| 62 |
|
|
| 63 |
|
Molecular dynamics has developed into a valuable tool for studying the |
| 64 |
|
phase behavior of systems ranging from small or simple |
| 65 |
< |
molecules\cite{smallStuff} to complex biological |
| 65 |
> |
molecules\cite{Matsumoto02andOthers} to complex biological |
| 66 |
|
species.\cite{bigStuff} Many techniques have been developed in order |
| 67 |
|
to investigate the thermodynamic properites of model substances, |
| 68 |
|
providing both qualitative and quantitative comparisons between |
| 74 |
|
Water has proven to be a challenging substance to depict in |
| 75 |
|
simulations, and has resulted in a variety of models that attempt to |
| 76 |
|
describe its behavior under a varying simulation |
| 77 |
< |
conditions.\cite{lotsOfWaterPapers} Many of these models have been |
| 78 |
< |
used to investigate important physical phenomena like phase |
| 79 |
< |
transitions and the hydrophobic effect.\cite{evenMorePapers} With the |
| 80 |
< |
advent of numerous differing models, it is only natural that attention |
| 81 |
< |
is placed on the properties of the models themselves in an attempt to |
| 82 |
< |
clarify their benefits and limitations when applied to a system of |
| 83 |
< |
interest.\cite{modelProps} One important but challenging property to |
| 84 |
< |
quantify is the free energy, particularly of the solid forms of |
| 85 |
< |
water. Difficulty in these types of studies typically arises from the |
| 86 |
< |
assortment of possible crystalline polymorphs that water that water |
| 87 |
< |
adopts over a wide range of pressures and temperatures. There are |
| 88 |
< |
currently 13 recognized forms of ice, and it is a challenging task to |
| 89 |
< |
investigate the entire free energy landscape.\cite{Sanz04} Ideally, |
| 90 |
< |
research is focused on the phases having the lowest free energy, |
| 91 |
< |
because these phases will dictate the true transition temperatures and |
| 92 |
< |
pressures for their respective model. |
| 77 |
> |
conditions.\cite{Berendsen81,Jorgensen83,Bratko85,Berendsen87,Liu96,Mahoney00,Fennell04} |
| 78 |
> |
Many of these models have been used to investigate important physical |
| 79 |
> |
phenomena like phase transitions and the hydrophobic |
| 80 |
> |
effect.\cite{evenMorePapers} With the advent of numerous differing |
| 81 |
> |
models, it is only natural that attention is placed on the properties |
| 82 |
> |
of the models themselves in an attempt to clarify their benefits and |
| 83 |
> |
limitations when applied to a system of interest.\cite{modelProps} One |
| 84 |
> |
important but challenging property to quantify is the free energy, |
| 85 |
> |
particularly of the solid forms of water. Difficulty in these types of |
| 86 |
> |
studies typically arises from the assortment of possible crystalline |
| 87 |
> |
polymorphs that water that water adopts over a wide range of pressures |
| 88 |
> |
and temperatures. There are currently 13 recognized forms of ice, and |
| 89 |
> |
it is a challenging task to investigate the entire free energy |
| 90 |
> |
landscape.\cite{Sanz04} Ideally, research is focused on the phases |
| 91 |
> |
having the lowest free energy, because these phases will dictate the |
| 92 |
> |
true transition temperatures and pressures for their respective model. |
| 93 |
|
|
| 94 |
|
In this paper, standard reference state methods were applied to the |
| 95 |
|
study of crystalline water polymorphs in the low pressure regime. This |
| 97 |
|
arrived at through crystallization of a computationally efficient |
| 98 |
|
water model under constant pressure and temperature |
| 99 |
|
conditions. Crystallization events are interesting in and of |
| 100 |
< |
themselves\cite{nucleationStudies}; however, the crystal structure |
| 100 |
> |
themselves\cite{Matsumoto02,Yamada02}; however, the crystal structure |
| 101 |
|
obtained in this case was different from any previously observed ice |
| 102 |
|
polymorphs, in experiment or simulation.\cite{Fennell04} This crystal |
| 103 |
|
was termed Ice-{\it i} in homage to its origin in computational |
| 222 |
|
\end{figure} |
| 223 |
|
|
| 224 |
|
Charge, dipole, and Lennard-Jones interactions were modified by a |
| 225 |
< |
cubic switching between 100\% and 85\% of the cutoff value (9 \AA ). By |
| 226 |
< |
applying this function, these interactions are smoothly truncated, |
| 227 |
< |
thereby avoiding poor energy conserving dynamics resulting from |
| 228 |
< |
harsher truncation schemes. The effect of a long-range correction was |
| 229 |
< |
also investigated on select model systems in a variety of manners. For |
| 230 |
< |
the SSD/RF model, a reaction field with a fixed dielectric constant of |
| 231 |
< |
80 was applied in all simulations.\cite{Onsager36} For a series of the |
| 232 |
< |
least computationally expensive models (SSD/E, SSD/RF, and TIP3P), |
| 233 |
< |
simulations were performed with longer cutoffs of 12 and 15 \AA\ to |
| 234 |
< |
compare with the 9 \AA\ cutoff results. Finally, results from the use |
| 235 |
< |
of an Ewald summation were estimated for TIP3P and SPC/E by performing |
| 225 |
> |
cubic switching between 100\% and 85\% of the cutoff value (9 \AA |
| 226 |
> |
). By applying this function, these interactions are smoothly |
| 227 |
> |
truncated, thereby avoiding poor energy conserving dynamics resulting |
| 228 |
> |
from harsher truncation schemes. The effect of a long-range correction |
| 229 |
> |
was also investigated on select model systems in a variety of |
| 230 |
> |
manners. For the SSD/RF model, a reaction field with a fixed |
| 231 |
> |
dielectric constant of 80 was applied in all |
| 232 |
> |
simulations.\cite{Onsager36} For a series of the least computationally |
| 233 |
> |
expensive models (SSD/E, SSD/RF, and TIP3P), simulations were |
| 234 |
> |
performed with longer cutoffs of 12 and 15 \AA\ to compare with the 9 |
| 235 |
> |
\AA\ cutoff results. Finally, results from the use of an Ewald |
| 236 |
> |
summation were estimated for TIP3P and SPC/E by performing |
| 237 |
|
calculations with Particle-Mesh Ewald (PME) in the TINKER molecular |
| 238 |
< |
mechanics software package. TINKER was chosen because it can also |
| 239 |
< |
propagate the motion of rigid-bodies, and provides the most direct |
| 240 |
< |
comparison to the results from OOPSE. The calculated energy difference |
| 241 |
< |
in the presence and absence of PME was applied to the previous results |
| 242 |
< |
in order to predict changes in the free energy landscape. |
| 238 |
> |
mechanics software package.\cite{Tinker} TINKER was chosen because it |
| 239 |
> |
can also propagate the motion of rigid-bodies, and provides the most |
| 240 |
> |
direct comparison to the results from OOPSE. The calculated energy |
| 241 |
> |
difference in the presence and absence of PME was applied to the |
| 242 |
> |
previous results in order to predict changes in the free energy |
| 243 |
> |
landscape. |
| 244 |
|
|
| 245 |
|
\section{Results and discussion} |
| 246 |
|
|
