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 |
113 |
|
open octagonal cavities that are typically greater than 6.3 \AA\ in |
114 |
|
diameter. This relatively open overall structure leads to crystals |
115 |
|
that are 0.07 g/cm$^3$ less dense on average than ice $I_h$. |
116 |
+ |
\begin{figure} |
117 |
+ |
\includegraphics[scale=1.0]{unitCell.eps} |
118 |
+ |
\caption{Unit cells for (A) Ice-{\it i} and (B) Ice-2{\it i}, the elongated variant of Ice-{\it i}. For Ice-{\it i}, the $a$ to $c$ relation is given by $a = 2.1214c$, while for Ice-2{\it i}, $a = 1.7850c$.} |
119 |
+ |
\label{iceiCell} |
120 |
+ |
\end{figure} |
121 |
+ |
\begin{figure} |
122 |
+ |
\includegraphics[scale=1.0]{orderedIcei.eps} |
123 |
+ |
\caption{Image of a proton ordered crystal of Ice-{\it i} looking |
124 |
+ |
down the (001) crystal face. The rows of water tetramers surrounded by |
125 |
+ |
octagonal pores leads to a crystal structure that is significantly |
126 |
+ |
less dense than ice $I_h$.} |
127 |
+ |
\label{protOrder} |
128 |
+ |
\end{figure} |
129 |
|
|
130 |
|
Results in the previous study indicated that Ice-{\it i} is the |
131 |
|
minimum energy crystal structure for the single point water models |
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 |
|
|