23 |
|
|
24 |
|
\begin{document} |
25 |
|
|
26 |
< |
This document includes individual system-based comparisons of the |
27 |
< |
studied methods with smooth particle mesh Ewald {\sc spme}. Each of |
28 |
< |
the seven systems comprises its own section and has its own discussion |
29 |
< |
and tabular listing of the results for the $\Delta E$, force and |
30 |
< |
torque vector magnitude, and force and torque vector direction |
31 |
< |
comparisons. |
26 |
> |
This document includes comparisons of the new pairwise electrostatic |
27 |
> |
methods with {\sc spme} for each of the individual systems mentioned |
28 |
> |
in paper. Each of the seven sections contains information about a |
29 |
> |
single system type and has its own discussion and tabular listing of |
30 |
> |
the results for the comparisons of $\Delta E$, the magnitudes of the |
31 |
> |
forces and torques, and directionality of the force and torque |
32 |
> |
vectors. |
33 |
|
|
34 |
|
\section{\label{app:water}Liquid Water} |
35 |
|
|
139 |
|
\label{tab:spceAng} |
140 |
|
\end{table} |
141 |
|
|
142 |
< |
The water results appear to parallel the combined results seen in the |
143 |
< |
discussion section of the main paper. There is good agreement with |
144 |
< |
{\sc spme} in both energetic and dynamic behavior when using the {\sc sf} |
145 |
< |
method with and without damping. The {\sc sp} method does well with an |
142 |
> |
The water results parallel the combined results seen in the discussion |
143 |
> |
section of the main paper. There is good agreement with {\sc spme} in |
144 |
> |
both energetic and dynamic behavior when using the {\sc sf} method |
145 |
> |
with and without damping. The {\sc sp} method does well with an |
146 |
|
$\alpha$ around 0.2 \AA$^{-1}$, particularly with cutoff radii greater |
147 |
< |
than 12 \AA. Overdamping the electrostatics reduces the agreement between both these methods and {\sc spme}. |
147 |
> |
than 12 \AA. Overdamping the electrostatics reduces the agreement |
148 |
> |
between both these methods and {\sc spme}. |
149 |
|
|
150 |
|
The pure cutoff ({\sc pc}) method performs poorly, again mirroring the |
151 |
|
observations in the main portion of this paper. In contrast to the |
287 |
|
\end{table} |
288 |
|
|
289 |
|
Highly ordered systems are a difficult test for the pairwise methods |
290 |
< |
in that they lack the periodicity term of the Ewald summation. As |
290 |
> |
in that they lack the implicit periodicity of the Ewald summation. As |
291 |
|
expected, the energy gap agreement with {\sc spme} is reduced for the |
292 |
|
{\sc sp} and {\sc sf} methods with parameters that were acceptable for |
293 |
|
the disordered liquid system. Moving to higher $R_\textrm{c}$ helps |
308 |
|
\section{\label{app:melt}NaCl Melt} |
309 |
|
|
310 |
|
A high temperature NaCl melt was tested to gauge the accuracy of the |
311 |
< |
pairwise summation methods in a charged disordered system. The results |
312 |
< |
for the energy gap comparisons and the force vector magnitude |
311 |
> |
pairwise summation methods in a disordered system of charges. The |
312 |
> |
results for the energy gap comparisons and the force vector magnitude |
313 |
|
comparisons are shown in table \ref{tab:melt}. The force vector |
314 |
|
directionality results are displayed separately in table |
315 |
|
\ref{tab:meltAng}. |
599 |
|
regarding these methods carry over from section \ref{app:water}. The |
600 |
|
differences between these systems are more visible for the {\sc rf} |
601 |
|
method. Though good force agreement is still maintained, the energy |
602 |
< |
gaps show a significant increase in the data scatter. This foreshadows |
601 |
< |
the breakdown of the method as we introduce charged inhomogeneities. |
602 |
> |
gaps show a significant increase in the scatter of the data. |
603 |
|
|
604 |
|
\section{\label{app:solnStr}Strong NaCl Solution} |
605 |
|
|