--- trunk/ssdePaper/nptSSD.tex	2004/02/04 18:51:43	1017
+++ trunk/ssdePaper/nptSSD.tex	2004/02/04 22:13:36	1022
@@ -209,8 +209,10 @@ cubic switching function at a cutoff radius.  Under th
 
 Long-range dipole-dipole interactions were accounted for in this study
 by using either the reaction field method or by resorting to a simple
-cubic switching function at a cutoff radius.  Under the first method,
-the magnitude of the reaction field acting on dipole $i$ is
+cubic switching function at a cutoff radius.  The reaction field
+method was actually first used in Monte Carlo simulations of liquid
+water.\cite{Barker73} Under this method, the magnitude of the reaction
+field acting on dipole $i$ is
 \begin{equation}
 \mathcal{E}_{i} = \frac{2(\varepsilon_{s} - 1)}{2\varepsilon_{s} + 1}
 \frac{1}{r_{c}^{3}} \sum_{j\in{\mathcal{R}}} {\bf \mu}_{j} f(r_{ij})\  ,
@@ -233,8 +235,8 @@ at the cutoff radius) and as a result we have two repa
  
 We have also performed a companion set of simulations {\it without} a
 surrounding dielectric (i.e. using a simple cubic switching function
-at the cutoff radius) and as a result we have two reparamaterizations
-of SSD which could be used either with or without the Reaction Field
+at the cutoff radius), and as a result we have two reparamaterizations
+of SSD which could be used either with or without the reaction field
 turned on.
 
 Simulations to obtain the preferred density were performed in the
@@ -252,12 +254,11 @@ traditional quaternion integration.\cite{Evans77,Evans
 symplectic splitting method proposed by Dullweber {\it et
 al.}\cite{Dullweber1997} Our reason for selecting this integrator
 centers on poor energy conservation of rigid body dynamics using
-traditional quaternion integration.\cite{Evans77,Evans77b} While quaternions
-may work well for orientational motion under NVT or NPT integrators,
-our limits on energy drift in the microcanonical ensemble were quite
-strict, and the drift under quaternions was substantially greater than
-in the symplectic splitting method.  This steady drift in the total
-energy has also been observed by Kol {\it et al.}\cite{Laird97}
+traditional quaternion integration.\cite{Evans77,Evans77b} In typical
+microcanonical ensemble simulations, the energy drift when using
+quaternions was substantially greater than when using the symplectic
+splitting method (fig. \ref{timestep}).  This steady drift in the
+total energy has also been observed by Kol {\it et al.}\cite{Laird97}
 
 The key difference in the integration method proposed by Dullweber
 \emph{et al.} is that the entire rotation matrix is propagated from
@@ -447,7 +448,7 @@ results.\cite{Gillen72,Mills73,Clancy94,Jorgensen01} 
 mean-square displacement as a function of time. The averaged results
 from five sets of NVE simulations are displayed in figure
 \ref{diffuse}, alongside experimental, SPC/E, and TIP5P
-results.\cite{Gillen72,Mills73,Clancy94,Jorgensen01} 
+results.\cite{Gillen72,Holz00,Clancy94,Jorgensen01} 
 
 \begin{figure}
 \begin{center}
@@ -455,7 +456,7 @@ and Experimental data [Refs. \citen{Gillen72} and \cit
 \epsfbox{betterDiffuse.epsi} 
 \caption{Average self-diffusion constant as a function of temperature for 
 SSD, SPC/E [Ref. \citen{Clancy94}], TIP5P [Ref. \citen{Jorgensen01}],
-and Experimental data [Refs. \citen{Gillen72} and \citen{Mills73}]. Of
+and Experimental data [Refs. \citen{Gillen72} and \citen{Holz00}]. Of
 the three water models shown, SSD has the least deviation from the
 experimental values. The rapidly increasing diffusion constants for
 TIP5P and SSD correspond to significant decrease in density at the
@@ -891,7 +892,18 @@ respectively.
 radial location of the minima following the first solvation shell
 peak, and g$(r)$ is either g$_\text{OO}(r)$ or g$_\text{OH}(r)$ for
 calculation of the coordination number or hydrogen bonds per particle
-respectively.
+respectively. The number of hydrogen bonds stays relatively constant
+across all of the models, but the coordination numbers of SSD/E and
+SSD/RF show an improvement over SSD1. This improvement is primarily
+due to the widening of the first solvation shell peak, allowing the
+first minima to push outward. Comparing the coordination number with
+the number of hydrogen bonds can lead to more insight into the
+structural character of the liquid.  Because of the near identical
+values for SSD1, it appears to be a little too exclusive, in that all
+molecules in the first solvation shell are involved in forming ideal
+hydrogen bonds.  The differing numbers for the newly parameterized
+models indicate the allowance of more fluid configurations in addition
+to the formation of an acceptable number of ideal hydrogen bonds.
 
 The time constants for the self orientational autocorrelation function
 are also displayed in Table \ref{liquidproperties}. The dipolar
@@ -906,7 +918,21 @@ performed at the STP density for each of the respectiv
 vector can be calculated from an exponential fit in the long-time
 regime ($t > \tau_l^\mu$).\cite{Rothschild84} Calculation of these
 time constants were averaged from five detailed NVE simulations
-performed at the STP density for each of the respective models.
+performed at the STP density for each of the respective models. It
+should be noted that the commonly cited value for $\tau_2$ of 1.9 ps
+was determined from the NMR data in reference \citen{Krynicki66} at a
+temperature near 34$^\circ$C.\cite{Rahman73} Because of the strong
+temperature dependence of $\tau_2$, it is necessary to recalculate it
+at 298 K to make proper comparisons. The value shown in Table
+\ref{liquidproperties} was calculated from the same NMR data in the 
+fashion described in reference \citen{Krynicki66}. Again, SSD/E and
+SSD/RF show improved behavior over SSD1, both with and without an
+active reaction field. Turning on the reaction field leads to much
+improved time constants for SSD1; however, these results also include
+a corresponding decrease in system density. Numbers published from the
+original SSD dynamics studies appear closer to the experimental
+values, and this difference can be attributed to the use of the Ewald
+sum technique versus a reaction field.\cite{Ichiye99}
 
 \subsection{Additional Observations}