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%\documentclass[prb,aps,twocolumn,tabularx]{revtex4} |
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\documentclass[12pt]{article} |
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\usepackage{endfloat} |
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%\usepackage{endfloat} |
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\usepackage{amsmath} |
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\usepackage{amssymb} |
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\usepackage{epsf} |
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\begin{document} |
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This document includes system based comparisons of the studied methods with smooth particle-mesh Ewald. Each of the seven systems comprises it's own section and has it's own discussion and tabular listing of the results for the $\Delta E$, force and torque vector magnitude, and force and torque vector direction comparisons. |
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This document includes individual system-based comparisons of the |
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studied methods with smooth particle-mesh Ewald. Each of the seven |
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systems comprises its own section and has its own discussion and |
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tabular listing of the results for the $\Delta E$, force and torque |
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vector magnitude, and force and torque vector direction comparisons. |
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|
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\section{\label{app-water}Liquid Water} |
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|
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500 liquid state configurations were generated as described in the |
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Methods section using the SPC/E model of water.\cite{Berendsen87} The |
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results for the energy gap comparisons and the force and torque vector |
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magnitude comparisons are shown in table \ref{tab:spce}. The force |
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and torque vector directionality results are displayed separately in |
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table \ref{tab:spceAng}, where the effect of group-based cutoffs and |
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switching functions on the {\sc sp} and {\sc sf} potentials are |
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investigated. |
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\begin{table}[htbp] |
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\centering |
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< |
\caption{Regression results for the liquid water system. Tabulated results include $\Delta E$ values (top set), force vector magnitudes (middle set) and torque vector magnitudes (bottom set). PC = Pure Cutoff, SP = Shifted Potential, SF = Shifted Force, GSC = Group Switched Cutoff, and RF = Reaction Field (where $\varepsilon \approx \infty$).} |
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\caption{Regression results for the liquid water system. Tabulated |
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results include $\Delta E$ values (top set), force vector magnitudes |
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(middle set) and torque vector magnitudes (bottom set). PC = Pure |
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Cutoff, SP = Shifted Potential, SF = Shifted Force, GSC = Group |
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Switched Cutoff, and RF = Reaction Field (where $\varepsilon \approx |
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\infty$).} |
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\begin{tabular}{@{} ccrrrrrr @{}} |
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\\ |
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\toprule |
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RF & & 0.993 & 0.989 & 0.998 & 0.996 & 1.000 & 0.999 \\ |
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\bottomrule |
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\end{tabular} |
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\label{spceTabTMag} |
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\label{tab:spce} |
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\end{table} |
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|
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\begin{table}[htbp] |
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\centering |
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< |
\caption{Variance results from Gaussian fits to angular distributions of the force and torque vectors in the liquid water system. PC = Pure Cutoff, SP = Shifted Potential, SF = Shifted Force, GSC = Group Switched Cutoff, RF = Reaction Field (where $\varepsilon \approx \infty$), GSSP = Group Switched Shifted Potential, and GSSF = Group Switched Shifted Force.} |
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\caption{Variance results from Gaussian fits to angular |
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distributions of the force and torque vectors in the liquid water |
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system. PC = Pure Cutoff, SP = Shifted Potential, SF = Shifted Force, |
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GSC = Group Switched Cutoff, RF = Reaction Field (where $\varepsilon |
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\approx \infty$), GSSP = Group Switched Shifted Potential, and GSSF = |
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Group Switched Shifted Force.} |
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\begin{tabular}{@{} ccrrrrrr @{}} |
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\\ |
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\toprule |
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& 0.3 & 0.728 & 0.694 & 0.692 & 7.410 & 6.942 & 6.748 \\ |
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\bottomrule |
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\end{tabular} |
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\label{spceTabAng} |
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\label{tab:spceAng} |
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\end{table} |
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|
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For the most parts, the water results appear to parallel the combined |
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results seen in the discussion in the main paper. There is good |
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agreement with SPME in both energetic and dynamic behavior when using |
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the {\sc sf} method with and without damping. The {\sc sp} method does |
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well with an $\alpha$ around 0.2 \AA$^{-1}$, particularly with cutoff |
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radii greater than 12 \AA. The results for both of these methods also |
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begin to decay as damping gets too large. |
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|
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The pure cutoff (PC) method performs poorly, as seen in the main |
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discussion section. In contrast to the combined values, however, the |
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use of a switching function and group based cutoffs really improves |
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the results for these neutral water molecules. The group switched |
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cutoff (GSC) shows mimics the energetics of SPME more poorly than the |
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{\sc sp} (with moderate damping) and {\sc sf} methods, but the |
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dynamics are quite good. The switching functions corrects |
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discontinuities in the potential and forces, leading to the improved |
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results. Such improvements with the use of a switching function has |
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been recognized in previous studies,\cite{Andrea83,Steinbach94} and it |
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is a useful tactic for stably incorporating local area electrostatic |
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effects. |
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|
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The reaction field (RF) method simply extends the results observed in |
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the GSC case. Both methods are similar in form (i.e. neutral groups, |
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switching function), but RF incorporates an added effect from the |
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external dielectric. This similarity translates into the same good |
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dynamic results and improved energetic results. These still fall |
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short of the moderately damped {\sc sp} and {\sc sf} methods, but they |
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display how incorporating some implicit properties of the surroundings |
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(i.e. $\epsilon_\textrm{S}$) can improve results. |
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|
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A final note for the liquid water system, use of group cutoffs and a |
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switching function also leads to noticeable improvements in the {\sc |
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sp} and {\sc sf} methods, primarily in directionality of the force and |
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torque vectors (table \ref{tab:spceAng}). {\sc sp} shows significant |
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narrowing of the angle distribution in the cases with little to no |
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damping and only modest improvement for the ideal conditions ($\alpha$ |
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= 0.2 \AA${-1}$ and $R_\textrm{c} \geqslant 12$~\AA). The {\sc sf} |
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method simply shows modest narrowing across all damping and cutoff |
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ranges of interest. Group cutoffs and the switching function do |
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nothing for cases were error is introduced by overdamping the |
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potentials. |
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|
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\section{\label{app-ice}Solid Water: Ice I$_\textrm{c}$} |
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|
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In addition to the disordered molecular system above, the ordered |
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molecular system of ice I$_\textrm{c}$ was also considered. The |
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results for the energy gap comparisons and the force and torque vector |
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magnitude comparisons are shown in table \ref{tab:ice}. The force and |
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torque vector directionality results are displayed separately in table |
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\ref{tab:iceAng}, where the effect of group-based cutoffs and |
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switching functions on the {\sc sp} and {\sc sf} potentials are |
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investigated. |
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|
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\begin{table}[htbp] |
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\centering |
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\caption{Regression results for the ice I$_\textrm{c}$ system. Tabulated results include $\Delta E$ values (top set), force vector magnitudes (middle set) and torque vector magnitudes (bottom set). PC = Pure Cutoff, SP = Shifted Potential, SF = Shifted Force, GSC = Group Switched Cutoff, and RF = Reaction Field (where $\varepsilon \approx \infty$).} |
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\caption{Regression results for the ice I$_\textrm{c}$ |
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system. Tabulated results include $\Delta E$ values (top set), force |
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vector magnitudes (middle set) and torque vector magnitudes (bottom |
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set). PC = Pure Cutoff, SP = Shifted Potential, SF = Shifted Force, |
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GSC = Group Switched Cutoff, and RF = Reaction Field (where |
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$\varepsilon \approx \infty$).} |
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\begin{tabular}{@{} ccrrrrrr @{}} |
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\\ |
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\toprule |
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RF & & 0.994 & 0.997 & 0.997 & 0.999 & 1.000 & 1.000 \\ |
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\bottomrule |
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\end{tabular} |
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\label{iceTab} |
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\label{tab:ice} |
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\end{table} |
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|
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\begin{table}[htbp] |
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& 0.3 & 0.251 & 0.251 & 0.259 & 2.387 & 2.395 & 2.328 \\ |
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\bottomrule |
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\end{tabular} |
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< |
\label{iceTabAng} |
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> |
\label{tab:iceAng} |
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\end{table} |
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|
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Highly ordered systems are a difficult test for the pairwise systems |
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in that they lack the periodicity inherent to the Ewald summation. As |
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expected, the energy gap agreement with SPME reduces for the {\sc sp} |
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and {\sc sf} with parameters that were perfectly acceptable for the |
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disordered liquid system. Moving to higher $R_\textrm{c}$ remedies |
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this degraded performance, though at increase in computational cost. |
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However, the dynamics of this crystalline system (both in magnitude |
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and direction) are little affected. Both methods still reproduce the |
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Ewald behavior with the same parameter recommendations from the |
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previous section. |
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|
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It is also worth noting that RF exhibits a slightly improved energy |
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gap results over the liquid water system. One possible explanation is |
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that the ice I$_\textrm{c}$ crystal is ordered such that the net |
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dipole moment of the crystal is zero. With $\epsilon_\textrm{S} = |
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\infty$, the reaction field incorporates this structural organization |
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by actively enforcing a zeroed dipole moment within each cutoff |
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sphere. |
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|
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\section{\label{app-melt}NaCl Melt} |
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|
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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 highly charge disordered system. The |
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results for the energy gap comparisons and the force and torque vector |
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magnitude comparisons are shown in table \ref{tab:melt}. The force |
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and torque vector directionality results are displayed separately in |
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table \ref{tab:meltAng}, where the effect of group-based cutoffs and |
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switching functions on the {\sc sp} and {\sc sf} potentials are |
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investigated. |
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|
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\begin{table}[htbp] |
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\centering |
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\caption{Regression results for the molten NaCl system. Tabulated results include $\Delta E$ values (top set) and force vector magnitudes (bottom set). PC = Pure Cutoff, SP = Shifted Potential, and SF = Shifted Force.} |
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Method & $\alpha$ & slope & $R^2$ & slope & $R^2$ & slope & $R^2$ \\ |
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\midrule |
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PC & & -0.008 & 0.000 & -0.049 & 0.005 & -0.136 & 0.020 \\ |
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SP & 0.0 & 0.937 & 0.996 & 0.880 & 0.995 & 0.971 & 0.999 \\ |
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& 0.1 & 1.004 & 0.999 & 0.958 & 1.000 & 0.928 & 0.994 \\ |
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SP & 0.0 & 0.928 & 0.996 & 0.931 & 0.998 & 0.950 & 0.999 \\ |
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& 0.1 & 0.977 & 0.998 & 0.998 & 1.000 & 0.997 & 1.000 \\ |
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& 0.2 & 0.960 & 1.000 & 0.813 & 0.996 & 0.811 & 0.954 \\ |
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& 0.3 & 0.671 & 0.994 & 0.439 & 0.929 & 0.535 & 0.831 \\ |
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SF & 0.0 & 1.001 & 1.000 & 0.949 & 1.000 & 1.008 & 1.000 \\ |
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& 0.1 & 1.025 & 1.000 & 0.960 & 1.000 & 0.929 & 0.994 \\ |
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SF & 0.0 & 0.996 & 1.000 & 0.995 & 1.000 & 0.997 & 1.000 \\ |
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& 0.1 & 1.021 & 1.000 & 1.024 & 1.000 & 1.007 & 1.000 \\ |
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& 0.2 & 0.966 & 1.000 & 0.813 & 0.996 & 0.811 & 0.954 \\ |
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& 0.3 & 0.671 & 0.994 & 0.439 & 0.929 & 0.535 & 0.831 \\ |
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\midrule |
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PC & & 1.103 & 0.000 & 0.989 & 0.000 & 0.802 & 0.000 \\ |
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SP & 0.0 & 0.976 & 0.983 & 1.001 & 0.991 & 0.985 & 0.995 \\ |
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& 0.1 & 0.996 & 0.997 & 0.997 & 0.998 & 0.996 & 0.996 \\ |
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SP & 0.0 & 0.973 & 0.981 & 0.975 & 0.988 & 0.979 & 0.992 \\ |
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& 0.1 & 0.987 & 0.992 & 0.993 & 0.998 & 0.997 & 0.999 \\ |
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& 0.2 & 0.993 & 0.996 & 0.985 & 0.988 & 0.986 & 0.981 \\ |
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& 0.3 & 0.956 & 0.956 & 0.940 & 0.912 & 0.948 & 0.929 \\ |
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SF & 0.0 & 0.997 & 0.998 & 0.995 & 0.999 & 0.999 & 1.000 \\ |
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& 0.1 & 1.001 & 0.997 & 0.997 & 0.999 & 0.996 & 0.996 \\ |
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SF & 0.0 & 0.996 & 0.997 & 0.997 & 0.999 & 0.998 & 1.000 \\ |
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& 0.1 & 1.000 & 0.997 & 1.001 & 0.999 & 1.000 & 1.000 \\ |
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& 0.2 & 0.994 & 0.996 & 0.985 & 0.988 & 0.986 & 0.981 \\ |
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& 0.3 & 0.956 & 0.956 & 0.940 & 0.912 & 0.948 & 0.929 \\ |
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\bottomrule |
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\end{tabular} |
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< |
\label{meltTab} |
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> |
\label{tab:melt} |
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\end{table} |
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|
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\begin{table}[htbp] |
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& 0.3 & 23.734 & 67.305 & 57.252 \\ |
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\bottomrule |
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\end{tabular} |
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< |
\label{meltTabAng} |
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> |
\label{tab:meltAng} |
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|
\end{table} |
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|
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The molten NaCl system shows the a |
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|
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\section{\label{app-salt}NaCl Crystal} |
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|
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A 1000K NaCl crystal was used to investigate the accuracy of the |
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pairwise summation methods in an ordered system of charged |
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particles. The results for the energy gap comparisons and the force |
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and torque vector magnitude comparisons are shown in table |
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\ref{tab:salt}. The force and torque vector directionality results |
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are displayed separately in table \ref{tab:saltAng}, where the effect |
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+ |
of group-based cutoffs and switching functions on the {\sc sp} and |
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{\sc sf} potentials are investigated. |
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|
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|
\begin{table}[htbp] |
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|
\centering |
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< |
\caption{Regression results for the crystalline NaCl system. Tabulated results include $\Delta E$ values (top set) and force vector magnitudes (bottom set). PC = Pure Cutoff, SP = Shifted Potential, and SF = Shifted Force.} |
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> |
\caption{Regression results for the crystalline NaCl |
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> |
system. Tabulated results include $\Delta E$ values (top set) and |
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> |
force vector magnitudes (bottom set). PC = Pure Cutoff, SP = Shifted |
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> |
Potential, and SF = Shifted Force.} |
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|
\begin{tabular}{@{} ccrrrrrr @{}} |
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\\ |
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\toprule |
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|
& 0.3 & 0.950 & 0.952 & 0.950 & 0.953 & 0.950 & 0.953 \\ |
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|
\bottomrule |
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|
\end{tabular} |
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< |
\label{saltTab} |
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> |
\label{tab:salt} |
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|
\end{table} |
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|
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|
\begin{table}[htbp] |
| 434 |
|
\centering |
| 435 |
< |
\caption{Variance results from Gaussian fits to angular distributions of the force vectors in the crystalline NaCl system. PC = Pure Cutoff, SP = Shifted Potential, SF = Shifted Force, GSC = Group Switched Cutoff, and RF = Reaction Field (where $\varepsilon \approx \infty$).} |
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> |
\caption{Variance results from Gaussian fits to angular |
| 436 |
> |
distributions of the force vectors in the crystalline NaCl system. PC |
| 437 |
> |
= Pure Cutoff, SP = Shifted Potential, SF = Shifted Force, GSC = Group |
| 438 |
> |
Switched Cutoff, and RF = Reaction Field (where $\varepsilon \approx |
| 439 |
> |
\infty$).} |
| 440 |
|
\begin{tabular}{@{} ccrrrrrr @{}} |
| 441 |
|
\\ |
| 442 |
|
\toprule |
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|
& 0.3 & 31.120 & 31.105 & 31.029 \\ |
| 457 |
|
\bottomrule |
| 458 |
|
\end{tabular} |
| 459 |
< |
\label{saltTabAng} |
| 459 |
> |
\label{tab:saltAng} |
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|
\end{table} |
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|
|
| 462 |
|
\section{\label{app-sol1}Weak NaCl Solution} |
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|
|
| 464 |
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In an effort to bridge the charged atomic and neutral molecular |
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systems, Na$^+$ and Cl$^-$ ion charge defects were incorporated into |
| 466 |
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the liquid water system. This low ionic strength system consists of 4 |
| 467 |
+ |
ions in the 1000 SPC/E water solvent ($\approx$0.11 M). The results |
| 468 |
+ |
for the energy gap comparisons and the force and torque vector |
| 469 |
+ |
magnitude comparisons are shown in table \ref{tab:solnWeak}. The |
| 470 |
+ |
force and torque vector directionality results are displayed |
| 471 |
+ |
separately in table \ref{tab:solnWeakAng}, where the effect of |
| 472 |
+ |
group-based cutoffs and switching functions on the {\sc sp} and {\sc |
| 473 |
+ |
sf} potentials are investigated. |
| 474 |
+ |
|
| 475 |
|
\begin{table}[htbp] |
| 476 |
|
\centering |
| 477 |
< |
\caption{Regression results for the weak NaCl solution system. Tabulated results include $\Delta E$ values (top set), force vector magnitudes (middle set) and torque vector magnitudes (bottom set). PC = Pure Cutoff, SP = Shifted Potential, SF = Shifted Force, GSC = Group Switched Cutoff, RF = Reaction Field (where $\varepsilon \approx \infty$), GSSP = Group Switched Shifted Potential, and GSSF = Group Switched Shifted Force.} |
| 477 |
> |
\caption{Regression results for the weak NaCl solution |
| 478 |
> |
system. Tabulated results include $\Delta E$ values (top set), force |
| 479 |
> |
vector magnitudes (middle set) and torque vector magnitudes (bottom |
| 480 |
> |
set). PC = Pure Cutoff, SP = Shifted Potential, SF = Shifted Force, |
| 481 |
> |
GSC = Group Switched Cutoff, RF = Reaction Field (where $\varepsilon |
| 482 |
> |
\approx \infty$), GSSP = Group Switched Shifted Potential, and GSSF = |
| 483 |
> |
Group Switched Shifted Force.} |
| 484 |
|
\begin{tabular}{@{} ccrrrrrr @{}} |
| 485 |
|
\\ |
| 486 |
|
\toprule |
| 527 |
|
RF & & 0.984 & 0.975 & 0.996 & 0.995 & 0.998 & 0.998 \\ |
| 528 |
|
\bottomrule |
| 529 |
|
\end{tabular} |
| 530 |
< |
\label{sol1Tab} |
| 530 |
> |
\label{tab:solnWeak} |
| 531 |
|
\end{table} |
| 532 |
|
|
| 533 |
|
\begin{table}[htbp] |
| 534 |
|
\centering |
| 535 |
< |
\caption{Variance results from Gaussian fits to angular distributions of the force and torque vectors in the weak NaCl solution system. PC = Pure Cutoff, SP = Shifted Potential, SF = Shifted Force, GSC = Group Switched Cutoff, RF = Reaction Field (where $\varepsilon \approx \infty$), GSSP = Group Switched Shifted Potential, and GSSF = Group Switched Shifted Force.} |
| 535 |
> |
\caption{Variance results from Gaussian fits to angular |
| 536 |
> |
distributions of the force and torque vectors in the weak NaCl |
| 537 |
> |
solution system. PC = Pure Cutoff, SP = Shifted Potential, SF = |
| 538 |
> |
Shifted Force, GSC = Group Switched Cutoff, RF = Reaction Field (where |
| 539 |
> |
$\varepsilon \approx \infty$), GSSP = Group Switched Shifted |
| 540 |
> |
Potential, and GSSF = Group Switched Shifted Force.} |
| 541 |
|
\begin{tabular}{@{} ccrrrrrr @{}} |
| 542 |
|
\\ |
| 543 |
|
\toprule |
| 568 |
|
& 0.3 & 0.954 & 0.759 & 0.780 & 12.337 & 7.684 & 7.849 \\ |
| 569 |
|
\bottomrule |
| 570 |
|
\end{tabular} |
| 571 |
< |
\label{sol1TabAng} |
| 571 |
> |
\label{tab:solnWeakAng} |
| 572 |
|
\end{table} |
| 573 |
|
|
| 574 |
|
\section{\label{app-sol10}Strong NaCl Solution} |
| 575 |
|
|
| 576 |
+ |
The bridging of the charged atomic and neutral molecular systems was |
| 577 |
+ |
furthered by considering a high ionic strength system consisting of 40 |
| 578 |
+ |
ions in the 1000 SPC/E water solvent ($\approx$1.1 M). The results for |
| 579 |
+ |
the energy gap comparisons and the force and torque vector magnitude |
| 580 |
+ |
comparisons are shown in table \ref{tab:solnWeak}. The force and |
| 581 |
+ |
torque vector directionality results are displayed separately in table |
| 582 |
+ |
\ref{tab:solnWeakAng}, where the effect of group-based cutoffs and |
| 583 |
+ |
switching functions on the {\sc sp} and {\sc sf} potentials are |
| 584 |
+ |
investigated. |
| 585 |
+ |
|
| 586 |
|
\begin{table}[htbp] |
| 587 |
|
\centering |
| 588 |
< |
\caption{Regression results for the strong NaCl solution system. Tabulated results include $\Delta E$ values (top set), force vector magnitudes (middle set) and torque vector magnitudes (bottom set). PC = Pure Cutoff, SP = Shifted Potential, SF = Shifted Force, GSC = Group Switched Cutoff, and RF = Reaction Field (where $\varepsilon \approx \infty$).} |
| 588 |
> |
\caption{Regression results for the strong NaCl solution |
| 589 |
> |
system. Tabulated results include $\Delta E$ values (top set), force |
| 590 |
> |
vector magnitudes (middle set) and torque vector magnitudes (bottom |
| 591 |
> |
set). PC = Pure Cutoff, SP = Shifted Potential, SF = Shifted Force, |
| 592 |
> |
GSC = Group Switched Cutoff, and RF = Reaction Field (where |
| 593 |
> |
$\varepsilon \approx \infty$).} |
| 594 |
|
\begin{tabular}{@{} ccrrrrrr @{}} |
| 595 |
|
\\ |
| 596 |
|
\toprule |
| 637 |
|
RF & & 0.949 & 0.939 & 0.988 & 0.988 & 0.992 & 0.993 \\ |
| 638 |
|
\bottomrule |
| 639 |
|
\end{tabular} |
| 640 |
< |
\label{sol10Tab} |
| 640 |
> |
\label{tab:solnStr} |
| 641 |
|
\end{table} |
| 642 |
|
|
| 643 |
|
\begin{table}[htbp] |
| 673 |
|
& 0.3 & 1.752 & 1.454 & 1.451 & 23.587 & 14.390 & 14.245 \\ |
| 674 |
|
\bottomrule |
| 675 |
|
\end{tabular} |
| 676 |
< |
\label{sol10TabAng} |
| 676 |
> |
\label{tab:solnStrAng} |
| 677 |
|
\end{table} |
| 678 |
|
|
| 679 |
|
\section{\label{app-argon}Argon Sphere in Water} |
| 680 |
|
|
| 681 |
+ |
The final model system studied was 6 \AA\ sphere of Argon solvated by |
| 682 |
+ |
SPC/E water. The results for the energy gap comparisons and the force |
| 683 |
+ |
and torque vector magnitude comparisons are shown in table |
| 684 |
+ |
\ref{tab:solnWeak}. The force and torque vector directionality |
| 685 |
+ |
results are displayed separately in table \ref{tab:solnWeakAng}, where |
| 686 |
+ |
the effect of group-based cutoffs and switching functions on the {\sc |
| 687 |
+ |
sp} and {\sc sf} potentials are investigated. |
| 688 |
+ |
|
| 689 |
|
\begin{table}[htbp] |
| 690 |
|
\centering |
| 691 |
< |
\caption{Regression results for the 6 \AA\ argon sphere in liquid water system. Tabulated results include $\Delta E$ values (top set), force vector magnitudes (middle set) and torque vector magnitudes (bottom set). PC = Pure Cutoff, SP = Shifted Potential, SF = Shifted Force, GSC = Group Switched Cutoff, and RF = Reaction Field (where $\varepsilon \approx \infty$).} |
| 691 |
> |
\caption{Regression results for the 6 \AA\ argon sphere in liquid |
| 692 |
> |
water system. Tabulated results include $\Delta E$ values (top set), |
| 693 |
> |
force vector magnitudes (middle set) and torque vector magnitudes |
| 694 |
> |
(bottom set). PC = Pure Cutoff, SP = Shifted Potential, SF = Shifted |
| 695 |
> |
Force, GSC = Group Switched Cutoff, and RF = Reaction Field (where |
| 696 |
> |
$\varepsilon \approx \infty$).} |
| 697 |
|
\begin{tabular}{@{} ccrrrrrr @{}} |
| 698 |
|
\\ |
| 699 |
|
\toprule |
| 740 |
|
RF & & 0.993 & 0.988 & 0.997 & 0.995 & 0.999 & 0.998 \\ |
| 741 |
|
\bottomrule |
| 742 |
|
\end{tabular} |
| 743 |
< |
\label{argonTab} |
| 743 |
> |
\label{tab:argon} |
| 744 |
|
\end{table} |
| 745 |
|
|
| 746 |
|
\begin{table}[htbp] |
| 747 |
|
\centering |
| 748 |
< |
\caption{Variance results from Gaussian fits to angular distributions of the force and torque vectors in the 6 \AA\ sphere of argon in liquid water system. PC = Pure Cutoff, SP = Shifted Potential, SF = Shifted Force, GSC = Group Switched Cutoff, RF = Reaction Field (where $\varepsilon \approx \infty$), GSSP = Group Switched Shifted Potential, and GSSF = Group Switched Shifted Force.} |
| 748 |
> |
\caption{Variance results from Gaussian fits to angular |
| 749 |
> |
distributions of the force and torque vectors in the 6 \AA\ sphere of |
| 750 |
> |
argon in liquid water system. PC = Pure Cutoff, SP = Shifted |
| 751 |
> |
Potential, SF = Shifted Force, GSC = Group Switched Cutoff, RF = |
| 752 |
> |
Reaction Field (where $\varepsilon \approx \infty$), GSSP = Group |
| 753 |
> |
Switched Shifted Potential, and GSSF = Group Switched Shifted Force.} |
| 754 |
|
\begin{tabular}{@{} ccrrrrrr @{}} |
| 755 |
|
\\ |
| 756 |
|
\toprule |
| 781 |
|
& 0.3 & 0.814 & 0.825 & 0.816 & 8.325 & 8.447 & 8.132 \\ |
| 782 |
|
\bottomrule |
| 783 |
|
\end{tabular} |
| 784 |
< |
\label{argonTabAng} |
| 784 |
> |
\label{tab:argonAng} |
| 785 |
|
\end{table} |
| 786 |
|
|
| 787 |
< |
\end{document} |
| 787 |
> |
\newpage |
| 788 |
> |
|
| 789 |
> |
\bibliographystyle{jcp2} |
| 790 |
> |
\bibliography{electrostaticMethods} |
| 791 |
> |
|
| 792 |
> |
\end{document} |
