 |
> |
available, it is only natural to compare them under interesting |
| 12 |
|
thermodynamic conditions in an attempt to clarify the limitations of |
| 13 |
< |
each of the models.\cite{Jorgensen83,Jorgensen98b,Baez94,Mahoney01} |
| 14 |
< |
Two important property to quantify are the Gibbs and Helmholtz free |
| 15 |
< |
energies, particularly for the solid forms of water, as these predict |
| 16 |
< |
the thermodynamic stability of the various phases. Water has a |
| 13 |
> |
each.\cite{Jorgensen83,Jorgensen98b,Baez94,Mahoney01} Two important |
| 14 |
> |
property to quantify are the Gibbs and Helmholtz free energies, |
| 15 |
> |
particularly for the solid forms of water, as these predict the |
| 16 |
> |
thermodynamic stability of the various phases. Water has a |
| 17 |
|
particularly rich phase diagram and takes on a number of different and |
| 18 |
|
stable crystalline structures as the temperature and pressure are |
| 19 |
|
varied. This complexity makes it a challenging task to investigate the |
| 279 |
|
\cmidrule(l){7-8} |
| 280 |
|
& \multicolumn{5}{c}{(kcal mol$^{-1}$)} & \multicolumn{2}{c}{(K)}\\ |
| 281 |
|
\midrule |
| 282 |
– |
TIP3P & -11.41(2) & -11.23(3) & -11.82(3) & -12.30(3) & - & 269(7) & 357(4)\\ |
| 283 |
– |
TIP4P & -11.84(3) & -12.04(2) & -12.08(3) & - & -12.33(3) & 262(6) & 354(4)\\ |
| 282 |
|
TIP5P & -11.85(3) & -11.86(2) & -11.96(2) & - & -12.29(2) & 266(7) & 337(4)\\ |
| 283 |
+ |
TIP4P & -11.84(3) & -12.04(2) & -12.08(3) & - & -12.33(3) & 262(6) & 354(4)\\ |
| 284 |
+ |
TIP3P & -11.41(2) & -11.23(3) & -11.82(3) & -12.30(3) & - & 269(7) & 357(4)\\ |
| 285 |
|
SPC/E & -12.87(2) & -13.05(2) & -13.26(3) & - & -13.55(2) & 299(6) & 396(4)\\ |
| 286 |
|
SSD/E & -11.27(2) & -11.19(4) & -12.09(2) & -12.54(2) & - & *355(4) & -\\ |
| 287 |
|
SSD/RF & -11.96(2) & -11.60(2) & -12.53(3) & -12.79(2) & - & 278(7) & 382(4)\\ |
| 403 |
|
|
| 404 |
|
\section{Expanded Results Using Damped Shifted Force Electrostatics} |
| 405 |
|
|
| 406 |
+ |
In chapter \ref{chap:electrostatics}, we discussed in detail a |
| 407 |
+ |
pairwise method for handling electrostatics (shifted force, {\sc sf}) |
| 408 |
+ |
that can be used as a simple and efficient replacement for the Ewald |
| 409 |
+ |
summation. Answering the question of the free energies of these ice |
| 410 |
+ |
polymorphs with varying water models would be an interesting |
| 411 |
+ |
application of this technique. To this end, we set up thermodynamic |
| 412 |
+ |
integrations of all of the previously discussed ice polymorphs using |
| 413 |
+ |
the {\sc sf} technique with a cutoff radius of 12~\AA\ and an $\alpha$ |
| 414 |
+ |
of 0.2125~\AA . These calculations were performed on TIP5P-E and |
| 415 |
+ |
TIP4P-Ew (variants of the root models optimized for the Ewald |
| 416 |
+ |
summation) as well as SPC/E, SSD/RF, and TRED (see section |
| 417 |
+ |
\ref{sec:tredWater}). |
| 418 |
|
|
| 419 |
+ |
\begin{table} |
| 420 |
+ |
\centering |
| 421 |
+ |
\caption{HELMHOLTZ FREE ENERGIES OF ICE POLYMORPHS USING THE DAMPED |
| 422 |
+ |
SHIFTED FORCE CORRECTION} |
| 423 |
+ |
\begin{tabular}{ lccccc } |
| 424 |
+ |
\toprule |
| 425 |
+ |
\toprule |
| 426 |
+ |
Model & I$_\textrm{h}$ & I$_\textrm{c}$ & B & Ice-$i$ & Ice-$i^\prime$ \\ |
| 427 |
+ |
\cmidrule(lr){2-6} |
| 428 |
+ |
& \multicolumn{5}{c}{(kcal mol$^{-1}$)} \\ |
| 429 |
+ |
\midrule |
| 430 |
+ |
TIP5P-E & -10.76(4) & -10.72(4) & & - & -10.68(4) \\ |
| 431 |
+ |
TIP4P-Ew & & -11.77(3) & & - & -11.60(3) \\ |
| 432 |
+ |
SPC/E & -12.98(3) & -11.60(3) & & - & -12.93(3) \\ |
| 433 |
+ |
SSD/RF & -11.81(4) & -11.65(3) & & -12.41(4) & - \\ |
| 434 |
+ |
TRED & -12.58(3) & -12.44(3) & & -13.09(4) & - \\ |
| 435 |
+ |
\end{tabular} |
| 436 |
+ |
\label{tab:dampedFreeEnergy} |
| 437 |
+ |
\end{table} |
| 438 |
+ |
|
| 439 |
+ |
|
| 440 |
|
\section{Conclusions} |
| 441 |
|
|
| 442 |
|
In this work, thermodynamic integration was used to determine the |
