--- trunk/electrostaticMethodsPaper/electrostaticMethods.tex	2006/03/24 02:39:59	2667
+++ trunk/electrostaticMethodsPaper/electrostaticMethods.tex	2006/04/26 15:22:09	2741
@@ -27,7 +27,7 @@ Pairwise alternatives to the accepted standard for \\
 
 \title{Is the Ewald summation still necessary? \\
 Pairwise alternatives to the accepted standard for \\
-long-range electrostatics}
+long-range electrostatics in molecular simulations}
 
 \author{Christopher J. Fennell and J. Daniel Gezelter\footnote{Corresponding author. \ Electronic mail:
 gezelter@nd.edu} \\
@@ -106,8 +106,8 @@ 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 +167,11 @@ 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}
 
@@ -201,10 +201,11 @@ can prove problematic.  The Ewald sum has been reformu
 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}
+new methods are computationally expensive.\cite{Spohr97,Yeh99} More
+recently, there have been several successful efforts toward reducing
+the computational cost of 2D lattice summations, often enabling the
+use of the mentioned
+optimizations.\cite{Yeh99,Kawata01,Arnold02,deJoannis02,Brodka04}
 
 Several studies have recognized that the inherent periodicity in the
 Ewald sum can also have an effect on three-dimensional
@@ -538,11 +539,11 @@ 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
@@ -621,14 +622,15 @@ 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),
