| 839 |
|
\epsfbox{povIce.ps} |
| 840 |
|
\caption{A water lattice built from the crystal structure assumed by |
| 841 |
|
SSD/E when undergoing an extremely restricted temperature NPT |
| 842 |
< |
simulation. This form of ice is referred to as ice 0 to emphasize its |
| 843 |
< |
simulation origins. This image was taken of the (001) face of the |
| 844 |
< |
crystal.} |
| 842 |
> |
simulation. This form of ice is referred to as ice \emph{i} to |
| 843 |
> |
emphasize its simulation origins. This image was taken of the (001) |
| 844 |
> |
face of the crystal.} |
| 845 |
|
\label{weirdice} |
| 846 |
|
\end{center} |
| 847 |
|
\end{figure} |
| 855 |
|
zeolite-like crystal structure that does not correspond to any known |
| 856 |
|
form of ice. For convenience, and to help distinguish it from the |
| 857 |
|
experimentally observed forms of ice, this crystal structure will |
| 858 |
< |
henceforth be referred to as ice-zero (ice 0). The crystallinity was |
| 859 |
< |
extensive enough that a near ideal crystal structure of ice 0 could be |
| 860 |
< |
obtained. Figure \ref{weirdice} shows the repeating crystal structure |
| 861 |
< |
of a typical crystal at 5 K. Each water molecule is hydrogen bonded to |
| 862 |
< |
four others; however, the hydrogen bonds are flexed rather than |
| 863 |
< |
perfectly straight. This results in a skewed tetrahedral geometry |
| 864 |
< |
about the central molecule. Referring to figure \ref{isosurface}, |
| 865 |
< |
these flexed hydrogen bonds are allowed due to the conical shape of |
| 866 |
< |
the attractive regions, with the greatest attraction along the direct |
| 867 |
< |
hydrogen bond configuration. Though not ideal, these flexed hydrogen |
| 868 |
< |
bonds are favorable enough to stabilize an entire crystal generated |
| 869 |
< |
around them. In fact, the imperfect ice 0 crystals were so stable that |
| 858 |
> |
henceforth be referred to as ice $\sqrt{\smash[b]{-\text{I}}}$ (ice |
| 859 |
> |
\emph{i}). The crystallinity was extensive enough that a near ideal |
| 860 |
> |
crystal structure of ice \emph{i} could be obtained. Figure |
| 861 |
> |
\ref{weirdice} shows the repeating crystal structure of a typical |
| 862 |
> |
crystal at 5 K. Each water molecule is hydrogen bonded to four others; |
| 863 |
> |
however, the hydrogen bonds are flexed rather than perfectly |
| 864 |
> |
straight. This results in a skewed tetrahedral geometry about the |
| 865 |
> |
central molecule. Referring to figure \ref{isosurface}, these flexed |
| 866 |
> |
hydrogen bonds are allowed due to the conical shape of the attractive |
| 867 |
> |
regions, with the greatest attraction along the direct hydrogen bond |
| 868 |
> |
configuration. Though not ideal, these flexed hydrogen bonds are |
| 869 |
> |
favorable enough to stabilize an entire crystal generated around |
| 870 |
> |
them. In fact, the imperfect ice \emph{i} crystals were so stable that |
| 871 |
|
they melted at temperatures nearly 100 K greater than both ice I$_c$ |
| 872 |
|
and I$_h$. |
| 873 |
|
|
| 874 |
< |
These initial simulations indicated that ice 0 is the preferred ice |
| 875 |
< |
structure for at least the SSD/E model. To verify this, a comparison |
| 876 |
< |
was made between near ideal crystals of ice $I_h$, ice $I_c$, and ice |
| 877 |
< |
0 at constant pressure with SSD/E, SSD/RF, and SSD1. Near ideal |
| 878 |
< |
versions of the three types of crystals were cooled to 1 K, and the |
| 879 |
< |
potential energies of each were compared using all three water |
| 880 |
< |
models. With every water model, ice 0 turned out to have the lowest |
| 881 |
< |
potential energy: 5\% lower than $I_h$ with SSD1, 6.5\% lower with |
| 882 |
< |
SSD/E, and 7.5\% lower with SSD/RF. |
| 874 |
> |
These initial simulations indicated that ice \emph{i} is the preferred |
| 875 |
> |
ice structure for at least the SSD/E model. To verify this, a |
| 876 |
> |
comparison was made between near ideal crystals of ice $I_h$, ice |
| 877 |
> |
$I_c$, and ice 0 at constant pressure with SSD/E, SSD/RF, and |
| 878 |
> |
SSD1. Near ideal versions of the three types of crystals were cooled |
| 879 |
> |
to 1 K, and the potential energies of each were compared using all |
| 880 |
> |
three water models. With every water model, ice \emph{i} turned out to |
| 881 |
> |
have the lowest potential energy: 5\% lower than $I_h$ with SSD1, |
| 882 |
> |
6.5\% lower with SSD/E, and 7.5\% lower with SSD/RF. |
| 883 |
|
|
| 884 |
|
In addition to these low temperature comparisons, melting sequences |
| 885 |
< |
were performed with ice 0 as the initial configuration using SSD/E, |
| 886 |
< |
SSD/RF, and SSD1 both with and without a reaction field. The melting |
| 887 |
< |
transitions for both SSD/E and SSD1 without a reaction field occurred |
| 888 |
< |
at temperature in excess of 375 K. SSD/RF and SSD1 with a reaction |
| 889 |
< |
field showed more reasonable melting transitions near 325 K. These |
| 890 |
< |
melting point observations emphasize the preference for this crystal |
| 891 |
< |
structure over the most common types of ice when using these single |
| 892 |
< |
point water models. |
| 885 |
> |
were performed with ice \emph{i} as the initial configuration using |
| 886 |
> |
SSD/E, SSD/RF, and SSD1 both with and without a reaction field. The |
| 887 |
> |
melting transitions for both SSD/E and SSD1 without a reaction field |
| 888 |
> |
occurred at temperature in excess of 375 K. SSD/RF and SSD1 with a |
| 889 |
> |
reaction field showed more reasonable melting transitions near 325 |
| 890 |
> |
K. These melting point observations emphasize the preference for this |
| 891 |
> |
crystal structure over the most common types of ice when using these |
| 892 |
> |
single point water models. |
| 893 |
|
|
| 894 |
< |
Recognizing that the above tests show ice 0 to be both the most stable |
| 895 |
< |
and lowest density crystal structure for these single point water |
| 896 |
< |
models, it is interesting to speculate on the relative stability of |
| 897 |
< |
this crystal structure with charge based water models. As a quick |
| 894 |
> |
Recognizing that the above tests show ice \emph{i} to be both the most |
| 895 |
> |
stable and lowest density crystal structure for these single point |
| 896 |
> |
water models, it is interesting to speculate on the relative stability |
| 897 |
> |
of this crystal structure with charge based water models. As a quick |
| 898 |
|
test, these 3 crystal types were converted from SSD type particles to |
| 899 |
|
TIP3P waters and read into CHARMM.\cite{Karplus83} Identical energy |
| 900 |
|
minimizations were performed on the crystals to compare the system |
| 901 |
< |
energies. Again, ice 0 was observed to have the lowest total system |
| 902 |
< |
energy. The total energy of ice 0 was ~2\% lower than ice $I_h$, which |
| 903 |
< |
was in turn ~3\% lower than ice $I_c$. Based on these initial studies, |
| 904 |
< |
it would not be surprising if results from the other common water |
| 905 |
< |
models show ice 0 to be the lowest energy crystal structure. A |
| 906 |
< |
continuation of this work studying ice 0 with multi-point water models |
| 907 |
< |
will be published in a coming article. |
| 901 |
> |
energies. Again, ice \emph{i} was observed to have the lowest total |
| 902 |
> |
system energy. The total energy of ice \emph{i} was ~2\% lower than |
| 903 |
> |
ice $I_h$, which was in turn ~3\% lower than ice $I_c$. Based on these |
| 904 |
> |
initial studies, it would not be surprising if results from the other |
| 905 |
> |
common water models show ice \emph{i} to be the lowest energy crystal |
| 906 |
> |
structure. A continuation of this work studying ice \emph{i} with |
| 907 |
> |
multi-point water models will be published in a coming article. |
| 908 |
|
|
| 909 |
|
\section{Conclusions} |
| 910 |
|
The density maximum and temperature dependent transport for the SSD |
