| 246 |
|
of the ice polymorphs.\cite{Ponder87} The calculated energy difference |
| 247 |
|
in the presence and absence of PME was applied to the previous results |
| 248 |
|
in order to predict changes to the free energy landscape. |
| 249 |
+ |
|
| 250 |
+ |
In addition to the above procedures, we also tested how the inclusion |
| 251 |
+ |
of the Lennard-Jones long-range correction affects the free energy |
| 252 |
+ |
results. The correction for the Lennard-Jones trucation was included |
| 253 |
+ |
by integration of the equation discussed in section |
| 254 |
+ |
\ref{sec:LJCorrections}. Rather than discuss its affect alongside the |
| 255 |
+ |
free energy results, we will just mention that while the correction |
| 256 |
+ |
does lower the free energy of the higher density states more than the |
| 257 |
+ |
lower density states, the effect is so small that it is entirely |
| 258 |
+ |
overwelmed by the error in the free energy calculation. Since its |
| 259 |
+ |
inclusion does not influence the results, the Lennard-Jones correction |
| 260 |
+ |
was omitted from all the calculations below. |
| 261 |
|
|
| 262 |
|
\section{Initial Free Energy Results} |
| 263 |
|
|
| 447 |
|
\cmidrule(lr){2-6} |
| 448 |
|
& \multicolumn{5}{c}{(kcal mol$^{-1}$)} \\ |
| 449 |
|
\midrule |
| 450 |
< |
TIP5P-E & -11.98(4) & -11.96(4) & & - & -11.95(3) \\ |
| 450 |
> |
TIP5P-E & -11.98(4) & -11.96(4) & -11.87(3) & - & -11.95(3) \\ |
| 451 |
|
TIP4P-Ew & -13.11(3) & -13.09(3) & -12.97(3) & - & -12.98(3) \\ |
| 452 |
|
SPC/E & -12.99(3) & -13.00(3) & -13.03(3) & - & -12.99(3) \\ |
| 453 |
|
SSD/RF & -11.83(3) & -11.66(4) & -12.32(3) & -12.39(3) & - \\ |
| 485 |
|
higher in energy, though overlapping within error, and the less |
| 486 |
|
realistic ice B and Ice-$i^\prime$ are destabilized relative to these |
| 487 |
|
polymorphs. TIP5P-E shows similar behavior to SPC/E, where there is no |
| 488 |
< |
real free energy distinction between the various polymorphs and lend |
| 489 |
< |
credence to other results indicating the preferred form of TIP5P at |
| 490 |
< |
1~atm is a structure similar to ice B.\cite{Yamada02,Vega05,Abascal05} |
| 491 |
< |
These results indicate that TIP4P-Ew is a better mimic of real water |
| 492 |
< |
than these other models when studying crystallization and solid forms |
| 493 |
< |
of water. |
| 488 |
> |
real free energy distinction between the various polymorphs because |
| 489 |
> |
many overlap within error. While ice B is close in free energy to the |
| 490 |
> |
other polymorphs, these results fail to support the findings of other |
| 491 |
> |
researchers indicating the preferred form of TIP5P at 1~atm is a |
| 492 |
> |
structure similar to ice B.\cite{Yamada02,Vega05,Abascal05} It should |
| 493 |
> |
be noted that we are looking at TIP5P-E rather than TIP5P, and the |
| 494 |
> |
differences in the Lennard-Jones parameters could be a reason for this |
| 495 |
> |
dissimilarity. Overall, these results indicate that TIP4P-Ew is a |
| 496 |
> |
better mimic of real water than these other models when studying |
| 497 |
> |
crystallization and solid forms of water. |
| 498 |
|
|
| 499 |
|
\section{Conclusions} |
| 500 |
|
|
| 501 |
|
In this work, thermodynamic integration was used to determine the |
| 502 |
|
absolute free energies of several ice polymorphs. The new polymorph, |
| 503 |
< |
Ice-{\it i} was observed to be the stable crystalline state for {\it |
| 503 |
> |
Ice-$i$ was observed to be the stable crystalline state for {\it |
| 504 |
|
all} the water models when using a 9.0~\AA\ cutoff. However, the free |
| 505 |
|
energy partially depends on simulation conditions (particularly on the |
| 506 |
< |
choice of long range correction method). Regardless, Ice-{\it i} was |
| 506 |
> |
choice of long range correction method). Regardless, Ice-$i$ was |
| 507 |
|
still observed to be a stable polymorph for all of the studied water |
| 508 |
|
models. |
| 509 |
|
|
| 510 |
|
So what is the preferred solid polymorph for simulated water? As |
| 511 |
|
indicated above, the answer appears to be dependent both on the |
| 512 |
|
conditions and the model used. In the case of short cutoffs without a |
| 513 |
< |
long-range interaction correction, Ice-{\it i} and Ice-$i^\prime$ have |
| 513 |
> |
long-range interaction correction, Ice-$i$ and Ice-$i^\prime$ have |
| 514 |
|
the lowest free energy of the studied polymorphs with all the models. |
| 515 |
|
Ideally, crystallization of each model under constant pressure |
| 516 |
|
conditions, as was done with SSD/E, would aid in the identification of |
| 519 |
|
insight about important behavior of others. |
| 520 |
|
|
| 521 |
|
We also note that none of the water models used in this study are |
| 522 |
< |
polarizable or flexible models. It is entirely possible that the |
| 523 |
< |
polarizability of real water makes Ice-{\it i} substantially less |
| 524 |
< |
stable than ice I$_h$. However, the calculations presented above seem |
| 525 |
< |
interesting enough to communicate before the role of polarizability |
| 526 |
< |
(or flexibility) has been thoroughly investigated. |
| 522 |
> |
polarizable or flexible models. It is entirely possible that the |
| 523 |
> |
polarizability of real water makes Ice-$i$ substantially less stable |
| 524 |
> |
than ice I$_\textrm{h}$. The dipole moment of the water molecules |
| 525 |
> |
increases as the system becomes more condensed, and the increasing |
| 526 |
> |
dipole moment should destabilize the tetramer structures in |
| 527 |
> |
Ice-$i$. Right now, using TIP4P-Ew with an electrostatic correction |
| 528 |
> |
gives the proper thermodynamically preferred state, and we recommend |
| 529 |
> |
this arrangement for study of crystallization processes if the |
| 530 |
> |
computational cost increase that comes with including polarizability |
| 531 |
> |
is an issue. |
| 532 |
|
|
| 533 |
< |
Finally, due to the stability of Ice-{\it i} in the investigated |
| 533 |
> |
Finally, due to the stability of Ice-$i$ in the investigated |
| 534 |
|
simulation conditions, the question arises as to possible experimental |
| 535 |
|
observation of this polymorph. The rather extensive past and current |
| 536 |
|
experimental investigation of water in the low pressure regime makes |
