--- trunk/electrostaticMethodsPaper/electrostaticMethods.tex	2006/03/20 21:40:49	2645
+++ trunk/electrostaticMethodsPaper/electrostaticMethods.tex	2006/03/21 14:58:12	2649
@@ -140,10 +140,10 @@ V_\textrm{elec} = \frac{1}{2}& \sum_{i=1}^N\sum_{j=1}^
 \end{split}
 \label{eq:EwaldSum}
 \end{equation}
-where $\alpha$ is a damping parameter, or separation constant, with
-units of \AA$^{-1}$, $\mathbf{k}$ are the reciprocal vectors and are
-equal to $2\pi\mathbf{n}/L^2$, and $\epsilon_\textrm{S}$ is the
-dielectric constant of the surrounding medium. The final two terms of
+where $\alpha$ is the damping or convergence parameter with units of
+\AA$^{-1}$, $\mathbf{k}$ are the reciprocal vectors and are equal to
+$2\pi\mathbf{n}/L^2$, and $\epsilon_\textrm{S}$ is the dielectric
+constant of the surrounding medium. The final two terms of
 eq. (\ref{eq:EwaldSum}) are a particle-self term and a dipolar term
 for interacting with a surrounding dielectric.\cite{Allen87} This
 dipolar term was neglected in early applications in molecular
@@ -159,8 +159,9 @@ convergent behavior.  Indeed, it has often been observ
 convergence.  In more modern simulations, the simulation boxes have
 grown large enough that a real-space cutoff could potentially give
 convergent behavior.  Indeed, it has often been observed that the
-reciprocal-space portion of the Ewald sum can be vanishingly
-small compared to the real-space portion.\cite{XXX}
+reciprocal-space portion of the Ewald sum can be small and rapidly
+convergent compared to the real-space portion with the choice of small
+$\alpha$.\cite{Karasawa89,Kolafa92}
 
 \begin{figure}
 \centering
@@ -176,7 +177,7 @@ The original Ewald summation is an $\mathscr{O}(N^2)$ 
 \end{figure}
 
 The original Ewald summation is an $\mathscr{O}(N^2)$ algorithm.  The
-separation constant $(\alpha)$ plays an important role in balancing
+convergence parameter $(\alpha)$ plays an important role in balancing
 the computational cost between the direct and reciprocal-space
 portions of the summation.  The choice of this value allows one to
 select whether the real-space or reciprocal space portion of the
@@ -714,18 +715,18 @@ The althernative methods were also evaluated with thre
 manner across all systems and configurations.
 
 The althernative methods were also evaluated with three different
-cutoff radii (9, 12, and 15 \AA).  It should be noted that the damping
-parameter chosen in SPME, or so called ``Ewald Coefficient'', has a
-significant effect on the energies and forces calculated.  Typical
-molecular mechanics packages set this to a value dependent on the
-cutoff radius and a tolerance (typically less than $1 \times 10^{-4}$
-kcal/mol).  Smaller tolerances are typically associated with increased
-accuracy at the expense of increased time spent calculating the
-reciprocal-space portion of the summation.\cite{Perram88,Essmann95}
-The default TINKER tolerance of $1 \times 10^{-8}$ kcal/mol was used
-in all SPME calculations, resulting in Ewald Coefficients of 0.4200,
-0.3119, and 0.2476 \AA$^{-1}$ for cutoff radii of 9, 12, and 15 \AA\
-respectively.
+cutoff radii (9, 12, and 15 \AA).  As noted previously, the
+convergence parameter ($\alpha$) plays a role in the balance of the
+real-space and reciprocal-space portions of the Ewald calculation.
+Typical molecular mechanics packages set this to a value dependent on
+the cutoff radius and a tolerance (typically less than $1 \times
+10^{-4}$ kcal/mol).  Smaller tolerances are typically associated with
+increased accuracy at the expense of increased time spent calculating
+the reciprocal-space portion of the
+summation.\cite{Perram88,Essmann95} The default TINKER tolerance of $1
+\times 10^{-8}$ kcal/mol was used in all SPME calculations, resulting
+in Ewald Coefficients of 0.4200, 0.3119, and 0.2476 \AA$^{-1}$ for
+cutoff radii of 9, 12, and 15 \AA\ respectively.
 
 \section{Results and Discussion}