--- trunk/ssdePaper/nptSSD.tex	2003/09/03 21:36:09	743
+++ trunk/ssdePaper/nptSSD.tex	2003/11/13 15:55:20	863
@@ -1,57 +1,54 @@
-\documentclass[prb,aps,times,twocolumn,tabularx]{revtex4}
-%\documentclass[prb,aps,times,tabularx,preprint]{revtex4}
+%\documentclass[prb,aps,times,twocolumn,tabularx]{revtex4}
+\documentclass[11pt]{article}
+\usepackage{endfloat}
 \usepackage{amsmath}
+\usepackage{epsf}
+\usepackage{berkeley}
+\usepackage{setspace}
+\usepackage{tabularx}
 \usepackage{graphicx}
-
-%\usepackage{endfloat}
+\usepackage[ref]{overcite}
 %\usepackage{berkeley}
-%\usepackage{epsf}
-%\usepackage[ref]{overcite}
-%\usepackage{setspace}
-%\usepackage{tabularx}
-%\usepackage{graphicx}
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-%\usepackage{amsmath}
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-%\topmargin -21pt \headsep 10pt
-%\textheight 9.0in \textwidth 6.5in
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+\pagestyle{plain}
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+\topmargin -21pt \headsep 10pt
+\textheight 9.0in \textwidth 6.5in
+\brokenpenalty=10000
+\renewcommand{\baselinestretch}{1.2}
+\renewcommand\citemid{\ } % no comma in optional reference note
 
 \begin{document}
 
-\title{On the temperature dependent structural and transport properties of the soft sticky dipole (SSD) and related single point water models}
+\title{On the temperature dependent properties of the soft sticky dipole (SSD) and related single point water models}
 
-\author{Christopher J. Fennell and J. Daniel Gezelter{\thefootnote}
-\footnote[1]{Corresponding author. \ Electronic mail: gezelter@nd.edu}}
-
-\address{Department of Chemistry and Biochemistry\\ University of Notre Dame\\
+\author{Christopher J. Fennell and J. Daniel Gezelter\footnote{Corresponding author. \ Electronic mail: gezelter@nd.edu} \\
+Department of Chemistry and Biochemistry\\ University of Notre Dame\\
 Notre Dame, Indiana 46556}
 
 \date{\today}
 
+\maketitle
+
 \begin{abstract}
 NVE and NPT molecular dynamics simulations were performed in order to
 investigate the density maximum and temperature dependent transport
-for the SSD water model, both with and without the use of reaction
-field. The constant pressure simulations of the melting of both $I_h$
-and $I_c$ ice showed a density maximum near 260 K. In most cases, the
-calculated densities were significantly lower than the densities
-calculated in simulations of other water models. Analysis of particle
-diffusion showed SSD to capture the transport properties of
-experimental very well in both the normal and super-cooled liquid
-regimes. In order to correct the density behavior, SSD was
+for SSD and related water models, both with and without the use of
+reaction field. The constant pressure simulations of the melting of
+both $I_h$ and $I_c$ ice showed a density maximum near 260 K. In most
+cases, the calculated densities were significantly lower than the
+densities calculated in simulations of other water models. Analysis of
+particle diffusion showed SSD to capture the transport properties of
+experimental water very well in both the normal and super-cooled
+liquid regimes. In order to correct the density behavior, SSD was
 reparameterized for use both with and without a long-range interaction
-correction, SSD/RF and SSD/E respectively. In addition to correcting
-the abnormally low densities, these new versions were show to maintain
-or improve upon the transport and structural features of the original
-water model.
+correction, SSD/RF and SSD/E respectively. Compared to the density
+corrected version of SSD (SSD1), these modified models were shown to
+maintain or improve upon the structural and transport properties.
 \end{abstract}
 
-\maketitle
+\newpage
 
 %\narrowtext 
 
@@ -62,27 +59,26 @@ One of the most important tasks in simulations of bioc
 
 \section{Introduction}
 
-One of the most important tasks in simulations of biochemical systems
-is the proper depiction of water and water solvation. In fact, the
-bulk of the calculations performed in solvated simulations are of
+One of the most important tasks in the simulation of biochemical
+systems is the proper depiction of water and water solvation. In fact,
+the bulk of the calculations performed in solvated simulations are of
 interactions with or between solvent molecules. Thus, the outcomes of
 these types of simulations are highly dependent on the physical
-properties of water, both as individual molecules and in
-groups/bulk. Due to the fact that explicit solvent accounts for a
-massive portion of the calculations, it necessary to simplify the
-solvent to some extent in order to complete simulations in a
-reasonable amount of time. In the case of simulating water in
-bio-molecular studies, the balance between accurate properties and
-computational efficiency is especially delicate, and it has resulted
-in a variety of different water
-models.\cite{Jorgensen83,Berendsen87,Jorgensen00} Many of these models
-get specific properties correct or better than their predecessors, but
-this is often at a cost of some other properties or of computer
-time. As an example, compare TIP3P or TIP4P to TIP5P. TIP5P succeeds
-in improving the structural and transport properties over its
-predecessors, yet this comes at a greater than 50\% increase in
+properties of water, both as individual molecules and in clusters or
+bulk. Due to the fact that explicit solvent accounts for a massive
+portion of the calculations, it necessary to simplify the solvent to
+some extent in order to complete simulations in a reasonable amount of
+time. In the case of simulating water in biomolecular studies, the
+balance between accurate properties and computational efficiency is
+especially delicate, and it has resulted in a variety of different
+water models.\cite{Jorgensen83,Berendsen87,Jorgensen00} Many of these
+models predict specific properties more accurately than their
+predecessors, but often at the cost of other properties or of computer
+time. As an example, compare TIP3P or TIP4P to TIP5P. TIP5P improves
+upon the structural and transport properties of water relative to the
+previous TIP models, yet this comes at a greater than 50\% increase in
 computational cost.\cite{Jorgensen01,Jorgensen00} One recently
-developed model that succeeds in both retaining accuracy of system
+developed model that succeeds in both retaining the accuracy of system
 properties and simplifying calculations to increase computational
 efficiency is the Soft Sticky Dipole water model.\cite{Ichiye96}
 
@@ -101,11 +97,11 @@ where the $\mathbf{r}_{ij}$ is the position vector bet
 (\mathbf{r}_{ij},\boldsymbol{\Omega}_i,\boldsymbol{\Omega}_j),
 \end{equation}
 where the $\mathbf{r}_{ij}$ is the position vector between molecules
-\emph{i} and \emph{j} with magnitude equal to the distance $r_ij$, and
+\emph{i} and \emph{j} with magnitude equal to the distance $r_{ij}$, and
 $\boldsymbol{\Omega}_i$ and $\boldsymbol{\Omega}_j$ represent the
 orientations of the respective molecules. The Lennard-Jones, dipole,
 and sticky parts of the potential are giving by the following
-equations,
+equations:
 \begin{equation}
 u_{ij}^{LJ}(r_{ij}) = 4\epsilon \left[\left(\frac{\sigma}{r_{ij}}\right)^{12}-\left(\frac{\sigma}{r_{ij}}\right)^{6}\right],
 \end{equation}
@@ -113,20 +109,15 @@ u_{ij}^{dp} = \frac{\boldsymbol{\mu}_i\cdot\boldsymbol
 u_{ij}^{dp} = \frac{\boldsymbol{\mu}_i\cdot\boldsymbol{\mu}_j}{r_{ij}^3}-\frac{3(\boldsymbol{\mu}_i\cdot\mathbf{r}_{ij})(\boldsymbol{\mu}_j\cdot\mathbf{r}_{ij})}{r_{ij}^5}\ ,
 \end{equation}
 \begin{equation}
-\begin{split}
 u_{ij}^{sp}
-(\mathbf{r}_{ij},\boldsymbol{\Omega}_i,\boldsymbol{\Omega}_j) 
-&=
-\frac{\nu_0}{2}[s(r_{ij})w(\mathbf{r}_{ij},\boldsymbol{\Omega}_i,\boldsymbol{\Omega}_j)\\
-& \quad \ +
-s^\prime(r_{ij})w^\prime(\mathbf{r}_{ij},\boldsymbol{\Omega}_i,\boldsymbol{\Omega}_j)]\ ,
-\end{split}
+(\mathbf{r}_{ij},\boldsymbol{\Omega}_i,\boldsymbol{\Omega}_j) =
+\frac{\nu_0}{2}[s(r_{ij})w(\mathbf{r}_{ij},\boldsymbol{\Omega}_i,\boldsymbol{\Omega}_j) + s^\prime(r_{ij})w^\prime(\mathbf{r}_{ij},\boldsymbol{\Omega}_i,\boldsymbol{\Omega}_j)]\ ,
 \end{equation}
 where $\boldsymbol{\mu}_i$ and $\boldsymbol{\mu}_j$ are the dipole
 unit vectors of particles \emph{i} and \emph{j} with magnitude 2.35 D,
-$\nu_0$ scales the strength of the overall sticky potential, $s$ and
-$s^\prime$ are cubic switching functions. The $w$ and $w^\prime$
-functions take the following forms,
+$\nu_0$ scales the strength of the overall sticky potential, and $s$
+and $s^\prime$ are cubic switching functions. The $w$ and $w^\prime$
+functions take the following forms:
 \begin{equation}
 w(\mathbf{r}_{ij},\boldsymbol{\Omega}_i,\boldsymbol{\Omega}_j)=\sin\theta_{ij}\sin2\theta_{ij}\cos2\phi_{ij},
 \end{equation}
@@ -143,35 +134,41 @@ simulations using this model, Ichiye \emph{et al.} rep
 
 Being that this is a one-site point dipole model, the actual force
 calculations are simplified significantly. In the original Monte Carlo
-simulations using this model, Ichiye \emph{et al.} reported a
-calculation speed up of up to an order of magnitude over other
-comparable models while maintaining the structural behavior of
-water.\cite{Ichiye96} In the original molecular dynamics studies of
-SSD, it was shown that it actually improves upon the prediction of
-water's dynamical properties 3 and 4-point models.\cite{Ichiye99} This
+simulations using this model, Ichiye \emph{et al.} reported an
+increase in calculation efficiency of up to an order of magnitude over
+other comparable models, while maintaining the structural behavior of
+water.\cite{Ichiye96} In the original molecular dynamics studies, it
+was shown that SSD improves on the prediction of many of water's
+dynamical properties over TIP3P and SPC/E.\cite{Ichiye99} This
 attractive combination of speed and accurate depiction of solvent
 properties makes SSD a model of interest for the simulation of large
-scale biological systems, such as membrane phase behavior, a specific
-interest within our group.
+scale biological systems, such as membrane phase behavior.
 
-Up to this point, a detailed look at the model's structure and ion
-solvation abilities has been performed.\cite{Ichiye96} In addition, a
-thorough investigation of the dynamic properties of SSD was performed
-by Chandra and Ichiye focusing on translational and orientational
-properties at 298 K.\cite{Ichiye99} This study focuses on determining
-the density maximum for SSD utilizing both microcanonical and
-isobaric-isothermal ensemble molecular dynamics, while using the
-reaction field method for handling long-ranged dipolar interactions. A
-reaction field method has been previously implemented in Monte Carlo
-simulations by Liu and Ichiye in order to study the static dielectric
-constant for the model.\cite{Ichiye96b} This paper will expand the
-scope of these original simulations to look on how the reaction field
-affects the physical and dynamic properties of SSD systems.
+One of the key limitations of this water model, however, is that it
+has been parameterized for use with the Ewald Sum technique for the
+handling of long-ranged interactions.  When studying very large
+systems, the Ewald summation and even particle-mesh Ewald become
+computational burdens, with their respective ideal $N^\frac{3}{2}$ and
+$N\log N$ calculation scaling orders for $N$ particles.\cite{Darden99}
+In applying this water model in these types of systems, it would be
+useful to know its properties and behavior with the more
+computationally efficient reaction field (RF) technique, and even with
+a cutoff that lacks any form of long-range correction. This study
+addresses these issues by looking at the structural and transport
+behavior of SSD over a variety of temperatures with the purpose of
+utilizing the RF correction technique. We then suggest alterations to
+the parameters that result in more water-like behavior. It should be
+noted that in a recent publication, some of the original investigators of
+the SSD water model have put forth adjustments to the SSD water model
+to address abnormal density behavior (also observed here), calling the
+corrected model SSD1.\cite{Ichiye03} This study will make comparisons
+with SSD1's behavior with the goal of improving upon the
+depiction of water under conditions without the Ewald Sum.
 
 \section{Methods}
 
-As stated previously, in this study the long-range dipole-dipole
-interactions were accounted for using the reaction field method. The
+As stated previously, the long-range dipole-dipole interactions were
+accounted for in this study by using the reaction field method. The
 magnitude of the reaction field acting on dipole \emph{i} is given by
 \begin{equation}
 \mathcal{E}_{i} = \frac{2(\varepsilon_{s} - 1)}{2\varepsilon_{s} + 1}
@@ -192,79 +189,82 @@ large-scale system, the computational cost benefit of 
 in the length of the cutoff radius.\cite{Berendsen98} This variable
 behavior makes reaction field a less attractive method than other
 methods, like the Ewald summation; however, for the simulation of
-large-scale system, the computational cost benefit of reaction field
+large-scale systems, the computational cost benefit of reaction field
 is dramatic. To address some of the dynamical property alterations due
 to the use of reaction field, simulations were also performed without
-a surrounding dielectric and suggestions are proposed on how to make
-SSD more compatible with a reaction field.
- 
+a surrounding dielectric and suggestions are presented on how to make
+SSD more accurate both with and without a reaction field.
+
 Simulations were performed in both the isobaric-isothermal and
 microcanonical ensembles. The constant pressure simulations were
 implemented using an integral thermostat and barostat as outlined by
-Hoover.\cite{Hoover85,Hoover86} For the constant pressure
-simulations, the \emph{Q} parameter for the was set to 5.0 amu
-\(\cdot\)\AA\(^{2}\), and the relaxation time (\(\tau\))\ was set at
-100 ps.
+Hoover.\cite{Hoover85,Hoover86} All particles were treated as
+non-linear rigid bodies. Vibrational constraints are not necessary in
+simulations of SSD, because there are no explicit hydrogen atoms, and
+thus no molecular vibrational modes need to be considered.
 
 Integration of the equations of motion was carried out using the
 symplectic splitting method proposed by Dullweber \emph{et
-al.}.\cite{Dullweber1997} The reason for this integrator selection
+al.}\cite{Dullweber1997} The reason for this integrator selection
 deals with poor energy conservation of rigid body systems using
 quaternions. While quaternions work well for orientational motion in
 alternate ensembles, the microcanonical ensemble has a constant energy
-requirement that is actually quite sensitive to errors in the
-equations of motion. The original implementation of this code utilized
-quaternions for rotational motion propagation; however, a detailed
-investigation showed that they resulted in a steady drift in the total
-energy, something that has been observed by others.\cite{Laird97}
+requirement that is quite sensitive to errors in the equations of
+motion. The original implementation of this code utilized quaternions
+for rotational motion propagation; however, a detailed investigation
+showed that they resulted in a steady drift in the total energy,
+something that has been observed by others.\cite{Laird97}
 
 The key difference in the integration method proposed by Dullweber
 \emph{et al.} is that the entire rotation matrix is propagated from
 one time step to the next. In the past, this would not have been as
-feasible a option, being that the rotation matrix for a single body is
+feasible an option, being that the rotation matrix for a single body is
 nine elements long as opposed to 3 or 4 elements for Euler angles and
 quaternions respectively. System memory has become much less of an
 issue in recent times, and this has resulted in substantial benefits
-in energy conservation. There is still the issue of an additional 5 or
-6 additional elements for describing the orientation of each particle,
-which will increase dump files substantially. Simply translating the
-rotation matrix into its component Euler angles or quaternions for
-storage purposes relieves this burden.
+in energy conservation. There is still the issue of 5 or 6 additional
+elements for describing the orientation of each particle, which will
+increase dump files substantially. Simply translating the rotation
+matrix into its component Euler angles or quaternions for storage
+purposes relieves this burden.
 
 The symplectic splitting method allows for Verlet style integration of
-both linear and angular motion of rigid bodies. In the integration
+both linear and angular motion of rigid bodies. In this integration
 method, the orientational propagation involves a sequence of matrix
 evaluations to update the rotation matrix.\cite{Dullweber1997} These
-matrix rotations end up being more costly computationally than the
-simpler arithmetic quaternion propagation. On average, a 1000 SSD
-particle simulation shows a 7\% increase in simulation time using the
-symplectic step method in place of quaternions. This cost is more than
-justified when comparing the energy conservation of the two methods as
-illustrated in figure \ref{timestep}.
+matrix rotations are more costly computationally than the simpler
+arithmetic quaternion propagation. With the same time step, a 1000 SSD
+particle simulation shows an average 7\% increase in computation time
+using the symplectic step method in place of quaternions. This cost is
+more than justified when comparing the energy conservation of the two
+methods as illustrated in figure \ref{timestep}.
 
 \begin{figure}
-\includegraphics[width=61mm, angle=-90]{timeStep.epsi}
+\begin{center}
+\epsfxsize=6in
+\epsfbox{timeStep.epsi}
 \caption{Energy conservation using quaternion based integration versus 
 the symplectic step method proposed by Dullweber \emph{et al.} with
-increasing time step. For each time step, the dotted line is total
-energy using the symplectic step integrator, and the solid line comes
-from the quaternion integrator. The larger time step plots are shifted
-up from the true energy baseline for clarity.}
+increasing time step. The larger time step plots are shifted up from
+the true energy baseline (that of $\Delta t$ = 0.1 fs) for clarity.}
 \label{timestep}
+\end{center}
 \end{figure}
 
 In figure \ref{timestep}, the resulting energy drift at various time
 steps for both the symplectic step and quaternion integration schemes
 is compared. All of the 1000 SSD particle simulations started with the
-same configuration, and the only difference was the method for
-handling rotational motion. At time steps of 0.1 and 0.5 fs, both
+same configuration, and the only difference was the method used to
+handle rotational motion. At time steps of 0.1 and 0.5 fs, both
 methods for propagating particle rotation conserve energy fairly well,
 with the quaternion method showing a slight energy drift over time in
 the 0.5 fs time step simulation. At time steps of 1 and 2 fs, the
 energy conservation benefits of the symplectic step method are clearly
-demonstrated.
+demonstrated. Thus, while maintaining the same degree of energy
+conservation, one can take considerably longer time steps, leading to
+an overall reduction in computation time.
 
-Energy drift in these SSD particle simulations was unnoticeable for
+Energy drift in the symplectic step simulations was unnoticeable for
 time steps up to three femtoseconds. A slight energy drift on the
 order of 0.012 kcal/mol per nanosecond was observed at a time step of
 four femtoseconds, and as expected, this drift increases dramatically
@@ -273,21 +273,21 @@ starting points for all the simulations. The $I_h$ cry
 constant pressure simulations as well.
 
 Ice crystals in both the $I_h$ and $I_c$ lattices were generated as
-starting points for all the simulations. The $I_h$ crystals were
-formed by first arranging the center of masses of the SSD particles
-into a ``hexagonal'' ice lattice of 1024 particles. Because of the
-crystal structure of $I_h$ ice, the simulation box assumed a
-rectangular shape with a edge length ratio of approximately
+starting points for all simulations. The $I_h$ crystals were formed by
+first arranging the centers of mass of the SSD particles into a
+``hexagonal'' ice lattice of 1024 particles. Because of the crystal
+structure of $I_h$ ice, the simulation box assumed a rectangular shape
+with an edge length ratio of approximately
 1.00$\times$1.06$\times$1.23. The particles were then allowed to
 orient freely about fixed positions with angular momenta randomized at
 400 K for varying times. The rotational temperature was then scaled
-down in stages to slowly cool the crystals down to 25 K. The particles
-were then allowed translate with fixed orientations at a constant
+down in stages to slowly cool the crystals to 25 K. The particles were
+then allowed to translate with fixed orientations at a constant
 pressure of 1 atm for 50 ps at 25 K. Finally, all constraints were
 removed and the ice crystals were allowed to equilibrate for 50 ps at
 25 K and a constant pressure of 1 atm.  This procedure resulted in
 structurally stable $I_h$ ice crystals that obey the Bernal-Fowler
-rules\cite{Bernal33,Rahman72}.  This method was also utilized in the
+rules.\cite{Bernal33,Rahman72} This method was also utilized in the
 making of diamond lattice $I_c$ ice crystals, with each cubic
 simulation box consisting of either 512 or 1000 particles. Only
 isotropic volume fluctuations were performed under constant pressure,
@@ -297,579 +297,614 @@ constant pressure and temperature dynamics. This invol
 \section{Results and discussion}
 
 Melting studies were performed on the randomized ice crystals using
-constant pressure and temperature dynamics. This involved an initial
-randomization of velocities about the starting temperature of 25 K for
-varying amounts of time. The systems were all equilibrated for 100 ps
-prior to a 200 ps data collection run at each temperature setting,
-ranging from 25 to 400 K, with a maximum degree increment of 25 K. For
-regions of interest along this stepwise progression, the temperature
-increment was decreased from 25 K to 10 and then 5 K. The above
-equilibration and production times were sufficient in that the system
-volume fluctuations dampened out in all but the very cold simulations
-(below 225 K). In order to further improve statistics, five separate
-simulation progressions were performed, and the averaged results from
-the $I_h$ melting simulations are shown in figure \ref{dense1}.
+constant pressure and temperature dynamics. During melting
+simulations, the melting transition and the density maximum can both
+be observed, provided that the density maximum occurs in the liquid
+and not the supercooled regime. An ensemble average from five separate
+melting simulations was acquired, each starting from different ice
+crystals generated as described previously. All simulations were
+equilibrated for 100 ps prior to a 200 ps data collection run at each
+temperature setting. The temperature range of study spanned from 25 to
+400 K, with a maximum degree increment of 25 K. For regions of
+interest along this stepwise progression, the temperature increment
+was decreased from 25 K to 10 and 5 K. The above equilibration and
+production times were sufficient in that the system volume
+fluctuations dampened out in all but the very cold simulations (below
+225 K).
 
-\begin{figure}
-\includegraphics[width=65mm, angle=-90]{1hdense.epsi}
-\caption{Average density of SSD water at increasing temperatures 
-starting from ice $I_h$ lattice.}
-\label{dense1}
-\end{figure}
-
 \subsection{Density Behavior}
-In the initial average density versus temperature plot, the density
-maximum clearly appears between 255 and 265 K. The calculated
-densities within this range were nearly indistinguishable, as can be
-seen in the zoom of this region of interest, shown in figure
-\ref{dense1}. The greater certainty of the average value at 260 K makes 
-a good argument for the actual density maximum residing at this
-midpoint value. Figure \ref{dense1} was constructed using ice $I_h$
-crystals for the initial configuration; and though not pictured, the
-simulations starting from ice $I_c$ crystal configurations showed
-similar results, with a liquid-phase density maximum in this same
-region (between 255 and 260 K). In addition, the $I_c$ crystals are
-more fragile than the $I_h$ crystals, leading them to deform into a
-dense glassy state at lower temperatures. This resulted in an overall
-low temperature density maximum at 200 K, but they still retained a
-common liquid state density maximum with the $I_h$ simulations.
+Initial simulations focused on the original SSD water model, and an
+average density versus temperature plot is shown in figure
+\ref{dense1}. Note that the density maximum when using a reaction 
+field appears between 255 and 265 K, where the calculated densities
+within this range were nearly indistinguishable. The greater certainty
+of the average value at 260 K makes a good argument for the actual
+density maximum residing at this midpoint value. Figure \ref{dense1}
+was constructed using ice $I_h$ crystals for the initial
+configuration; though not pictured, the simulations starting from ice
+$I_c$ crystal configurations showed similar results, with a
+liquid-phase density maximum in this same region (between 255 and 260
+K). In addition, the $I_c$ crystals are more fragile than the $I_h$
+crystals, leading to deformation into a dense glassy state at lower
+temperatures. This resulted in an overall low temperature density
+maximum at 200 K, while still retaining a liquid state density maximum
+in common with the $I_h$ simulations.
 
 \begin{figure}
-\includegraphics[width=65mm,angle=-90]{dense2.eps}
-\caption{Density versus temperature for TIP4P\cite{Jorgensen98b}, 
-TIP3P\cite{Jorgensen98b}, SPC/E\cite{Clancy94}, SSD without Reaction
-Field, SSD, and Experiment\cite{CRC80}. }
-\label{dense2}
+\begin{center}
+\epsfxsize=6in
+\epsfbox{denseSSD.eps}
+\caption{Density versus temperature for TIP4P,\cite{Jorgensen98b} 
+ TIP3P,\cite{Jorgensen98b} SPC/E,\cite{Clancy94} SSD without Reaction
+ Field, SSD, and experiment.\cite{CRC80} The arrows indicate the
+ change in densities observed when turning off the reaction field. The
+ the lower than expected densities for the SSD model were what
+ prompted the original reparameterization.\cite{Ichiye03}}
+\label{dense1}
+\end{center}
 \end{figure}
 
 The density maximum for SSD actually compares quite favorably to other
-simple water models. Figure \ref{dense2} shows a plot of these
-findings with the density progression of several other models and
-experiment obtained from other
+simple water models. Figure \ref{dense1} also shows calculated
+densities of several other models and experiment obtained from other
 sources.\cite{Jorgensen98b,Clancy94,CRC80} Of the listed simple water
 models, SSD has results closest to the experimentally observed water
 density maximum. Of the listed water models, TIP4P has a density
-maximum behavior most like that seen in SSD. Though not shown, it is
-useful to note that TIP5P has a water density maximum nearly identical
-to experiment.
+maximum behavior most like that seen in SSD. Though not included in
+this particular plot, it is useful to note that TIP5P has a water
+density maximum nearly identical to experiment.
 
-Possibly of more importance is the density scaling of SSD relative to
-other common models at any given temperature (Fig. \ref{dense2}). Note
-that the SSD model assumes a lower density than any of the other
-listed models at the same pressure, behavior which is especially
-apparent at temperatures greater than 300 K. Lower than expected
-densities have been observed for other systems with the use of a
-reaction field for long-range electrostatic interactions, so the most
-likely reason for these significantly lower densities in these
-simulations is the presence of the reaction field.\cite{Berendsen98}
-In order to test the effect of the reaction field on the density of
-the systems, the simulations were repeated for the temperature region
-of interest without a reaction field present. The results of these
-simulations are also displayed in figure \ref{dense2}. Without
-reaction field, these densities increase considerably to more
-experimentally reasonable values, especially around the freezing point
-of liquid water. The shape of the curve is similar to the curve
-produced from SSD simulations using reaction field, specifically the
-rapidly decreasing densities at higher temperatures; however, a slight
-shift in the density maximum location, down to 245 K, is
-observed. This is probably a more accurate comparison to the other
-listed water models in that no long range corrections were applied in
-those simulations.\cite{Clancy94,Jorgensen98b}
-
 It has been observed that densities are dependent on the cutoff radius
 used for a variety of water models in simulations both with and
 without the use of reaction field.\cite{Berendsen98} In order to
 address the possible affect of cutoff radius, simulations were
 performed with a dipolar cutoff radius of 12.0 \AA\ to compliment the
 previous SSD simulations, all performed with a cutoff of 9.0 \AA. All
-the resulting densities overlapped within error and showed no
-significant trend in lower or higher densities as a function of cutoff
-radius, both for simulations with and without reaction field. These
-results indicate that there is no major benefit in choosing a longer
-cutoff radius in simulations using SSD. This is comforting in that the
-use of a longer cutoff radius results in a near doubling of the time
-required to compute a single trajectory.
+of the resulting densities overlapped within error and showed no
+significant trend toward lower or higher densities as a function of
+cutoff radius, for simulations both with and without reaction
+field. These results indicate that there is no major benefit in
+choosing a longer cutoff radius in simulations using SSD. This is
+advantageous in that the use of a longer cutoff radius results in
+significant increases in the time required to obtain a single
+trajectory.
 
+The key feature to recognize in figure \ref{dense1} is the density
+scaling of SSD relative to other common models at any given
+temperature. Note that the SSD model assumes a lower density than any
+of the other listed models at the same pressure, behavior which is
+especially apparent at temperatures greater than 300 K. Lower than
+expected densities have been observed for other systems using a
+reaction field for long-range electrostatic interactions, so the most
+likely reason for the significantly lower densities seen in these
+simulations is the presence of the reaction
+field.\cite{Berendsen98,Nezbeda02} In order to test the effect of the
+reaction field on the density of the systems, the simulations were
+repeated without a reaction field present. The results of these
+simulations are also displayed in figure \ref{dense1}. Without
+reaction field, the densities increase considerably to more
+experimentally reasonable values, especially around the freezing point
+of liquid water. The shape of the curve is similar to the curve
+produced from SSD simulations using reaction field, specifically the
+rapidly decreasing densities at higher temperatures; however, a shift
+in the density maximum location, down to 245 K, is observed. This is a
+more accurate comparison to the other listed water models, in that no
+long range corrections were applied in those
+simulations.\cite{Clancy94,Jorgensen98b} However, even without a
+reaction field, the density around 300 K is still significantly lower
+than experiment and comparable water models. This anomalous behavior
+was what lead Ichiye \emph{et al.} to recently reparameterize SSD and
+make SSD1.\cite{Ichiye03} In discussing potential adjustments later in
+this paper, all comparisons were performed with this new model.
+
 \subsection{Transport Behavior}
 Of importance in these types of studies are the transport properties
-of the particles and how they change when altering the environmental
-conditions. In order to probe transport, constant energy simulations
-were performed about the average density uncovered by the constant
-pressure simulations. Simulations started with randomized velocities
-and underwent 50 ps of temperature scaling and 50 ps of constant
-energy equilibration before obtaining a 200 ps trajectory. Diffusion
-constants were calculated via root-mean square deviation analysis. The
-averaged results from 5 sets of these NVE simulations is displayed in
-figure \ref{diffuse}, alongside experimental, SPC/E, and TIP5P
-results.\cite{Gillen72,Mills73,Clancy94,Jorgensen01} 
+of the particles and their change in responce to altering
+environmental conditions. In order to probe transport, constant energy
+simulations were performed about the average density uncovered by the
+constant pressure simulations. Simulations started with randomized
+velocities and underwent 50 ps of temperature scaling and 50 ps of
+constant energy equilibration before obtaining a 200 ps
+trajectory. Diffusion constants were calculated via root-mean square
+deviation analysis. 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}
 
 \begin{figure}
-\includegraphics[width=65mm, angle=-90]{betterDiffuse.epsi} 
+\begin{center}
+\epsfxsize=6in
+\epsfbox{betterDiffuse.epsi} 
 \caption{Average diffusion coefficient over increasing temperature for 
-SSD, SPC/E\cite{Clancy94}, TIP5P\cite{Jorgensen01}, and Experimental
-data from Gillen \emph{et al.}\cite{Gillen72}, and from
-Mills\cite{Mills73}.}
+SSD, SPC/E,\cite{Clancy94} TIP5P,\cite{Jorgensen01} and Experimental
+data.\cite{Gillen72,Mills73} 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 higher temperatures.}
 \label{diffuse}
+\end{center}
 \end{figure} 
 
 The observed values for the diffusion constant point out one of the
 strengths of the SSD model. Of the three experimental models shown,
 the SSD model has the most accurate depiction of the diffusion trend
-seen in experiment in both the supercooled and normal regimes. SPC/E
-does a respectable job by getting similar values as SSD and experiment
-around 290 K; however, it deviates at both higher and lower
-temperatures, failing to predict the experimental trend. TIP5P and SSD
-both start off low at the colder temperatures and tend to diffuse too
-rapidly at the higher temperatures. This type of trend at the higher
-temperatures is not surprising in that the densities of both TIP5P and
-SSD are lower than experimental water at temperatures higher than room
-temperature. When calculating the diffusion coefficients for SSD at
+seen in experiment in both the supercooled and liquid temperature
+regimes. SPC/E does a respectable job by producing values similar to
+SSD and experiment around 290 K; however, it deviates at both higher
+and lower temperatures, failing to predict the experimental
+trend. TIP5P and SSD both start off low at colder temperatures and
+tend to diffuse too rapidly at higher temperatures. This trend at
+higher temperatures is not surprising in that the densities of both
+TIP5P and SSD are lower than experimental water at these higher
+temperatures. When calculating the diffusion coefficients for SSD at
 experimental densities, the resulting values fall more in line with
-experiment at these temperatures, albeit not at standard
-pressure. Results under these conditions can be found later in this
-paper.
+experiment at these temperatures, albeit not at standard pressure.
 
 \subsection{Structural Changes and Characterization}
 By starting the simulations from the crystalline state, the melting
 transition and the ice structure can be studied along with the liquid
-phase behavior beyond the melting point. To locate the melting
-transition, the constant pressure heat capacity (C$_\text{p}$) was
-monitored in each of the simulations. In the melting simulations of
-the 1024 particle ice $I_h$ simulations, a large spike in C$_\text{p}$
-occurs at 245 K, indicating a first order phase transition for the
-melting of these ice crystals. When the reaction field is turned off,
-the melting transition occurs at 235 K.  These melting transitions are
-considerably lower than the experimental value, but this is not
-surprising in that SSD is a simple rigid body model with a fixed
-dipole.
+phase behavior beyond the melting point. The constant pressure heat
+capacity (C$_\text{p}$) was monitored to locate the melting transition
+in each of the simulations. In the melting simulations of the 1024
+particle ice $I_h$ simulations, a large spike in C$_\text{p}$ occurs
+at 245 K, indicating a first order phase transition for the melting of
+these ice crystals. When the reaction field is turned off, the melting
+transition occurs at 235 K.  These melting transitions are
+considerably lower than the experimental value, but this is not a
+surprise considering the simplicity of the SSD model.
 
-\begin{figure} 
-\includegraphics[width=85mm]{fullContours.eps} 
+\begin{figure}
+\begin{center}
+\epsfxsize=6in
+\epsfbox{corrDiag.eps} 
+\caption{Two dimensional illustration of angles involved in the 
+correlations observed in figure \ref{contour}.}
+\label{corrAngle}
+\end{center}
+\end{figure}
+
+\begin{figure}
+\begin{center} 
+\epsfxsize=6in
+\epsfbox{fullContours.eps} 
 \caption{Contour plots of 2D angular g($r$)'s for 512 SSD systems at 
 100 K (A \& B) and 300 K (C \& D). Contour colors are inverted for
 clarity: dark areas signify peaks while light areas signify
 depressions. White areas have g(\emph{r}) values below 0.5 and black
 areas have values above 1.5.}
 \label{contour} 
+\end{center}
 \end{figure} 
 
-Additional analyses for understanding the melting phase-transition
-process were performed via two-dimensional structure and dipole angle
-correlations. Expressions for the correlations are as follows:
+Additional analysis of the melting phase-transition process was
+performed by using two-dimensional structure and dipole angle
+correlations. Expressions for these correlations are as follows:
 
-\begin{figure}
-\includegraphics[width=45mm]{corrDiag.eps} 
-\caption{Two dimensional illustration of the angles involved in the 
-correlations observed in figure \ref{contour}.}
-\label{corrAngle}
-\end{figure}
-
-\begin{multline}
-g_{\text{AB}}(r,\cos\theta) = \\
-\frac{V}{N_\text{A}N_\text{B}}\langle\sum_{i\in\text{A}}\sum_{j\in\text{B}}\delta(\cos\theta-\cos\theta_{ij})\delta(r-\left|\mathbf{r}_{ij}\right|)\rangle\ ,
-\end{multline}
-\begin{multline}
-g_{\text{AB}}(r,\cos\omega) = \\
+\begin{equation}
+g_{\text{AB}}(r,\cos\theta) = \frac{V}{N_\text{A}N_\text{B}}\langle\sum_{i\in\text{A}}\sum_{j\in\text{B}}\delta(\cos\theta-\cos\theta_{ij})\delta(r-\left|\mathbf{r}_{ij}\right|)\rangle\ ,
+\end{equation}
+\begin{equation}
+g_{\text{AB}}(r,\cos\omega) = 
 \frac{V}{N_\text{A}N_\text{B}}\langle\sum_{i\in\text{A}}\sum_{j\in\text{B}}\delta(\cos\omega-\cos\omega_{ij})\delta(r-\left|\mathbf{r}_{ij}\right|)\rangle\ ,
-\end{multline}
-where $\theta$ and $\omega$ refer to the angles shown in the above
-illustration. By binning over both distance and the cosine of the
+\end{equation}
+where $\theta$ and $\omega$ refer to the angles shown in figure
+\ref{corrAngle}. By binning over both distance and the cosine of the
 desired angle between the two dipoles, the g(\emph{r}) can be
 dissected to determine the common dipole arrangements that constitute
 the peaks and troughs. Frames A and B of figure \ref{contour} show a
 relatively crystalline state of an ice $I_c$ simulation. The first
-peak of the g(\emph{r}) primarily consists of the preferred hydrogen
-bonding arrangements as dictated by the tetrahedral sticky potential,
+peak of the g(\emph{r}) consists primarily of the preferred hydrogen
+bonding arrangements as dictated by the tetrahedral sticky potential -
 one peak for the donating and the other for the accepting hydrogen
 bonds. Due to the high degree of crystallinity of the sample, the
 second and third solvation shells show a repeated peak arrangement
 which decays at distances around the fourth solvation shell, near the
 imposed cutoff for the Lennard-Jones and dipole-dipole interactions.
-In the higher temperature simulation shown in frames C and D, the
-repeated peak features are significantly blurred. The first solvation
-shell still shows the strong effect of the sticky-potential, although
-it covers a larger area, extending to include a fraction of aligned
-dipole peaks within the first solvation shell. The latter peaks lose
-definition as thermal motion and the competing dipole force overcomes
-the sticky potential's tight tetrahedral structuring of the fluid.
+In the higher temperature simulation shown in frames C and D, these
+longer-ranged repeated peak features deteriorate rapidly. The first
+solvation shell still shows the strong effect of the sticky-potential,
+although it covers a larger area, extending to include a fraction of
+aligned dipole peaks within the first solvation shell. The latter
+peaks lose definition as thermal motion and the competing dipole force
+overcomes the sticky potential's tight tetrahedral structuring of the
+fluid.
 
 This complex interplay between dipole and sticky interactions was
 remarked upon as a possible reason for the split second peak in the
 oxygen-oxygen g(\emph{r}).\cite{Ichiye96} At low temperatures, the
-second solvation shell peak appears to have two distinct parts that
-blend together to form one observable peak. At higher temperatures,
-this split character alters to show the leading 4 \AA\ peak dominated
-by equatorial anti-parallel dipole orientations, and there is tightly
-bunched group of axially arranged dipoles that most likely consist of
-the smaller fraction aligned dipole pairs. The trailing part of the
-split peak at 5 \AA\ is dominated by aligned dipoles that range
-primarily within the axial to the chief hydrogen bond arrangements
-similar to those seen in the first solvation shell. This evidence
-indicates that the dipole pair interaction begins to dominate outside
-of the range of the dipolar repulsion term, with the primary
-energetically favorable dipole arrangements populating the region
-immediately outside of it's range (around 4 \AA), and arrangements
-that seek to ideally satisfy both the sticky and dipole forces locate
-themselves just beyond this region (around 5 \AA).
+second solvation shell peak appears to have two distinct components
+that blend together to form one observable peak. At higher
+temperatures, this split character alters to show the leading 4 \AA\
+peak dominated by equatorial anti-parallel dipole orientations. There
+is also a tightly bunched group of axially arranged dipoles that most
+likely consist of the smaller fraction of aligned dipole pairs. The
+trailing component of the split peak at 5 \AA\ is dominated by aligned
+dipoles that assume hydrogen bond arrangements similar to those seen
+in the first solvation shell. This evidence indicates that the dipole
+pair interaction begins to dominate outside of the range of the
+dipolar repulsion term. Primary energetically favorable dipole
+arrangements populate the region immediately outside this repulsion
+region (around 4 \AA), while arrangements that seek to ideally satisfy
+both the sticky and dipole forces locate themselves just beyond this
+initial buildup (around 5 \AA).
 
 From these findings, the split second peak is primarily the product of
-the dipolar repulsion term of the sticky potential. In fact, the
-leading of the two peaks can be pushed out and merged with the outer
-split peak just by extending the switching function cutoff
-($s^\prime(r_{ij})$) from its normal 4.0 \AA\ to values of 4.5 or even
-5 \AA. This type of correction is not recommended for improving the
-liquid structure, because the second solvation shell will still be
-shifted too far out. In addition, this would have an even more
-detrimental effect on the system densities, leading to a liquid with a
-more open structure and a density considerably lower than the normal
-SSD behavior shown previously. A better correction would be to include
-the quadrupole-quadrupole interactions for the water particles outside
-of the first solvation shell, but this reduces the simplicity and
-speed advantage of SSD, so it is not the most desirable path to take.
+the dipolar repulsion term of the sticky potential. In fact, the inner
+peak can be pushed out and merged with the outer split peak just by
+extending the switching function cutoff ($s^\prime(r_{ij})$) from its
+normal 4.0 \AA\ to values of 4.5 or even 5 \AA. This type of
+correction is not recommended for improving the liquid structure,
+since the second solvation shell would still be shifted too far
+out. In addition, this would have an even more detrimental effect on
+the system densities, leading to a liquid with a more open structure
+and a density considerably lower than the normal SSD behavior shown
+previously. A better correction would be to include the
+quadrupole-quadrupole interactions for the water particles outside of
+the first solvation shell, but this reduces the simplicity and speed
+advantage of SSD.
 
-\subsection{Adjusted Potentials: SSD/E and SSD/RF}
+\subsection{Adjusted Potentials: SSD/RF and SSD/E}
 The propensity of SSD to adopt lower than expected densities under
 varying conditions is troubling, especially at higher temperatures. In
-order to correct this behavior, it's necessary to adjust the force
-field parameters for the primary intermolecular interactions. In
-undergoing a reparameterization, it is important not to focus on just
-one property and neglect the other important properties. In this case,
-it would be ideal to correct the densities while maintaining the
-accurate transport properties.
+order to correct this model for use with a reaction field, it is
+necessary to adjust the force field parameters for the primary
+intermolecular interactions. In undergoing a reparameterization, it is
+important not to focus on just one property and neglect the other
+important properties. In this case, it would be ideal to correct the
+densities while maintaining the accurate transport properties.
 
-The possible parameters for tuning include the $\sigma$ and $\epsilon$
+The parameters available for tuning include the $\sigma$ and $\epsilon$
 Lennard-Jones parameters, the dipole strength ($\mu$), and the sticky
 attractive and dipole repulsive terms with their respective
 cutoffs. To alter the attractive and repulsive terms of the sticky
 potential independently, it is necessary to separate the terms as
 follows:
 \begin{equation}
-\begin{split}
 u_{ij}^{sp}
-(\mathbf{r}_{ij},\boldsymbol{\Omega}_i,\boldsymbol{\Omega}_j) &=
-\frac{\nu_0}{2}[s(r_{ij})w(\mathbf{r}_{ij},\boldsymbol{\Omega}_i,\boldsymbol{\Omega}_j)]\\
-& \quad \ + \frac{\nu_0^\prime}{2}
-[s^\prime(r_{ij})w^\prime(\mathbf{r}_{ij},\boldsymbol{\Omega}_i,\boldsymbol{\Omega}_j)],
-\end{split}
+(\mathbf{r}_{ij},\boldsymbol{\Omega}_i,\boldsymbol{\Omega}_j) =
+\frac{\nu_0}{2}[s(r_{ij})w(\mathbf{r}_{ij},\boldsymbol{\Omega}_i,\boldsymbol{\Omega}_j)] + \frac{\nu_0^\prime}{2} [s^\prime(r_{ij})w^\prime(\mathbf{r}_{ij},\boldsymbol{\Omega}_i,\boldsymbol{\Omega}_j)],
 \end{equation}
 
 where $\nu_0$ scales the strength of the tetrahedral attraction and
 $\nu_0^\prime$ acts in an identical fashion on the dipole repulsion
-term. For purposes of the reparameterization, the separation was
-performed, but the final parameters were adjusted so that it is
-unnecessary to separate the terms when implementing the adjusted water
-potentials. The results of the reparameterizations are shown in table
-\ref{params}. Note that both the tetrahedral attractive and dipolar 
-repulsive don't share the same lower cutoff ($r_l$) in the newly
-parameterized potentials - soft sticky dipole enhanced (SSD/E) and
-soft sticky dipole reaction field (SSD/RF).
+term. The separation was performed for purposes of the
+reparameterization, but the final parameters were adjusted so that it
+is unnecessary to separate the terms when implementing the adjusted
+water potentials. The results of the reparameterizations are shown in
+table \ref{params}. Note that the tetrahedral attractive and dipolar
+repulsive terms do not share the same lower cutoff ($r_l$) in the
+newly parameterized potentials - soft sticky dipole reaction field
+(SSD/RF - for use with a reaction field) and soft sticky dipole
+enhanced (SSD/E - an attempt to improve the liquid structure in
+simulations without a long-range correction).
 
 \begin{table}
+\begin{center}
 \caption{Parameters for the original and adjusted models}
-\begin{tabular}{ l  c  c  c } 
+\begin{tabular}{ l  c  c  c  c } 
 \hline \\[-3mm]
-\ Parameters & \ \ \  SSD$^\dagger$\ \ \ \  & \ SSD/E\ \  & \ SSD/RF\ \ \\
+\ \ \ Parameters\ \ \  & \ \ \ SSD\cite{Ichiye96} \ \ \ & \ SSD1\cite{Ichiye03}\ \  & \ SSD/E\ \  & \ SSD/RF \\
 \hline \\[-3mm]
-\ \ \ $\sigma$ (\AA)  & 3.051 & 3.035 & 3.019\\
-\ \ \ $\epsilon$ (kcal/mol)\ \ & 0.152 & 0.152 & 0.152\\
-\ \ \ $\mu$ (D) & 2.35 & 2.418 & 2.480\\
-\ \ \ $\nu_0$ (kcal/mol)\ \ & 3.7284 & 3.90 & 3.90\\
-\ \ \ $r_l$ (\AA) & 2.75 & 2.40 & 2.40\\
-\ \ \ $r_u$ (\AA) & 3.35 & 3.80 & 3.80\\
-\ \ \ $\nu_0^\prime$ (kcal/mol)\ \ & 3.7284 & 3.90 & 3.90\\
-\ \ \ $r_l^\prime$ (\AA) & 2.75 & 2.75 & 2.75\\
-\ \ \ $r_u^\prime$ (\AA) & 4.00 & 3.35 & 3.35\\
-\\[-2mm]$^\dagger$ ref. \onlinecite{Ichiye96}
+\ \ \ $\sigma$ (\AA)  & 3.051 & 3.016 & 3.035 & 3.019\\
+\ \ \ $\epsilon$ (kcal/mol) & 0.152 & 0.152 & 0.152 & 0.152\\
+\ \ \ $\mu$ (D) & 2.35 & 2.35 & 2.42 & 2.48\\
+\ \ \ $\nu_0$ (kcal/mol) & 3.7284 & 3.6613 & 3.90 & 3.90\\
+\ \ \ $r_l$ (\AA) & 2.75 & 2.75 & 2.40 & 2.40\\
+\ \ \ $r_u$ (\AA) & 3.35 & 3.35 & 3.80 & 3.80\\
+\ \ \ $\nu_0^\prime$ (kcal/mol) & 3.7284 & 3.6613 & 3.90 & 3.90\\
+\ \ \ $r_l^\prime$ (\AA) & 2.75 & 2.75 & 2.75 & 2.75\\
+\ \ \ $r_u^\prime$ (\AA) & 4.00 & 4.00 & 3.35 & 3.35\\
 \end{tabular}
 \label{params}
+\end{center}
 \end{table}
 
-\begin{figure} 
-\includegraphics[width=85mm]{gofrCompare.epsi} 
+\begin{figure}
+\begin{center} 
+\epsfxsize=5in
+\epsfbox{GofRCompare.epsi} 
 \caption{Plots comparing experiment\cite{Head-Gordon00_1} with SSD/E 
-and SSD without reaction field (top), as well as SSD/RF and SSD with
+and SSD1 without reaction field (top), as well as SSD/RF and SSD1 with
 reaction field turned on (bottom). The insets show the respective
-first peaks in detail. Solid Line - experiment, dashed line - SSD/E
-and SSD/RF, and dotted line - SSD (with and without reaction field).}
+first peaks in detail. Note how the changes in parameters have lowered
+and broadened the first peak of SSD/E and SSD/RF.}
 \label{grcompare} 
+\end{center}
 \end{figure} 
 
-\begin{figure} 
-\includegraphics[width=85mm]{dualsticky.ps} 
-\caption{Isosurfaces of the sticky potential for SSD (left) and SSD/E \& 
+\begin{figure}
+\begin{center} 
+\epsfxsize=6in
+\epsfbox{dualsticky.ps} 
+\caption{Isosurfaces of the sticky potential for SSD1 (left) and SSD/E \& 
 SSD/RF (right). Light areas correspond to the tetrahedral attractive
-part, and the darker areas correspond to the dipolar repulsive part.}
+component, and darker areas correspond to the dipolar repulsive
+component.}
 \label{isosurface} 
+\end{center}
 \end{figure} 
 
 In the paper detailing the development of SSD, Liu and Ichiye placed
 particular emphasis on an accurate description of the first solvation
-shell. This resulted in a somewhat tall and sharp first peak that
-integrated to give similar coordination numbers to the experimental
-data obtained by Soper and Phillips.\cite{Ichiye96,Soper86} New
-experimental x-ray scattering data from the Head-Gordon lab indicates
-a slightly lower and shifted first peak in the g$_\mathrm{OO}(r)$, so
-adjustments to SSD were made while taking into consideration the new
-experimental findings.\cite{Head-Gordon00_1} Figure \ref{grcompare}
-shows the relocation of the first peak of the oxygen-oxygen
-g(\emph{r}) by comparing the original SSD (with and without reaction
-field), SSD-E, and SSD-RF to the new experimental results. Both the
-modified water models have shorter peaks that are brought in more
-closely to the experimental peak (as seen in the insets of figure
-\ref{grcompare}). This structural alteration was accomplished by a
-reduction in the Lennard-Jones $\sigma$ variable as well as adjustment
-of the sticky potential strength and cutoffs. The cutoffs for the
+shell. This resulted in a somewhat tall and narrow first peak in the
+g(\emph{r}) that integrated to give similar coordination numbers to
+the experimental data obtained by Soper and
+Phillips.\cite{Ichiye96,Soper86} New experimental x-ray scattering
+data from the Head-Gordon lab indicates a slightly lower and shifted
+first peak in the g$_\mathrm{OO}(r)$, so adjustments to SSD were made
+while taking into consideration the new experimental
+findings.\cite{Head-Gordon00_1} Figure \ref{grcompare} shows the
+relocation of the first peak of the oxygen-oxygen g(\emph{r}) by
+comparing the revised SSD model (SSD1), SSD-E, and SSD-RF to the new
+experimental results. Both modified water models have shorter peaks
+that are brought in more closely to the experimental peak (as seen in
+the insets of figure \ref{grcompare}).  This structural alteration was
+accomplished by the combined reduction in the Lennard-Jones $\sigma$
+variable and adjustment of the sticky potential strength and
+cutoffs. As can be seen in table \ref{params}, the cutoffs for the
 tetrahedral attractive and dipolar repulsive terms were nearly swapped
 with each other. Isosurfaces of the original and modified sticky
-potentials are shown in figure \cite{isosurface}. In these
-isosurfaces, it is easy to see how altering the cutoffs changes the
-repulsive and attractive character of the particles. With a reduced
-repulsive surface (the darker region), the particles can move closer
-to one another, increasing the density for the overall system. This
-change in interaction cutoff also results in a more gradual
-orientational motion by allowing the particles to maintain preferred
-dipolar arrangements before they begin to feel the pull of the
-tetrahedral restructuring. Upon moving closer together, the dipolar
-repulsion term becomes active and excludes the unphysical
-arrangements. This compares with the original SSD's excluding dipolar
-before the particles feel the pull of the ``hydrogen bonds''. Aside
-from improving the shape of the first peak in the g(\emph{r}), this
-improves the densities considerably by allowing the persistence of
-full dipolar character below the previous 4.0 \AA\ cutoff.
+potentials are shown in figure \ref{isosurface}. In these isosurfaces,
+it is easy to see how altering the cutoffs changes the repulsive and
+attractive character of the particles. With a reduced repulsive
+surface (darker region), the particles can move closer to one another,
+increasing the density for the overall system. This change in
+interaction cutoff also results in a more gradual orientational motion
+by allowing the particles to maintain preferred dipolar arrangements
+before they begin to feel the pull of the tetrahedral
+restructuring. As the particles move closer together, the dipolar
+repulsion term becomes active and excludes unphysical nearest-neighbor
+arrangements. This compares with how SSD and SSD1 exclude preferred
+dipole alignments before the particles feel the pull of the ``hydrogen
+bonds''. Aside from improving the shape of the first peak in the
+g(\emph{r}), this modification improves the densities considerably by
+allowing the persistence of full dipolar character below the previous
+4.0 \AA\ cutoff.
 
 While adjusting the location and shape of the first peak of
-g(\emph{r}) improves the densities to some degree, these changes alone
-are insufficient to bring the system densities up to the values
-observed experimentally. To finish bringing up the densities, the
-dipole moments were increased in both the adjusted models. Being a
-dipole based model, the structure and transport are very sensitive to
-changes in the dipole moment. The original SSD simply used the dipole
-moment calculated from the TIP3P water model, which at 2.35 D is
+g(\emph{r}) improves the densities, these changes alone are
+insufficient to bring the system densities up to the values observed
+experimentally. To further increase the densities, the dipole moments
+were increased in both of the adjusted models. Since SSD is a dipole
+based model, the structure and transport are very sensitive to changes
+in the dipole moment. The original SSD simply used the dipole moment
+calculated from the TIP3P water model, which at 2.35 D is
 significantly greater than the experimental gas phase value of 1.84
-D. The larger dipole moment is a more realistic value and improve the
+D. The larger dipole moment is a more realistic value and improves the
 dielectric properties of the fluid. Both theoretical and experimental
 measurements indicate a liquid phase dipole moment ranging from 2.4 D
-to values as high as 3.11 D, so there is quite a range available for
-adjusting the dipole
-moment.\cite{Sprik91,Kusalik02,Badyal00,Barriol64} The increasing of
-the dipole moments to 2.418 and 2.48 D for SSD/E and SSD/RF
-respectively is moderate in the range of the experimental values;
-however, it leads to significant changes in the density and transport
-of the water models.
+to values as high as 3.11 D, providing a substantial range of
+reasonable values for a dipole
+moment.\cite{Sprik91,Kusalik02,Badyal00,Barriol64} Moderately
+increasing the dipole moments to 2.42 and 2.48 D for SSD/E and SSD/RF,
+respectively, leads to significant changes in the density and
+transport of the water models.
 
-In order to demonstrate the benefits of this reparameterization, a
+In order to demonstrate the benefits of these reparameterizations, a
 series of NPT and NVE simulations were performed to probe the density
 and transport properties of the adapted models and compare the results
 to the original SSD model. This comparison involved full NPT melting
 sequences for both SSD/E and SSD/RF, as well as NVE transport
-calculations at both self-consistent and experimental
-densities. Again, the results come from five separate simulations of
-1024 particle systems, and the melting sequences were started from
-different ice $I_h$ crystals constructed as stated previously. Like
-before, all of the NPT simulations were equilibrated for 100 ps before
-a 200 ps data collection run, and they used the previous temperature's
-final configuration as a starting point. All of the NVE simulations
-had the same thermalization, equilibration, and data collection times
-stated earlier in this paper.
+calculations at the calculated self-consistent densities. Again, the
+results are obtained from five separate simulations of 1024 particle
+systems, and the melting sequences were started from different ice
+$I_h$ crystals constructed as described previously. Each NPT
+simulation was equilibrated for 100 ps before a 200 ps data collection
+run at each temperature step, and the final configuration from the
+previous temperature simulation was used as a starting point. All NVE
+simulations had the same thermalization, equilibration, and data
+collection times as stated earlier in this paper.
 
-\begin{figure} 
-\includegraphics[width=85mm]{ssdecompare.epsi} 
-\caption{Comparison of densities calculated with SSD/E to SSD without a 
-reaction field, TIP4P\cite{Jorgensen98b}, TIP3P\cite{Jorgensen98b},
-SPC/E\cite{Clancy94}, and Experiment\cite{CRC80}. The upper plot
-includes error bars, and the calculated results from the other
-references were removed for clarity.}
+\begin{figure}
+\begin{center} 
+\epsfxsize=6in
+\epsfbox{ssdeDense.epsi} 
+\caption{Comparison of densities calculated with SSD/E to SSD1 without a 
+reaction field, TIP3P,\cite{Jorgensen98b} TIP5P,\cite{Jorgensen00}
+SPC/E,\cite{Clancy94} and experiment.\cite{CRC80} The window shows a
+expansion around 300 K with error bars included to clarify this region
+of interest. Note that both SSD1 and SSD/E show good agreement with
+experiment when the long-range correction is neglected.}
 \label{ssdedense} 
+\end{center}
 \end{figure} 
 
-Figure \ref{ssdedense} shows the density profile for the SSD/E water
-model in comparison to the original SSD without a reaction field,
-experiment, and the other common water models considered
-previously. The calculated densities have increased significantly over
-the original SSD model and match the experimental value just below 298
-K. At 298 K, the density of SSD/E is 0.995$\pm$0.001 g/cm$^3$, which
-compares well with the experimental value of 0.997 g/cm$^3$ and is
-considerably better than the SSD value of 0.967$\pm$0.003
-g/cm$^3$. The increased dipole moment in SSD/E has helped to flatten
-out the curve at higher temperatures, only the improvement is marginal
-at best. This steep drop in densities is due to the dipolar rather
-than charge based interactions which decay more rapidly at longer
-distances.
- 
-By monitoring C$\text{p}$ throughout these simulations, the melting
-transition for SSD/E was observed at 230 K, about 5 degrees lower than
-SSD. The resulting density maximum is located at 240 K, again about 5
-degrees lower than the SSD value of 245 K. Though there is a decrease
-in both of these values, the corrected densities near room temperature
-justify the modifications taken.
+Figure \ref{ssdedense} shows the density profile for the SSD/E model
+in comparison to SSD1 without a reaction field, other common water
+models, and experimental results. The calculated densities for both
+SSD/E and SSD1 have increased significantly over the original SSD
+model (see figure \ref{dense1}) and are in better agreement with the
+experimental values. At 298 K, the densities of SSD/E and SSD1 without
+a long-range correction are 0.996$\pm$0.001 g/cm$^3$ and
+0.999$\pm$0.001 g/cm$^3$ respectively.  These both compare well with
+the experimental value of 0.997 g/cm$^3$, and they are considerably
+better than the SSD value of 0.967$\pm$0.003 g/cm$^3$. The changes to
+the dipole moment and sticky switching functions have improved the
+structuring of the liquid (as seen in figure \ref{grcompare}, but they
+have shifted the density maximum to much lower temperatures. This
+comes about via an increase in the liquid disorder through the
+weakening of the sticky potential and strengthening of the dipolar
+character. However, this increasing disorder in the SSD/E model has
+little effect on the melting transition. By monitoring C$\text{p}$
+throughout these simulations, the melting transition for SSD/E was
+shown to occur at 235 K, the same transition temperature observed with
+SSD and SSD1.
 
-\begin{figure} 
-\includegraphics[width=85mm]{ssdrfcompare.epsi} 
-\caption{Comparison of densities calculated with SSD/RF to SSD with a 
-reaction field, TIP4P\cite{Jorgensen98b}, TIP3P\cite{Jorgensen98b},
-SPC/E\cite{Clancy94}, and Experiment\cite{CRC80}. The upper plot
-includes error bars, and the calculated results from the other
-references were removed for clarity.}
+\begin{figure}
+\begin{center} 
+\epsfxsize=6in
+\epsfbox{ssdrfDense.epsi} 
+\caption{Comparison of densities calculated with SSD/RF to SSD1 with a 
+reaction field, TIP3P,\cite{Jorgensen98b} TIP5P,\cite{Jorgensen00}
+SPC/E,\cite{Clancy94} and experiment.\cite{CRC80} The inset shows the
+necessity of reparameterization when utilizing a reaction field
+long-ranged correction - SSD/RF provides significantly more accurate
+densities than SSD1 when performing room temperature simulations.}
 \label{ssdrfdense} 
+\end{center}
 \end{figure} 
 
-Figure \ref{ssdrfdense} shows a density comparison between SSD/RF and
-SSD with an active reaction field. Like in the simulations of SSD/E,
-the densities show a dramatic increase over normal SSD. At 298 K,
-SSD/RF has a density of 0.997$\pm$0.001 g/cm$^3$, right in line with
-experiment and considerably better than the SSD value of
-0.941$\pm$0.001 g/cm$^3$. The melting point is observed at 240 K,
-which is 5 degrees lower than SSD with a reaction field, and the
-density maximum at 255 K, again 5 degrees lower than SSD. The density
-at higher temperature still drops off more rapidly than the charge
-based models but is in better agreement than SSD/E.
+Including the reaction field long-range correction in the simulations
+results in a more interesting comparison. A density profile including
+SSD/RF and SSD1 with an active reaction field is shown in figure
+\ref{ssdrfdense}.  As observed in the simulations without a reaction
+field, the densities of SSD/RF and SSD1 show a dramatic increase over
+normal SSD (see figure \ref{dense1}). At 298 K, SSD/RF has a density
+of 0.997$\pm$0.001 g/cm$^3$, directly in line with experiment and
+considerably better than the SSD value of 0.941$\pm$0.001 g/cm$^3$ and
+the SSD1 value of 0.972$\pm$0.002 g/cm$^3$. These results further
+emphasize the importance of reparameterization in order to model the
+density properly under different simulation conditions. Again, these
+changes have only a minor effect on the melting point, which observed
+at 245 K for SSD/RF, is identical to SSD and only 5 K lower than SSD1
+with a reaction field. Additionally, the difference in density maxima
+is not as extreme, with SSD/RF showing a density maximum at 255 K,
+fairly close to the density maxima of 260 K and 265 K, shown by SSD
+and SSD1 respectively.
 
+\begin{figure}
+\begin{center} 
+\epsfxsize=6in
+\epsfbox{ssdeDiffuse.epsi} 
+\caption{Plots of the diffusion constants calculated from SSD/E and SSD1,
+ both without a reaction field, along with experimental
+ results.\cite{Gillen72,Mills73} The NVE calculations were performed
+ at the average densities observed in the 1 atm NPT simulations for
+ the respective models. SSD/E is slightly more fluid than experiment
+ at all of the temperatures, but it is closer than SSD1 without a
+ long-range correction.}
+\label{ssdediffuse} 
+\end{center}
+\end{figure} 
+
 The reparameterization of the SSD water model, both for use with and
 without an applied long-range correction, brought the densities up to
 what is expected for simulating liquid water. In addition to improving
 the densities, it is important that particle transport be maintained
 or improved. Figure \ref{ssdediffuse} compares the temperature
-dependence of the diffusion constant of SSD/E to SSD without an active
-reaction field, both at the densities calculated at 1 atm and at the
-experimentally calculated densities for super-cooled and liquid
-water. In the upper plot, the diffusion constant for SSD/E is
-consistently a little faster than experiment, while SSD starts off
-slower than experiment and crosses to merge with SSD/E at high
-temperatures. Both models follow the experimental trend well, but
-diffuse too rapidly at higher temperatures. This abnormally fast
-diffusion is caused by the decreased system density. Since the
-densities of SSD/E don't deviate as much from experiment as those of
-SSD, it follows the experimental trend more closely. This observation
-is backed up by looking at the lower plot. The diffusion constants for
-SSD/E track with the experimental values while SSD deviates on the low
-side of the trend with increasing temperature. This is again a product
-of SSD/E having densities closer to experiment, and not deviating to
-lower densities with increasing temperature as rapidly.
+dependence of the diffusion constant of SSD/E to SSD1 without an
+active reaction field, both at the densities calculated at 1 atm and
+at the experimentally calculated densities for super-cooled and liquid
+water. The diffusion constant for SSD/E is consistently a little
+higher than experiment, while SSD1 remains lower than experiment until
+relatively high temperatures (greater than 330 K). Both models follow
+the shape of the experimental curve well below 300 K but tend to
+diffuse too rapidly at higher temperatures, something that is
+especially apparent with SSD1. This accelerated increasing of
+diffusion is caused by the rapidly decreasing system density with
+increasing temperature. Though it is difficult to see in figure
+\ref{ssdedense}, the densities of SSD1 decay more rapidly with
+temperature than do those of SSD/E, leading to more visible deviation
+from the experimental diffusion trend. Thus, the changes made to
+improve the liquid structure may have had an adverse affect on the
+density maximum, but they improve the transport behavior of SSD/E
+relative to SSD1.
 
-\begin{figure} 
-\includegraphics[width=85mm]{ssdediffuse.epsi} 
-\caption{Plots of the diffusion constants calculated from SSD/E and SSD,
- both without a reaction field along with experimental results from
- Gillen \emph{et al.}\cite{Gillen72} and Mills\cite{Mills73}. The
- upper plot is at densities calculated from the NPT simulations at a
- pressure of 1 atm, while the lower plot is at the experimentally
- calculated densities.}
-\label{ssdediffuse} 
-\end{figure} 
-
-\begin{figure} 
-\includegraphics[width=85mm]{ssdrfdiffuse.epsi} 
-\caption{Plots of the diffusion constants calculated from SSD/RF and SSD,
- both with an active reaction field along with experimental results
- from Gillen \emph{et al.}\cite{Gillen72} and Mills\cite{Mills73}. The
- upper plot is at densities calculated from the NPT simulations at a
- pressure of 1 atm, while the lower plot is at the experimentally
- calculated densities.}
+\begin{figure}
+\begin{center} 
+\epsfxsize=6in
+\epsfbox{ssdrfDiffuse.epsi} 
+\caption{Plots of the diffusion constants calculated from SSD/RF and SSD1,
+ both with an active reaction field, along with experimental
+ results.\cite{Gillen72,Mills73} The NVE calculations were performed
+ at the average densities observed in the 1 atm NPT simulations for
+ both of the models. Note how accurately SSD/RF simulates the
+ diffusion of water throughout this temperature range. The more
+ rapidly increasing diffusion constants at high temperatures for both
+ models is attributed to the significantly lower densities than
+ observed in experiment.}
 \label{ssdrfdiffuse} 
+\end{center}
 \end{figure} 
 
 In figure \ref{ssdrfdiffuse}, the diffusion constants for SSD/RF are
-compared with SSD with an active reaction field. In the upper plot,
-SSD/RF tracks with the experimental results incredibly well, identical
-within error throughout the temperature range and only showing a
-slight increasing trend at higher temperatures. SSD also tracks
-experiment well, only it tends to diffuse a little more slowly at low
-temperatures and deviates to diffuse too rapidly at high
-temperatures. As was stated in the SSD/E comparisons, this deviation
-away from the ideal trend is due to a rapid decrease in density at
-higher temperatures. SSD/RF doesn't suffer from this problem as much
-as SSD, because the calculated densities are more true to
-experiment. This is again emphasized in the lower plot, where SSD/RF
-tracks the experimental diffusion exactly while SSD's diffusion
-constants are slightly too low due to its need for a lower density at
-the specified temperature.
+compared to SSD1 with an active reaction field. Note that SSD/RF
+tracks the experimental results incredibly well, identical within
+error throughout the temperature range shown and with only a slight
+increasing trend at higher temperatures. SSD1 tends to diffuse more
+slowly at low temperatures and deviates to diffuse too rapidly at
+temperatures greater than 330 K. As stated in relation to SSD/E, this
+deviation away from the ideal trend is due to a rapid decrease in
+density at higher temperatures. SSD/RF does not suffer from this
+problem as much as SSD1, because the calculated densities are closer
+to the experimental value. These results again emphasize the
+importance of careful reparameterization when using an altered
+long-range correction.
 
 \subsection{Additional Observations}
 
-While performing the melting sequences of SSD/E, some interesting
-observations were made. After melting at 230 K, two of the systems
-underwent crystallization events near 245 K. As the heating process
-continued, the two systems remained crystalline until finally melting
-between 320 and 330 K. These simulations were excluded from the data
-set shown in figure \ref{ssdedense} and replaced with two additional
-melting sequences that did not undergo this anomalous phase
-transition, while this crystallization event was investigated
-separately.
-
 \begin{figure}
-\includegraphics[width=85mm]{povIce.ps} 
-\caption{Crystal structure of an ice 0 lattice shown from the (001) face.}
+\begin{center}
+\epsfxsize=6in
+\epsfbox{povIce.ps} 
+\caption{A water lattice built from the crystal structure assumed by 
+ SSD/E when undergoing an extremely restricted temperature NPT
+ simulation. This form of ice is referred to as ice \emph{i} to
+ emphasize its simulation origins. This image was taken of the (001)
+ face of the crystal.}
 \label{weirdice} 
+\end{center}
 \end{figure}
 
-The final configurations of these two melting sequences shows an
-expanded zeolite-like crystal structure that does not correspond to
-any known form of ice. For convenience and to help distinguish it from
-the experimentally observed forms of ice, this crystal structure will
-henceforth be referred to as ice-zero (ice 0). The crystallinity was
-extensive enough than a near ideal crystal structure could be
-obtained. Figure \ref{weirdice} shows the repeating crystal structure
-of a typical crystal at 5 K. The unit cell contains eight molecules,
-and figure \ref{unitcell} shows a unit cell built from the water
-particle center of masses that can be used to construct a repeating
-lattice, similar to figure \ref{weirdice}. Each molecule is hydrogen
-bonded to four other water molecules; however, the hydrogen bonds are
-flexed rather than perfectly straight. This results in a skewed
-tetrahedral geometry about the central molecule. Looking back at
-figure \ref{isosurface}, it is easy to see how these flexed hydrogen
-bonds are allowed in that the attractive regions are conical in shape,
-with the greatest attraction in the central region. Though not ideal,
-these flexed hydrogen bonds are favorable enough to stabilize an
-entire crystal generated around them. In fact, the imperfect ice 0
-crystals were so stable that they melted at greater than room
-temperature.
+While performing restricted temperature melting sequences of SSD/E not
+previously discussed, some interesting observations were made. After
+melting at 235 K, two of five systems underwent crystallization events
+near 245 K. As the heating process continued, the two systems remained
+crystalline until finally melting between 320 and 330 K. The final
+configurations of these two melting sequences show an expanded
+zeolite-like crystal structure that does not correspond to any known
+form of ice. For convenience, and to help distinguish it from the
+experimentally observed forms of ice, this crystal structure will
+henceforth be referred to as ice $\sqrt{\smash[b]{-\text{I}}}$ (ice
+\emph{i}). The crystallinity was extensive enough that a near ideal
+crystal structure of ice \emph{i} could be obtained. Figure
+\ref{weirdice} shows the repeating crystal structure of a typical
+crystal at 5 K. Each water molecule is hydrogen bonded to four others;
+however, the hydrogen bonds are flexed rather than perfectly
+straight. This results in a skewed tetrahedral geometry about the
+central molecule. Referring to figure \ref{isosurface}, these flexed
+hydrogen bonds are allowed due to the conical shape of the attractive
+regions, with the greatest attraction along the direct hydrogen bond
+configuration. Though not ideal, these flexed hydrogen bonds are
+favorable enough to stabilize an entire crystal generated around
+them. In fact, the imperfect ice \emph{i} crystals were so stable that
+they melted at temperatures nearly 100 K greater than both ice I$_c$
+and I$_h$.
 
-\begin{figure}
-\includegraphics[width=65mm]{ice0cell.eps} 
-\caption{Simple unit cell for constructing ice 0. In this cell, $c$ is 
-equal to $0.4714\times a$, and a typical value for $a$ is 8.25 \AA.}
-\label{unitcell} 
-\end{figure}
+These initial simulations indicated that ice \emph{i} is the preferred
+ice structure for at least the SSD/E model. To verify this, a
+comparison was made between near ideal crystals of ice $I_h$, ice
+$I_c$, and ice 0 at constant pressure with SSD/E, SSD/RF, and
+SSD1. Near ideal versions of the three types of crystals were cooled
+to 1 K, and the potential energies of each were compared using all
+three water models. With every water model, ice \emph{i} turned out to
+have the lowest potential energy: 5\% lower than $I_h$ with SSD1,
+6.5\% lower with SSD/E, and 7.5\% lower with SSD/RF.
 
-The initial simulations indicated that ice 0 is the preferred ice
-structure for at least SSD/E. To verify this, a comparison was made
-between near ideal crystals of ice $I_h$, ice $I_c$, and ice 0 at
-constant pressure with SSD/E, SSD/RF, and SSD. Near ideal versions of
-the three types of crystals were cooled to ~1 K, and the potential
-energies of each were compared using all three water models. With
-every water model, ice 0 turned out to have the lowest potential
-energy: 5\% lower than $I_h$ with SSD, 6.5\% lower with SSD/E, and
-7.5\% lower with SSD/RF. In all three of these water models, ice $I_c$
-was observed to be ~2\% less stable than ice $I_h$. In addition to
-having the lowest potential energy, ice 0 was the most expanded of the
-three ice crystals, ~5\% less dense than ice $I_h$ with all of the
-water models. In all three water models, ice $I_c$ was observed to be
-~2\% more dense than ice $I_h$. 
+In addition to these low temperature comparisons, melting sequences
+were performed with ice \emph{i} as the initial configuration using
+SSD/E, SSD/RF, and SSD1 both with and without a reaction field. The
+melting transitions for both SSD/E and SSD1 without a reaction field
+occurred at temperature in excess of 375 K. SSD/RF and SSD1 with a
+reaction field showed more reasonable melting transitions near 325
+K. These melting point observations emphasize the preference for this
+crystal structure over the most common types of ice when using these
+single point water models.
 
-In addition to the low temperature comparisons, melting sequences were
-performed with ice 0 as the initial configuration using SSD/E, SSD/RF,
-and SSD both with and without a reaction field. The melting
-transitions for both SSD/E and SSD without a reaction field occurred
-at temperature in excess of 375 K. SSD/RF and SSD with a reaction
-field had more reasonable melting transitions, down near 325 K. These
-melting point observations emphasize how preferred this crystal
-structure is over the most common types of ice when using these single
-point water models.
-
-Recognizing that the above tests show ice 0 to be both the most stable
-and lowest density crystal structure for these single point water
-models, it is interesting to speculate on the favorability of this
-crystal structure with the different charge based models. As a quick
+Recognizing that the above tests show ice \emph{i} to be both the most
+stable and lowest density crystal structure for these single point
+water models, it is interesting to speculate on the relative stability
+of this crystal structure with charge based water models. As a quick
 test, these 3 crystal types were converted from SSD type particles to
 TIP3P waters and read into CHARMM.\cite{Karplus83} Identical energy
-minimizations were performed on all of these crystals to compare the
-system energies. Again, ice 0 was observed to have the lowest total
-system energy. The total energy of ice 0 was ~2\% lower than ice
-$I_h$, which was in turn ~3\% lower than ice $I_c$. From these initial
-results, we would not be surprised if results from the other common
-water models show ice 0 to be the lowest energy crystal structure. A
-continuation on work studing ice 0 with multipoint water models will
-be published in a coming article.
+minimizations were performed on the crystals to compare the system
+energies. Again, ice \emph{i} was observed to have the lowest total
+system energy. The total energy of ice \emph{i} was ~2\% lower than
+ice $I_h$, which was in turn ~3\% lower than ice $I_c$. Based on these
+initial studies, it would not be surprising if results from the other
+common water models show ice \emph{i} to be the lowest energy crystal
+structure. A continuation of this work studying ice \emph{i} with
+multi-point water models will be published in a coming article.
 
 \section{Conclusions}
 The density maximum and temperature dependent transport for the SSD
@@ -879,26 +914,29 @@ capture the transport properties of experimental very 
 density maximum near 260 K. In most cases, the calculated densities
 were significantly lower than the densities calculated in simulations
 of other water models. Analysis of particle diffusion showed SSD to
-capture the transport properties of experimental very well in both the
-normal and super-cooled liquid regimes. In order to correct the
-density behavior, SSD was reparameterized for use both with and
-without a long-range interaction correction, SSD/RF and SSD/E
-respectively. In addition to correcting the abnormally low densities,
-these new versions were show to maintain or improve upon the transport
-and structural features of the original water model, all while
-maintaining the fast performance of the SSD water model. This work
-shows these simple water models, and in particular SSD/E and SSD/RF,
-to be excellent choices to represent explicit water in future
-simulations of biochemical systems.
+capture the transport properties of experimental water well in both
+the liquid and super-cooled liquid regimes. In order to correct the
+density behavior, the original SSD model was reparameterized for use
+both with and without a reaction field (SSD/RF and SSD/E), and
+comparison simulations were performed with SSD1, the density corrected
+version of SSD. Both models improve the liquid structure, density
+values, and diffusive properties under their respective conditions,
+indicating the necessity of reparameterization when altering the
+long-range correction specifics. When taking into account the
+appropriate considerations, these simple water models are excellent
+choices for representing explicit water in large scale simulations of
+biochemical systems.
 
 \section{Acknowledgments}
-The authors would like to thank the National Science Foundation for
-funding under grant CHE-0134881. Computation time was provided by the
-Notre Dame Bunch-of-Boxes (B.o.B) computer cluster under NSF grant DMR
-00 79647.
+Support for this project was provided by the National Science
+Foundation under grant CHE-0134881. Computation time was provided by
+the Notre Dame Bunch-of-Boxes (B.o.B) computer cluster under NSF grant
+DMR 00 79647.
 
-\bibliographystyle{jcp}
 
+\newpage
+
+\bibliographystyle{jcp}
 \bibliography{nptSSD} 
 
 %\pagebreak