--- trunk/electrostaticMethodsPaper/SupportingInfo.tex	2006/03/23 15:03:33	2665
+++ trunk/electrostaticMethodsPaper/SupportingInfo.tex	2006/03/23 15:46:45	2666
@@ -1,5 +1,5 @@
 %\documentclass[prb,aps,twocolumn,tabularx]{revtex4}
-\documentclass[12pt]{article}
+\documentclass[11pt]{article}
 %\usepackage{endfloat}
 \usepackage{amsmath}
 \usepackage{amssymb}
@@ -24,21 +24,22 @@ studied methods with smooth particle-mesh Ewald.  Each
 \begin{document}
 
 This document includes individual system-based comparisons of the
-studied methods with smooth particle-mesh Ewald.  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.
+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.
 
 \section{\label{app:water}Liquid Water}
 
-500 liquid state configurations were generated as described in the
-Methods section using the SPC/E model of water.\cite{Berendsen87} The
-results for the energy gap comparisons and the force and torque vector
-magnitude comparisons are shown in table \ref{tab:spce}.  The force
-and torque vector directionality results are displayed separately in
-table \ref{tab:spceAng}, where the effect of group-based cutoffs and
+The first system considered was liquid water at 300K using the SPC/E
+model of water.\cite{Berendsen87} The results for the energy gap
+comparisons and the force and torque vector magnitude comparisons are
+shown in table \ref{tab:spce}.  The force and torque vector
+directionality results are displayed separately in table
+\ref{tab:spceAng}, where the effect of group-based cutoffs and
 switching functions on the {\sc sp} and {\sc sf} potentials are
-investigated. 
+investigated.
 \begin{table}[htbp]
    \centering
    \caption{Regression results for the liquid water system. Tabulated
@@ -137,47 +138,47 @@ For the most parts, the water results appear to parall
    \label{tab:spceAng}
 \end{table}
 
-For the most parts, the water results appear to parallel the combined
-results seen in the discussion in the main paper.  There is good
-agreement with 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. The results for both of these methods also
-begin to decay as damping gets too large.
+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
+$\alpha$ 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}.
 
-The pure cutoff (PC) method performs poorly, as seen in the main
-discussion section.  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 molecules.  The group switched
-cutoff (GSC) shows mimics the energetics of SPME more poorly than 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 forces, leading to the improved
-results.  Such improvements with the use of a switching function has
-been recognized in previous studies,\cite{Andrea83,Steinbach94} and it
-is a useful tactic for stably incorporating local area electrostatic
-effects.
+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
+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
+forces, leading to these improved results.  Such improvements with the
+use of a switching function has been recognized in previous
+studies,\cite{Andrea83,Steinbach94} and this proves to be a useful
+tactic for stably incorporating local area electrostatic effects.
 
-The reaction field (RF) method simply extends the results observed in
-the GSC case.  Both methods are similar in form (i.e. neutral groups,
-switching function), but RF incorporates an added effect from the
-external dielectric. This similarity translates into the same good
-dynamic results and improved energetic results.  These still fall
-short of the moderately damped {\sc sp} and {\sc sf} methods, but they
-display how incorporating some implicit properties of the surroundings
-(i.e. $\epsilon_\textrm{S}$) can improve results.
+The reaction field ({\sc rf}) method simply extends upon the results
+observed in the {\sc gsc} case.  Both methods are similar in form
+(i.e. neutral groups, switching function), but {\sc rf} incorporates
+an added effect from the external dielectric. This similarity
+translates into the same good dynamic results and improved energetic
+agreement with {\sc spme}.  Though this agreement is not to the level
+of the moderately damped {\sc sp} and {\sc sf} methods, these results
+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
-switching function also 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}).  {\sc sp} shows significant
-narrowing of the angle distribution in the cases with little to no
-damping and only modest improvement for the ideal conditions ($\alpha$
-= 0.2 \AA${-1}$ and $R_\textrm{c} \geqslant 12$~\AA).  The {\sc sf}
-method simply shows modest narrowing across all damping and cutoff
-ranges of interest.  Group cutoffs and the switching function do
-nothing for cases were error is introduced by overdamping the
-potentials.
+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
+significant narrowing of the angle distribution when using little to
+no damping and only modest improvement for the recommended conditions
+($\alpha$ = 0.2 \AA${-1}$ and $R_\textrm{c} \geqslant 12$~\AA).  The
+{\sc sf} method shows modest narrowing across all damping and cutoff
+ranges of interest.  When overdamping these methods, group cutoffs and
+the switching function do not improve the force and torque
+directionalities.
 
 \section{\label{app:ice}Solid Water: Ice I$_\textrm{c}$}
 
@@ -283,19 +284,19 @@ Highly ordered systems are a difficult test for the pa
    \label{tab:iceAng}
 \end{table}
 
-Highly ordered systems are a difficult test for the pairwise systems
-in that they lack the periodicity inherent to the Ewald summation.  As
-expected, the energy gap agreement with SPME reduces for the {\sc sp}
-and {\sc sf} with parameters that were perfectly acceptable for the
-disordered liquid system.  Moving to higher $R_\textrm{c}$ remedies
-this degraded performance, though at increase in computational cost.
-However, the dynamics of this crystalline system (both in magnitude
-and direction) are little affected. Both methods still reproduce the
-Ewald behavior with the same parameter recommendations from the
-previous section. 
+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
+{\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.
+The dynamics of this crystalline system (both in magnitude and
+direction) are little affected. Both methods still reproduce the Ewald
+behavior with the same parameter recommendations from the previous
+section.
 
-It is also worth noting that RF exhibits a slightly improved energy
-gap results over the liquid water system.  One possible explanation is
+It is also worth noting that {\sc rf} exhibits improved energy gap
+results over the liquid water system.  One possible explanation is
 that the ice I$_\textrm{c}$ crystal is ordered such that the net
 dipole moment of the crystal is zero.  With $\epsilon_\textrm{S} =
 \infty$, the reaction field incorporates this structural organization
@@ -305,13 +306,13 @@ pairwise summation methods in a highly charge disorder
 \section{\label{app:melt}NaCl Melt}
 
 A high temperature NaCl melt was tested to gauge the accuracy of the
-pairwise summation methods in a highly charge disordered system. The
-results for the energy gap comparisons and the force and torque vector
+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. 
+investigated.
 
 \begin{table}[htbp]
    \centering
@@ -470,17 +471,18 @@ method struggles in all cases with the exception of go
 {\sc sf} methods with a 12 \AA\ cutoff radius seem to be the best
 choices. These methods match well with {\sc spme} across the energy
 gap, force magnitude, and force directionality tests.  The {\sc sp}
-method struggles in all cases with the exception of good dynamics
+method struggles in all cases, with the exception of good dynamics
 reproduction when using weak electrostatic damping with a large cutoff
 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 these results are a test of instantaneous dynamics, this
-indicates that good long-time dynamics comes in part at the expense of
+system. Since the data tabulated in table \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 300 cm$^{-1}$ with increased
+distortion is introduced between 200 to 350 cm$^{-1}$ with increased
 $\alpha$.
 
 \section{\label{app:solnWeak}Weak NaCl Solution}
@@ -595,16 +597,16 @@ This weak ionic strength system can be considered as a
    \label{tab:solnWeakAng}
 \end{table}
 
-This weak ionic strength system can be considered as a perturbation of
-the pure liquid water system. The {\sc sp} and {\sc sf} methods are
-not significantly affected by the inclusion of a few ions. The aspect
-of cutoff sphere neutralization aids in the smooth incorporation of
-these ions; thus, all of the observations regarding these methods
-carry over from section \ref{app:water}. The differences between these
-systems are visible for the {\sc rf} method. Though good force
-reproduction is still maintained, the energy gaps show a significant
-increase in the data scatter. This foreshadows the breakdown of the
-method as we introduce system inhomogeneities.
+Because this system is a perturbation of the pure liquid water system,
+comparisons are best drawn between these two sets. The {\sc sp} and
+{\sc sf} methods are not significantly affected by the inclusion of a
+few ions. The aspect of cutoff sphere neutralization aids in the
+smooth incorporation of these ions; thus, all of the observations
+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.
 
 \section{\label{app:solnStr}Strong NaCl Solution}
 
@@ -614,7 +616,7 @@ results are displayed separately in table\ref{tab:soln
 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
+results are displayed separately in table \ref{tab:solnWeakAng}, where
 the effect of group-based cutoffs and switching functions on the {\sc
 sp} and {\sc sf} potentials are investigated.
 
@@ -712,10 +714,10 @@ configuration energy difference degrade to unuseable l
 \end{table}
 
 The {\sc rf} method struggles with the jump in ionic strength. The
-configuration energy difference degrade to unuseable levels while the
-forces and torques degrade in a more modest fashion. The {\sc rf}
-method was designed for homogeneous systems, and this restriction is
-apparent in these results.
+configuration energy difference 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.
 
 The {\sc sp} and {\sc sf} methods require larger cutoffs to maintain
 their agreement with {\sc spme}. With these results, we still
@@ -831,7 +833,17 @@ This system appears not to show in any significant dev
    \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 \ref{app:water}. The only significant difference is the improvement for 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, which the {\sc sp} and {\sc sf} methods explicity enforce, seems to play a greater role in the stability of the {\sc rf} method than the necessity of a homogeneous environment.
+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
+\ref{app:water}. The only significant difference is the improvement
+for 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
+spheres, which the {\sc sp} and {\sc sf} methods explicitly enforce,
+seems to play a greater role in the stability of the {\sc rf} method
+than the required homogeneity of the environment.
 
 \newpage