--- trunk/electrostaticMethodsPaper/electrostaticMethods.tex	2006/03/24 02:39:59	2667
+++ trunk/electrostaticMethodsPaper/electrostaticMethods.tex	2006/05/02 13:11:41	2744
@@ -20,14 +20,22 @@
 \topmargin -21pt \headsep 10pt
 \textheight 9.0in \textwidth 6.5in
 \brokenpenalty=10000
-\renewcommand{\baselinestretch}{1.2}
+%\renewcommand{\baselinestretch}{1.2}
+\renewcommand{\baselinestretch}{2}
 \renewcommand\citemid{\ } % no comma in optional reference note
+\AtBeginDelayedFloats{\renewcommand{\baselinestretch}{2}} %doublespace captions
+\let\Caption\caption
+\renewcommand\caption[1]{%
+	\Caption[#1]{}%
+}
+\setlength{\abovecaptionskip}{1.2in}
+\setlength{\belowcaptionskip}{1.2in}
 
 \begin{document}
 
 \title{Is the Ewald summation still necessary? \\
-Pairwise alternatives to the accepted standard for \\
-long-range electrostatics}
+Pairwise alternatives to the accepted standard \\
+for long-range electrostatics}
 
 \author{Christopher J. Fennell and J. Daniel Gezelter\footnote{Corresponding author. \ Electronic mail:
 gezelter@nd.edu} \\
@@ -38,7 +46,7 @@ Notre Dame, Indiana 46556}
 \date{\today}
 
 \maketitle
-\doublespacing
+%\doublespacing
 
 \begin{abstract}
 We investigate pairwise electrostatic interaction methods and show
@@ -52,7 +60,7 @@ to see how well they reproduce the energetics and dyna
 techniques.  Comparisons were performed with this and other pairwise
 methods against the smooth particle mesh Ewald ({\sc spme}) summation
 to see how well they reproduce the energetics and dynamics of a
-variety of simulation types.
+variety of molecular simulations.
 \end{abstract}
 
 \newpage
@@ -106,8 +114,8 @@ or which have one- or two-dimensional periodicity.  Be
 to the direct pairwise sum.  They also lack the added periodicity of
 the Ewald sum, so they can be used for systems which are non-periodic
 or which have one- or two-dimensional periodicity.  Below, these
-methods are evaluated using a variety of model systems to establish
-their usability in molecular simulations.
+methods are evaluated using a variety of model systems to
+establish their usability in molecular simulations.
 
 \subsection{The Ewald Sum}
 The complete accumulation of the electrostatic interactions in a system with
@@ -167,11 +175,11 @@ portion.\cite{Karasawa89,Kolafa92}
 \begin{figure}
 \centering
 \includegraphics[width = \linewidth]{./ewaldProgression.pdf}
-\caption{The change in the application of the Ewald sum with
-increasing computational power.  A:~Initially, only small systems could
-be studied, and the Ewald sum replicated the simulation box to
-convergence.  B:~Now, much larger systems of charges can be
-investigated with fixed-distance cutoffs.}
+\caption{The change in the need for the Ewald sum with
+increasing computational power.  A:~Initially, only small systems
+could be studied, and the Ewald sum replicated the simulation box to
+convergence.  B:~Now, radial cutoff methods should be able to reach
+convergence for the larger systems of charges that are common today.}
 \label{fig:ewaldTime}
 \end{figure}
 
@@ -200,12 +208,14 @@ can prove problematic.  The Ewald sum has been reformu
 conditions. However, in certain systems, such as vapor-liquid
 interfaces and membranes, the intrinsic three-dimensional periodicity
 can prove problematic.  The Ewald sum has been reformulated to handle
-2D systems,\cite{Parry75,Parry76,Heyes77,deLeeuw79,Rhee89}, but the
-new methods are computationally expensive.\cite{Spohr97,Yeh99}
-Inclusion of a correction term in the Ewald summation is a possible
-direction for handling 2D systems while still enabling the use of the
-modern optimizations.\cite{Yeh99}
+2-D systems,\cite{Parry75,Parry76,Heyes77,deLeeuw79,Rhee89} but these
+methods are computationally expensive.\cite{Spohr97,Yeh99} More
+recently, there have been several successful efforts toward reducing
+the computational cost of 2-D lattice
+summations,\cite{Yeh99,Kawata01,Arnold02,deJoannis02,Brodka04}
+bringing them more in line with the cost of the full 3-D summation.
 
+ 
 Several studies have recognized that the inherent periodicity in the
 Ewald sum can also have an effect on three-dimensional
 systems.\cite{Roberts94,Roberts95,Luty96,Hunenberger99a,Hunenberger99b,Weber00}
@@ -538,16 +548,16 @@ shows a data set with a good correlation coefficient.}
 \label{fig:linearFit} 
 \end{figure}
 
-Each system type (detailed in section \ref{sec:RepSims}) was
-represented using 500 independent configurations.  Additionally, we
-used seven different system types, so each of the alternative
-(non-Ewald) electrostatic summation methods was evaluated using
-873,250 configurational energy differences.
+Each of the seven system types (detailed in section \ref{sec:RepSims})
+were represented using 500 independent configurations.  Thus, each of
+the alternative (non-Ewald) electrostatic summation methods was
+evaluated using an accumulated 873,250 configurational energy
+differences.
 
 Results and discussion for the individual analysis of each of the
-system types appear in the supporting information, while the
-cumulative results over all the investigated systems appears below in
-section \ref{sec:EnergyResults}.
+system types appear in the supporting information,\cite{EPAPSdeposit}
+while the cumulative results over all the investigated systems appears
+below in section \ref{sec:EnergyResults}.
 
 \subsection{Molecular Dynamics and the Force and Torque Vectors}\label{sec:MDMethods}
 We evaluated the pairwise methods (outlined in section
@@ -621,14 +631,15 @@ were performed under the microcanonical ensemble, and 
 NaCl crystal is composed of two different atom types, the average of
 the two resulting power spectra was used for comparisons. Simulations
 were performed under the microcanonical ensemble, and velocity
-information was saved every 5 fs over 100 ps trajectories. 
+information was saved every 5~fs over 100~ps trajectories. 
 
 \subsection{Representative Simulations}\label{sec:RepSims}
-A variety of representative simulations were analyzed to determine the
-relative effectiveness of the pairwise summation techniques in
-reproducing the energetics and dynamics exhibited by {\sc spme}.  We wanted
-to span the space of modern simulations (i.e. from liquids of neutral
-molecules to ionic crystals), so the systems studied were:
+A variety of representative molecular simulations were analyzed to
+determine the relative effectiveness of the pairwise summation
+techniques in reproducing the energetics and dynamics exhibited by
+{\sc spme}.  We wanted to span the space of typical molecular
+simulations (i.e. from liquids of neutral molecules to ionic
+crystals), so the systems studied were:
 \begin{enumerate}
 \item liquid water (SPC/E),\cite{Berendsen87}
 \item crystalline water (Ice I$_\textrm{c}$ crystals of SPC/E),
@@ -742,7 +753,7 @@ readers can consult the accompanying supporting inform
 significant improvement using the group-switched cutoff because the
 salt and salt solution systems contain non-neutral groups.  Interested
 readers can consult the accompanying supporting information for a
-comparison where all groups are neutral.
+comparison where all groups are neutral.\cite{EPAPSdeposit}
 
 For the {\sc sp} method, inclusion of electrostatic damping improves
 the agreement with Ewald, and using an $\alpha$ of 0.2 \AA $^{-1}$
@@ -890,7 +901,7 @@ charged bodies, and this observation is investigated f
 particles in all seven systems, while torque vectors are only
 available for neutral molecular groups.  Damping is more beneficial to
 charged bodies, and this observation is investigated further in the
-accompanying supporting information.
+accompanying supporting information.\cite{EPAPSdeposit}
 
 Although not discussed previously, group based cutoffs can be applied
 to both the {\sc sp} and {\sc sf} methods.  The group-based cutoffs