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\usepackage{setspace} |
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\usepackage{tabularx} |
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\usepackage{graphicx} |
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%\usepackage{berkeley} |
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\usepackage[ref]{overcite} |
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\pagestyle{plain} |
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\pagenumbering{arabic} |
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\section{Introduction} |
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In this paper, a variety of simulation situations were analyzed to determine the relative effectiveness of the adapted Wolf spherical truncation schemes at reproducing the results obtained using a smooth particle mesh Ewald (SPME) summation technique. In addition to the Shifted-Potential (SP) and Shifted-Force (SF) adapted Wolf methods, both reaction field and uncorrected cutoff methods were included for comparison purposes. The general usability of these methods in both Monte Carlo (MC) and Molecular Dynamics (MD) calculations was assessed through statistical analysis over the combined results from all of the following studied systems: |
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\begin{list}{-}{} |
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\item Liquid Water |
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\item Crystalline Water (Ice I$_\textrm{c}$) |
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\item 1 M Solution of NaCl in Water |
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\item 10 M Solution of NaCl in Water |
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\item 6 \AA\ Radius Sphere of Argon in Water |
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\item NaCl Crystal |
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\item NaCl Melt |
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\end{list} |
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Additional discussion on the results from the individual systems was also performed to identify limitations of the considered methods in specific systems. |
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\section{Methods} |
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In each of the simulated systems, 500 distinct configurations were generated, and the electrostatic summation methods were compared via sequential application on each of these fixed configurations. The methods compared include SPME, the aforementioned SP and SF methods - both with damping parameters ($\alpha$) of 0, 0.1, 0.2, and 0.3 \AA$^{-1}$, reaction field with an infinite dielectric constant, and an unmodified cutoff. Group-based cutoffs with a fifth-order polynomial switching function were necessary for the reaction field simulations and were utilized in the SP, SF, and pure cutoff methods for comparison to the standard lack of group-based cutoffs with a hard truncation. |
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Generation of the system configurations was dependent on the system type. For the solid and liquid water configurations, configuration snapshots were taken at regular intervals from higher temperature 1000 SPC/E water molecule trajectories and individually equilibrated. The solid and liquid NaCl systems consisted of 500 Na+ and 500 Cl- ions and were selected and equilibrated in the same fashion as the water systems. For the 1 and 10 M NaCl solutions, 4 and 40 ions, respectively, were first solvated in a 1000 water molecule boxes. Ion and water positions were then randomly swapped, and the resulting configurations were again individually equilibrated. Finally, for the Argon/Water "charge void" systems, the identities of all the SPC/E waters within 6 \AA\ of the center of the equilibrated water configurations were converted to argon (Fig. \ref{argonSlice}). |
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\begin{figure} |
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\centering |
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\includegraphics[width=3.25in]{./slice.pdf} |
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\caption{A slice from the center of a water box used in a charge void simulation. The darkened region represents the boundary sphere within which the water molecules were converted to argon atoms.} |
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\label{argonSlice} |
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\end{figure} |
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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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\section{Conclusions} |
