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