--- trunk/electrostaticMethodsPaper/SupportingInfo.tex	2006/03/23 15:46:45	2666
+++ trunk/electrostaticMethodsPaper/SupportingInfo.tex	2006/03/24 17:28:09	2670
@@ -23,12 +23,13 @@
 
 \begin{document}
 
-This document includes individual system-based comparisons of the
-studied methods with smooth particle mesh Ewald {\sc spme}.  Each of
-the seven systems comprises its own section and has its own discussion
-and tabular listing of the results for the $\Delta E$, force and
-torque vector magnitude, and force and torque vector direction
-comparisons.
+This document includes comparisons of the new pairwise electrostatic
+methods with {\sc spme} for each of the individual systems mentioned
+in paper. Each of the seven sections contains information about a
+single system type and has its own discussion and tabular listing of
+the results for the comparisons of $\Delta E$, the magnitudes of the
+forces and torques, and directionality of the force and torque
+vectors.
 
 \section{\label{app:water}Liquid Water}
 
@@ -138,23 +139,24 @@ GSSF  & 0.0 & 1.298 & 0.270 & 0.083 & 3.098 & 0.992 & 
    \label{tab:spceAng}
 \end{table}
 
-The water results appear to parallel the combined results seen in the
-discussion section of the main paper.  There is good agreement with
-{\sc spme} in both energetic and dynamic behavior when using the {\sc sf}
-method with and without damping. The {\sc sp} method does well with an
+The water results parallel the combined results seen in the discussion
+section of the main paper.  There is good agreement with {\sc spme} in
+both energetic and dynamic behavior when using the {\sc sf} method
+with and without damping. The {\sc sp} method does well with an
 $\alpha$ around 0.2 \AA$^{-1}$, particularly with cutoff radii greater
-than 12 \AA. Overdamping the electrostatics reduces the agreement between both these methods and {\sc spme}.
+than 12 \AA. Overdamping the electrostatics reduces the agreement
+between both these methods and {\sc spme}.
 
 The pure cutoff ({\sc pc}) method performs poorly, again mirroring the
 observations in the main portion of this paper.  In contrast to the
 combined values, however, the use of a switching function and group
-based cutoffs really improves the results for these neutral water
+based cutoffs greatly improves the results for these neutral water
 molecules.  The group switched cutoff ({\sc gsc}) does not mimic the
 energetics of {\sc spme} as well as the {\sc sp} (with moderate
 damping) and {\sc sf} methods, but the dynamics are quite good.  The
-switching functions corrects discontinuities in the potential and
+switching functions correct discontinuities in the potential and
 forces, leading to these improved results.  Such improvements with the
-use of a switching function has been recognized in previous
+use of a switching function have been recognized in previous
 studies,\cite{Andrea83,Steinbach94} and this proves to be a useful
 tactic for stably incorporating local area electrostatic effects.
 
@@ -168,7 +170,7 @@ show how incorporating some implicit properties of the
 show how incorporating some implicit properties of the surroundings
 (i.e. $\epsilon_\textrm{S}$) can improve the solvent depiction.
 
-A final note for the liquid water system, use of group cutoffs and a
+As a final note for the liquid water system, use of group cutoffs and a
 switching function leads to noticeable improvements in the {\sc sp}
 and {\sc sf} methods, primarily in directionality of the force and
 torque vectors (table \ref{tab:spceAng}). The {\sc sp} method shows
@@ -285,8 +287,8 @@ Highly ordered systems are a difficult test for the pa
 \end{table}
 
 Highly ordered systems are a difficult test for the pairwise methods
-in that they lack the periodicity term of the Ewald summation.  As
-expected, the energy gap agreement with {\sc spme} reduces for the
+in that they lack the implicit periodicity of the Ewald summation.  As
+expected, the energy gap agreement with {\sc spme} is reduced for the
 {\sc sp} and {\sc sf} methods with parameters that were acceptable for
 the disordered liquid system.  Moving to higher $R_\textrm{c}$ helps
 improve the agreement, though at an increase in computational cost.
@@ -306,13 +308,11 @@ A high temperature NaCl melt was tested to gauge the a
 \section{\label{app:melt}NaCl Melt}
 
 A high temperature NaCl melt was tested to gauge the accuracy of the
-pairwise summation methods in a charged disordered system. The results
-for the energy gap comparisons and the force and torque vector
-magnitude comparisons are shown in table \ref{tab:melt}.  The force
-and torque vector directionality results are displayed separately in
-table \ref{tab:meltAng}, where the effect of group-based cutoffs and
-switching functions on the {\sc sp} and {\sc sf} potentials are
-investigated.
+pairwise summation methods in a disordered system of charges. The
+results for the energy gap comparisons and the force vector magnitude
+comparisons are shown in table \ref{tab:melt}.  The force vector
+directionality results are displayed separately in table
+\ref{tab:meltAng}.
 
 \begin{table}[htbp]
    \centering
@@ -391,11 +391,9 @@ particles. The results for the energy gap comparisons 
 A 1000K NaCl crystal was used to investigate the accuracy of the
 pairwise summation methods in an ordered system of charged
 particles. The results for the energy gap comparisons and the force
-and torque vector magnitude comparisons are shown in table
-\ref{tab:salt}.  The force and torque vector directionality results
-are displayed separately in table \ref{tab:saltAng}, where the effect
-of group-based cutoffs and switching functions on the {\sc sp} and
-{\sc sf} potentials are investigated. 
+vector magnitude comparisons are shown in table \ref{tab:salt}.  The
+force vector directionality results are displayed separately in table
+\ref{tab:saltAng}.
 
 \begin{table}[htbp]
    \centering
@@ -476,14 +474,11 @@ The moderate electrostatic damping case is not as good
 radius.
 
 The moderate electrostatic damping case is not as good as we would
-expect given the good long-time dynamics results observed for this
-system. Since the data tabulated in table \ref{tab:salt} and
+expect given the long-time dynamics results observed for this
+system. Since the data tabulated in tables \ref{tab:salt} and
 \ref{tab:saltAng} are a test of instantaneous dynamics, this indicates
 that good long-time dynamics comes in part at the expense of
-short-time dynamics. Further indication of this comes from the full
-power spectra shown in the main text. It appears as though a
-distortion is introduced between 200 to 350 cm$^{-1}$ with increased
-$\alpha$.
+short-time dynamics.
 
 \section{\label{app:solnWeak}Weak NaCl Solution}
 
@@ -504,9 +499,8 @@ set).  PC = Pure Cutoff, SP = Shifted Potential, SF = 
 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.}	 
+GSC = Group Switched Cutoff, and RF = Reaction Field (where $\varepsilon
+\approx \infty$).}	 
    \begin{tabular}{@{} ccrrrrrr @{}}
       \\
       \toprule
@@ -605,8 +599,7 @@ method. Though good force agreement is still maintaine
 regarding these methods carry over from section \ref{app:water}. The
 differences between these systems are more visible for the {\sc rf}
 method. Though good force agreement is still maintained, the energy
-gaps show a significant increase in the data scatter. This foreshadows
-the breakdown of the method as we introduce charged inhomogeneities.
+gaps show a significant increase in the scatter of the data.
 
 \section{\label{app:solnStr}Strong NaCl Solution}
 
@@ -615,8 +608,8 @@ torque vector magnitude comparisons are shown in table
 consisting of 40 ions in the 1000 SPC/E water solvent ($\approx$1.1
 M). The results for the energy gap comparisons and the force and
 torque vector magnitude comparisons are shown in table
-\ref{tab:solnWeak}.  The force and torque vector directionality
-results are displayed separately in table \ref{tab:solnWeakAng}, where
+\ref{tab:solnStr}.  The force and torque vector directionality
+results are displayed separately in table \ref{tab:solnStrAng}, where
 the effect of group-based cutoffs and switching functions on the {\sc
 sp} and {\sc sf} potentials are investigated.
 
@@ -714,7 +707,7 @@ The {\sc rf} method struggles with the jump in ionic s
 \end{table}
 
 The {\sc rf} method struggles with the jump in ionic strength. The
-configuration energy difference degrade to unusable levels while the
+configuration energy differences degrade to unusable levels while the
 forces and torques show a more modest reduction in the agreement with
 {\sc spme}. The {\sc rf} method was designed for homogeneous systems,
 and this attribute is apparent in these results.
@@ -727,17 +720,17 @@ damping for the {\sc sp} method, both with cutoffs gre
 
 \section{\label{app:argon}Argon Sphere in Water}
 
-The final model system studied was 6 \AA\ sphere of Argon solvated by
-SPC/E water. The results for the energy gap comparisons and the force
-and torque vector magnitude comparisons are shown in table
-\ref{tab:solnWeak}.  The force and torque vector directionality
-results are displayed separately in table \ref{tab:solnWeakAng}, where
+The final model system studied was a 6 \AA\ sphere of Argon solvated
+by SPC/E water. The results for the energy gap comparisons and the
+force and torque vector magnitude comparisons are shown in table
+\ref{tab:argon}.  The force and torque vector directionality
+results are displayed separately in table \ref{tab:argonAng}, where
 the effect of group-based cutoffs and switching functions on the {\sc
 sp} and {\sc sf} potentials are investigated. 
 
 \begin{table}[htbp]
    \centering
-   \caption{Regression results for the 6 \AA\ argon sphere in liquid
+   \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
@@ -796,7 +789,7 @@ distributions of the force and torque vectors in the 6
    \centering
    \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
+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.} 	
@@ -833,11 +826,11 @@ GSSF  & 0.0 & 1.173 & 0.292 & 0.113 & 3.452 & 1.347 & 
    \label{tab:argonAng}
 \end{table}
 
-This system appears not to show in any significant deviation in the
-previously observed results. The {\sc sp} and {\sc sf} methods give
-result qualities similar to those observed in section
+This system does not appear to show any significant deviations from
+the previously observed results. The {\sc sp} and {\sc sf} methods
+have aggrements similar to those observed in section
 \ref{app:water}. The only significant difference is the improvement
-for the configuration energy differences for the {\sc rf} method. This
+in the configuration energy differences for the {\sc rf} method. This
 is surprising in that we are introducing an inhomogeneity to the
 system; however, this inhomogeneity is charge-neutral and does not
 result in charged cutoff spheres. The charge-neutrality of the cutoff