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simulations using this model, Ichiye \emph{et al.} reported a |
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calculation speed up of up to an order of magnitude over other |
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comparable models while maintaining the structural behavior of |
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water.\cite{Ichiye96} In the original molecular dynamics studies of |
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SSD, it was shown that it actually improves upon the prediction of |
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water's dynamical properties 3 and 4-point models.\cite{Ichiye99} This |
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water.\cite{Ichiye96} In the original molecular dynamics studies, it |
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was shown that SSD improves on the prediction of many of water's |
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dynamical properties over TIP3P and SPC/E.\cite{Ichiye99} This |
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attractive combination of speed and accurate depiction of solvent |
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properties makes SSD a model of interest for the simulation of large |
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scale biological systems, such as membrane phase behavior, a specific |
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to the use of reaction field, simulations were also performed without |
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a surrounding dielectric and suggestions are proposed on how to make |
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SSD more compatible with a reaction field. |
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|
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|
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Simulations were performed in both the isobaric-isothermal and |
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microcanonical ensembles. The constant pressure simulations were |
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implemented using an integral thermostat and barostat as outlined by |
212 |
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Hoover.\cite{Hoover85,Hoover86} For the constant pressure |
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simulations, the \emph{Q} parameter for the was set to 5.0 amu |
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\(\cdot\)\AA\(^{2}\), and the relaxation time (\(\tau\))\ was set at |
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< |
100 ps. |
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> |
Hoover.\cite{Hoover85,Hoover86} All particles were treated as |
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non-linear rigid bodies. Vibrational constraints are not necessary in |
214 |
> |
simulations of SSD, because there are no explicit hydrogen atoms, and |
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> |
thus no molecular vibrational modes need to be considered. |
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|
|
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Integration of the equations of motion was carried out using the |
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symplectic splitting method proposed by Dullweber \emph{et |
220 |
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deals with poor energy conservation of rigid body systems using |
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quaternions. While quaternions work well for orientational motion in |
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|
alternate ensembles, the microcanonical ensemble has a constant energy |
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requirement that is actually quite sensitive to errors in the |
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equations of motion. The original implementation of this code utilized |
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quaternions for rotational motion propagation; however, a detailed |
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investigation showed that they resulted in a steady drift in the total |
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energy, something that has been observed by others.\cite{Laird97} |
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> |
requirement that is quite sensitive to errors in the equations of |
224 |
> |
motion. The original implementation of this code utilized quaternions |
225 |
> |
for rotational motion propagation; however, a detailed investigation |
226 |
> |
showed that they resulted in a steady drift in the total energy, |
227 |
> |
something that has been observed by others.\cite{Laird97} |
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|
|
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|
The key difference in the integration method proposed by Dullweber |
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|
\emph{et al.} is that the entire rotation matrix is propagated from |
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|
method, the orientational propagation involves a sequence of matrix |
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|
evaluations to update the rotation matrix.\cite{Dullweber1997} These |
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|
matrix rotations end up being more costly computationally than the |
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< |
simpler arithmetic quaternion propagation. On average, a 1000 SSD |
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< |
particle simulation shows a 7\% increase in computation time using the |
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< |
symplectic step method in place of quaternions. This cost is more than |
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< |
justified when comparing the energy conservation of the two methods as |
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< |
illustrated in figure \ref{timestep}. |
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> |
simpler arithmetic quaternion propagation. With the same time step, a |
248 |
> |
1000 SSD particle simulation shows an average 7\% increase in |
249 |
> |
computation time using the symplectic step method in place of |
250 |
> |
quaternions. This cost is more than justified when comparing the |
251 |
> |
energy conservation of the two methods as illustrated in figure |
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> |
\ref{timestep}. |
253 |
|
|
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|
\begin{figure} |
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|
\includegraphics[width=61mm, angle=-90]{timeStep.epsi} |
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|
increment was decreased from 25 K to 10 and then 5 K. The above |
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|
equilibration and production times were sufficient in that the system |
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|
volume fluctuations dampened out in all but the very cold simulations |
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< |
(below 225 K). In order to further improve statistics, five separate |
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< |
simulation progressions were performed, and the averaged results from |
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the $I_h$ melting simulations are shown in figure \ref{dense1}. |
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|
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\begin{figure} |
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\includegraphics[width=65mm, angle=-90]{1hdense.epsi} |
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\caption{Average density of SSD water at increasing temperatures |
326 |
< |
starting from ice $I_h$ lattice.} |
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\label{dense1} |
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< |
\end{figure} |
320 |
> |
(below 225 K). In order to further improve statistics, an ensemble |
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> |
average was accumulated from five separate simulation progressions, |
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> |
each starting from a different ice crystal. |
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|
|
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|
\subsection{Density Behavior} |
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|
In the initial average density versus temperature plot, the density |
896 |
|
simulations of biochemical systems. |
897 |
|
|
898 |
|
\section{Acknowledgments} |
899 |
< |
The authors would like to thank the National Science Foundation for |
900 |
< |
funding under grant CHE-0134881. Computation time was provided by the |
901 |
< |
Notre Dame Bunch-of-Boxes (B.o.B) computer cluster under NSF grant DMR |
902 |
< |
00 79647. |
899 |
> |
Support for this project was provided by the National Science |
900 |
> |
Foundation under grant CHE-0134881. Computation time was provided by |
901 |
> |
the Notre Dame Bunch-of-Boxes (B.o.B) computer cluster under NSF grant |
902 |
> |
DMR 00 79647. |
903 |
|
|
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|
\bibliographystyle{jcp} |
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|