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All of these comparisons were performed with three different cutoff radii (9, 12, and 15 \AA) to investigate the cutoff radius dependence of the various techniques. It should be noted that the damping parameter chosen in SPME, or so called ``Ewald Coefficient", has a significant effect on the energies and forces calculated. Typical molecular mechanics packages default this to a value dependent on the cutoff radius and a tolerance (typically less than $1 \times 10^{-5}$ kcal/mol). We chose a tolerance of $1 \times 10^{-8}$, resulting in Ewald Coefficients of 0.4200, 0.3119, and 0.2476 \AA$^{-1}$ for cutoff radii of 9, 12, and 15 \AA\ respectively. |
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\section{Results and Discussion} |
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In order to evaluate the performance of the adapted Wolf SP and SF electrostatic summation methods for Monte Carlo simulations, the energy differences between configurations need to be compared to the results using SPME. Considering the SPME results to be the correct or desired behavior, ideal performance of a tested method is taken to be agreement between the energy differences calculated. Linear least squares regression of the $\Delta$E values between configurations using SPME against $\Delta$E values using tested methods provides a quantitative comparison of this agreement. Unitary results for both the correlation and correlation coefficient for these regressions indicate equivalent energetic results between the methods. The correlation is the slope of the plotted data while the correlation coefficient ($R^2$) is a measure of the of the data scatter around the fitted line and gives an idea of the quality of the fit (Fig. \ref{linearFit}). |
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\begin{figure} |
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\centering |
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\includegraphics[width=3.25in]{./linearFit.pdf} |
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\caption{Example least squares regression of the $\Delta$E between configurations for the SF method against SPME in the pure water system. } |
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\label{linearFit} |
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\end{figure} |
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With 500 independent configurations, 124,750 $\Delta$E data points are used in a regression of a single system. A table with the results for analysis of To gauge the applicability of each method in the general case, all the different system types were included in a separate Figure \ref{delEplot} shows the results for analysis of all the simulation types |
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\section{Conclusions} |
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\section{Acknowledgments} |
