--- trunk/ssdePaper/nptSSD.tex	2004/02/05 18:42:59	1027
+++ trunk/ssdePaper/nptSSD.tex	2004/02/05 20:47:50	1029
@@ -22,7 +22,7 @@ dipole (SSD) and related single point water models}
 \begin{document}
 
 \title{On the structural and transport properties of the soft sticky
-dipole (SSD) and related single point water models}
+dipole ({\sc ssd}) and related single point water models}
 
 \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\\
@@ -34,7 +34,7 @@ constant were investigated for the soft sticky dipole 
 
 \begin{abstract}
 The density maximum and temperature dependence of the self-diffusion
-constant were investigated for the soft sticky dipole (SSD) water
+constant were investigated for the soft sticky dipole ({\sc ssd}) water
 model and two related re-parameterizations of this single-point model.
 A combination of microcanonical and isobaric-isothermal molecular
 dynamics simulations were used to calculate these properties, both
@@ -44,17 +44,17 @@ that the original SSD model captures the transport pro
 260 K.  In most cases, the use of the reaction field resulted in
 calculated densities which were were significantly lower than
 experimental densities.  Analysis of self-diffusion constants shows
-that the original SSD model captures the transport properties of
+that the original {\sc ssd} model captures the transport properties of
 experimental water very well in both the normal and super-cooled
-liquid regimes.  We also present our re-parameterized versions of SSD
+liquid regimes.  We also present our re-parameterized versions of {\sc ssd}
 for use both with the reaction field or without any long-range
-electrostatic corrections.  These are called the SSD/RF and SSD/E
+electrostatic corrections.  These are called the {\sc ssd/rf} and {\sc ssd/e}
 models respectively.  These modified models were shown to maintain or
 improve upon the experimental agreement with the structural and
-transport properties that can be obtained with either the original SSD
-or the density corrected version of the original model (SSD1).
+transport properties that can be obtained with either the original {\sc ssd}
+or the density corrected version of the original model ({\sc ssd1}).
 Additionally, a novel low-density ice structure is presented
-which appears to be the most stable ice structure for the entire SSD
+which appears to be the most stable ice structure for the entire {\sc ssd}
 family.
 \end{abstract}
 
@@ -89,11 +89,11 @@ cost is the Soft Sticky Dipole (SSD) water
 
 One recently developed model that largely succeeds in retaining the
 accuracy of bulk properties while greatly reducing the computational
-cost is the Soft Sticky Dipole (SSD) water
-model.\cite{Ichiye96,Ichiye96b,Ichiye99,Ichiye03} The SSD model was
+cost is the Soft Sticky Dipole ({\sc ssd}) water
+model.\cite{Ichiye96,Ichiye96b,Ichiye99,Ichiye03} The {\sc ssd} model was
 developed by Ichiye \emph{et al.} as a modified form of the
 hard-sphere water model proposed by Bratko, Blum, and
-Luzar.\cite{Bratko85,Bratko95} SSD is a {\it single point} model which
+Luzar.\cite{Bratko85,Bratko95} {\sc ssd} is a {\it single point} model which
 has an interaction site that is both a point dipole along with a
 Lennard-Jones core.  However, since the normal aligned and
 anti-aligned geometries favored by point dipoles are poor mimics of
@@ -102,7 +102,7 @@ The interaction between two SSD water molecules \emph{
 the proper hydrogen bond orientation in the first solvation
 shell.  
 
-The interaction between two SSD water molecules \emph{i} and \emph{j}
+The interaction between two {\sc ssd} water molecules \emph{i} and \emph{j}
 is given by the potential
 \begin{equation}
 u_{ij} = u_{ij}^{LJ} (r_{ij})\ + u_{ij}^{dp}
@@ -159,26 +159,26 @@ can be found in the original SSD
 enhances the tetrahedral geometry for hydrogen bonded structures),
 while $w^\prime$ is a purely empirical function.  A more detailed
 description of the functional parts and variables in this potential
-can be found in the original SSD
+can be found in the original {\sc ssd}
 articles.\cite{Ichiye96,Ichiye96b,Ichiye99,Ichiye03}
 
-Since SSD is a single-point {\it dipolar} model, the force
+Since {\sc ssd} is a single-point {\it dipolar} model, the force
 calculations are simplified significantly relative to the standard
 {\it charged} multi-point models. In the original Monte Carlo
 simulations using this model, Ichiye {\it et al.} reported that using
-SSD decreased computer time by a factor of 6-7 compared to other
+{\sc ssd} decreased computer time by a factor of 6-7 compared to other
 models.\cite{Ichiye96} What is most impressive is that this savings
 did not come at the expense of accurate depiction of the liquid state
-properties.  Indeed, SSD maintains reasonable agreement with the Soper
+properties.  Indeed, {\sc ssd} maintains reasonable agreement with the Soper
 data for the structural features of liquid
 water.\cite{Soper86,Ichiye96} Additionally, the dynamical properties
-exhibited by SSD agree with experiment better than those of more
+exhibited by {\sc ssd} agree with experiment better than those of more
 computationally expensive models (like TIP3P and
 SPC/E).\cite{Ichiye99} The combination of speed and accurate depiction
-of solvent properties makes SSD a very attractive model for the
+of solvent properties makes {\sc ssd} a very attractive model for the
 simulation of large scale biochemical simulations.
 
-One feature of the SSD model is that it was parameterized for use with
+One feature of the {\sc ssd} model is that it was parameterized for use with
 the Ewald sum to handle long-range interactions.  This would normally
 be the best way of handling long-range interactions in systems that
 contain other point charges.  However, our group has recently become
@@ -193,16 +193,16 @@ transport behavior of SSD over a variety of temperatur
 properties and behavior under the more computationally efficient
 reaction field (RF) technique, or even with a simple cutoff. This
 study addresses these issues by looking at the structural and
-transport behavior of SSD over a variety of temperatures with the
+transport behavior of {\sc ssd} over a variety of temperatures with the
 purpose of utilizing the RF correction technique.  We then suggest
 modifications to the parameters that result in more realistic bulk
 phase behavior.  It should be noted that in a recent publication, some
-of the original investigators of the SSD water model have suggested
-adjustments to the SSD water model to address abnormal density
+of the original investigators of the {\sc ssd} water model have suggested
+adjustments to the {\sc ssd} water model to address abnormal density
 behavior (also observed here), calling the corrected model
-SSD1.\cite{Ichiye03} In what follows, we compare our
-reparamaterization of SSD with both the original SSD and SSD1 models
-with the goal of improving the bulk phase behavior of an SSD-derived
+{\sc ssd1}.\cite{Ichiye03} In what follows, we compare our
+reparamaterization of {\sc ssd} with both the original {\sc ssd} and {\sc ssd1} models
+with the goal of improving the bulk phase behavior of an {\sc ssd}-derived
 model in simulations utilizing the Reaction Field.
 
 \section{Methods}
@@ -215,13 +215,13 @@ field acting on dipole $i$ is
 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}),
+\frac{1}{r_{c}^{3}} \sum_{j\in{\mathcal{R}}} {\bf \mu}_{j} s(r_{ij}),
 \label{rfequation}
 \end{equation}
 where $\mathcal{R}$ is the cavity defined by the cutoff radius
 ($r_{c}$), $\varepsilon_{s}$ is the dielectric constant imposed on the
 system (80 in the case of liquid water), ${\bf \mu}_{j}$ is the dipole
-moment vector of particle $j$, and $f(r_{ij})$ is a cubic switching
+moment vector of particle $j$, and $s(r_{ij})$ is a cubic switching
 function.\cite{AllenTildesley} The reaction field contribution to the
 total energy by particle $i$ is given by $-\frac{1}{2}{\bf
 \mu}_{i}\cdot\mathcal{E}_{i}$ and the torque on dipole $i$ by ${\bf
@@ -236,27 +236,27 @@ of SSD which could be used either with or without the 
 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
+of {\sc ssd} which could be used either with or without the reaction field
 turned on.
 
-Simulations to obtain the preferred density were performed in the
-isobaric-isothermal (NPT) ensemble, while all dynamical properties
-were obtained from microcanonical (NVE) simulations done at densities
-matching the NPT density for a particular target temperature.  The
-constant pressure simulations were implemented using an integral
-thermostat and barostat as outlined by Hoover.\cite{Hoover85,Hoover86}
-All molecules 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.
+Simulations to obtain the preferred densities of the models were
+performed in the isobaric-isothermal (NPT) ensemble, while all
+dynamical properties were obtained from microcanonical (NVE)
+simulations done at densities matching the NPT density for a
+particular target temperature.  The constant pressure simulations were
+implemented using an integral thermostat and barostat as outlined by
+Hoover.\cite{Hoover85,Hoover86} All molecules were treated as
+non-linear rigid bodies. Vibrational constraints are not necessary in
+simulations of {\sc 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, Leimkuhler, and
-McLachlan (DLM).\cite{Dullweber1997} Our reason for selecting this
+McLachlan ({\sc dlm}).\cite{Dullweber1997} Our reason for selecting this
 integrator centers on poor energy conservation of rigid body dynamics
 using traditional quaternion integration.\cite{Evans77,Evans77b} In
 typical microcanonical ensemble simulations, the energy drift when
-using quaternions was substantially greater than when using the DLM
+using quaternions was substantially greater than when using the {\sc dlm}
 method (fig. \ref{timestep}).  This steady drift in the total energy
 has also been observed by Kol {\it et al.}\cite{Laird97}
 
@@ -267,16 +267,16 @@ The DML method allows for Verlet style integration of 
 rotation matrix into quaternions for storage purposes makes trajectory
 data quite compact.
 
-The DML method allows for Verlet style integration of both
+The {\sc dlm} method allows for Verlet style integration of both
 translational and orientational 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 are more costly
 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 DML method in place of quaternions. The
+step, a 1000 {\sc ssd} particle simulation shows an average 7\% increase in
+computation time using the {\sc dlm} method in place of quaternions. The
 additional expense per step is justified when one considers the
-ability to use time steps that are nearly twice as large under DML
+ability to use time steps that are nearly twice as large under {\sc dlm}
 than would be usable under quaternion dynamics.  The energy
 conservation of the two methods using a number of different time steps
 is illustrated in figure
@@ -286,28 +286,28 @@ is illustrated in figure
 \begin{center}
 \epsfxsize=6in
 \epsfbox{timeStep.epsi}
-\caption{Energy conservation using both quaternion based integration and
-the symplectic splitting method proposed by Dullweber \emph{et al.}
-with increasing time step. The larger time step plots are shifted from
-the true energy baseline (that of $\Delta t$ = 0.1 fs) for clarity.}
+\caption{Energy conservation using both quaternion-based integration and
+the {\sc dlm} method with increasing time step. The larger time step plots
+are shifted 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 DML and quaternion integration schemes is compared.
-All of the 1000 SSD particle simulations started with the same
+steps for both the {\sc dlm} and quaternion integration schemes is compared.
+All of the 1000 {\sc ssd} particle simulations started with the same
 configuration, and the only difference was the method used to handle
 orientational motion. At time steps of 0.1 and 0.5 fs, both methods
 for propagating the orientational degrees of freedom 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 DML method are clearly
+fs, the energy conservation benefits of the {\sc dlm} method are clearly
 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 the simulations using DML integration was unnoticeable
+Energy drift in the simulations using {\sc dlm} integration was unnoticeable
 for time steps up to 3 fs. A slight energy drift on the order of 0.012
 kcal/mol per nanosecond was observed at a time step of 4 fs, and as
 expected, this drift increases dramatically with increasing time
@@ -317,7 +317,7 @@ crystals were formed by first arranging the centers of
 
 Proton-disordered ice crystals in both the $I_h$ and $I_c$ lattices
 were generated as starting points for all simulations. The $I_h$
-crystals were formed by first arranging the centers of mass of the SSD
+crystals were formed by first arranging the centers of mass of the {\sc ssd}
 particles into a ``hexagonal'' ice lattice of 1024 particles. Because
 of the crystal structure of $I_h$ ice, the simulation box assumed an
 orthorhombic shape with an edge length ratio of approximately
@@ -356,7 +356,7 @@ Our initial simulations focused on the original SSD wa
 
 \subsection{Density Behavior}
 
-Our initial simulations focused on the original SSD water model, and
+Our initial simulations focused on the original {\sc 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.  There were smaller fluctuations
@@ -372,24 +372,24 @@ maximum in this same region (between 255 and 260 K). 
 \epsfxsize=6in
 \epsfbox{denseSSD.eps}
 \caption{Density versus temperature for TIP4P [Ref. \citen{Jorgensen98b}],
- TIP3P [Ref. \citen{Jorgensen98b}], SPC/E [Ref. \citen{Clancy94}], SSD
- without Reaction Field, SSD, and experiment [Ref. \citen{CRC80}]. The
+ TIP3P [Ref. \citen{Jorgensen98b}], SPC/E [Ref. \citen{Clancy94}], {\sc ssd}
+ without Reaction Field, {\sc ssd}, and experiment [Ref. \citen{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 of SSD1
+ reaction field. The the lower than expected densities for the {\sc ssd}
+ model were what prompted the original reparameterization of {\sc ssd1}
  [Ref. \citen{Ichiye03}].}
 \label{dense1}
 \end{center}
 \end{figure}
 
-The density maximum for SSD compares quite favorably to other simple
+The density maximum for {\sc ssd} compares quite favorably to 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 a temperature closest to the experimentally observed
+models, {\sc ssd} has a temperature closest to the experimentally observed
 density maximum. Of the {\it charge-based} models in
 Fig. \ref{dense1}, TIP4P has a density maximum behavior most like that
-seen in SSD. Though not included in this plot, it is useful
+seen in {\sc ssd}. Though not included in this plot, it is useful
 to note that TIP5P has a density maximum nearly identical to the
 experimentally measured temperature.
 
@@ -397,19 +397,19 @@ cutoff radius of 12.0 \AA\ to complement the previous 
 dependent on the cutoff radius used both with and without the use of
 reaction field.\cite{Berendsen98} In order to address the possible
 effect of cutoff radius, simulations were performed with a dipolar
-cutoff radius of 12.0 \AA\ to complement the previous SSD simulations,
+cutoff radius of 12.0 \AA\ to complement the previous {\sc ssd} simulations,
 all performed with a cutoff of 9.0 \AA. All 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
+simulations using {\sc ssd}. This is advantageous in that the use of a
 longer cutoff radius results in a significant increase 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. SSD assumes a lower density than any of the other listed
+scaling of {\sc ssd} relative to other common models at any given
+temperature. {\sc ssd} 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
@@ -422,7 +422,7 @@ the curve produced from SSD simulations using reaction
 \ref{dense1}. Without the reaction field, the densities increase
 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,
+the curve produced from {\sc 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
@@ -431,8 +431,9 @@ SSD.\cite{Ichiye03} Throughout the remainder of the pa
 reaction field, the density around 300 K is still significantly lower
 than experiment and comparable water models. This anomalous behavior
 was what lead Tan {\it et al.} to recently reparameterize
-SSD.\cite{Ichiye03} Throughout the remainder of the paper our
-reparamaterizations of SSD will be compared with the newer SSD1 model.
+{\sc ssd}.\cite{Ichiye03} Throughout the remainder of the paper our
+reparamaterizations of {\sc ssd} will be compared with their newer {\sc ssd1}
+model.
 
 \subsection{Transport Behavior}
 
@@ -455,28 +456,28 @@ SSD, SPC/E [Ref. \citen{Clancy94}], TIP5P [Ref. \citen
 \epsfxsize=6in
 \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{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
-higher temperatures.}
+{\sc ssd}, SPC/E [Ref. \citen{Clancy94}], and TIP5P
+[Ref. \citen{Jorgensen01}] compared with experimental data
+[Refs. \citen{Gillen72} and \citen{Holz00}]. Of the three water models
+shown, {\sc ssd} has the least deviation from the experimental values. The
+rapidly increasing diffusion constants for TIP5P and {\sc ssd} correspond to
+significant decreases 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 models shown, the SSD model
+strengths of the {\sc ssd} model. Of the three models shown, the {\sc ssd} model
 has the most accurate depiction of self-diffusion in both the
 supercooled and liquid regimes.  SPC/E does a respectable job by
 reproducing values similar to experiment around 290 K; however, it
 deviates at both higher and lower temperatures, failing to predict the
-correct thermal trend. TIP5P and SSD both start off low at colder
+correct thermal trend. TIP5P and {\sc ssd} both start off low at colder
 temperatures and tend to diffuse too rapidly at higher temperatures.
 This behavior at higher temperatures is not particularly surprising
-since the densities of both TIP5P and SSD are lower than experimental
+since the densities of both TIP5P and {\sc ssd} are lower than experimental
 water densities at higher temperatures.  When calculating the
-diffusion coefficients for SSD at experimental densities (instead of
+diffusion coefficients for {\sc ssd} at experimental densities (instead of
 the densities from the NPT simulations), the resulting values fall
 more in line with experiment at these temperatures.
 
@@ -497,8 +498,7 @@ considerably lower than the experimental value.
 \begin{center}
 \epsfxsize=6in
 \epsfbox{corrDiag.eps} 
-\caption{Two dimensional illustration of angles involved in the 
-correlations observed in Fig. \ref{contour}.}
+\caption{An illustration of angles involved in the correlations observed in Fig. \ref{contour}.}
 \label{corrAngle}
 \end{center}
 \end{figure}
@@ -507,11 +507,11 @@ correlations observed in Fig. \ref{contour}.}
 \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 $g(r)$ values below 0.5 and black
-areas have values above 1.5.}
+\caption{Contour plots of 2D angular pair correlation functions for
+512 {\sc ssd} molecules at 100 K (A \& B) and 300 K (C \& D). Dark areas
+signify regions of enhanced density while light areas signify
+depletion relative to the bulk density. White areas have pair
+correlation values below 0.5 and black areas have values above 1.5.}
 \label{contour} 
 \end{center}
 \end{figure} 
@@ -550,22 +550,23 @@ oxygen-oxygen $g_\mathrm{OO}(r)$.\cite{Ichiye96} At lo
 
 This complex interplay between dipole and sticky interactions was
 remarked upon as a possible reason for the split second peak in the
-oxygen-oxygen $g_\mathrm{OO}(r)$.\cite{Ichiye96} At low temperatures,
-the 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.  The energetically favorable dipole
-arrangements populate the region immediately outside this repulsion
-region (around 4 \AA), while arrangements that seek to satisfy both
-the sticky and dipole forces locate themselves just beyond this
-initial buildup (around 5 \AA).
+oxygen-oxygen pair correlation function,
+$g_\mathrm{OO}(r)$.\cite{Ichiye96} At low temperatures, the 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.  The energetically favorable dipole arrangements
+populate the region immediately outside this repulsion region (around
+4 \AA), while arrangements that seek to 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 inner
@@ -576,15 +577,15 @@ and a density considerably lower than the already low 
 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 already low SSD density.  A
+and a density considerably lower than the already low {\sc ssd} density.  A
 better correction would be to include the quadrupole-quadrupole
 interactions for the water particles outside of the first solvation
 shell, but this would remove the simplicity and speed advantage of
-SSD.
+{\sc ssd}.
 
-\subsection{Adjusted Potentials: SSD/RF and SSD/E}
+\subsection{Adjusted Potentials: {\sc ssd/rf} and {\sc ssd/e}}
 
-The propensity of SSD to adopt lower than expected densities under
+The propensity of {\sc ssd} to adopt lower than expected densities under
 varying conditions is troubling, especially at higher temperatures. In
 order to correct this model for use with a reaction field, it is
 necessary to adjust the force field parameters for the primary
@@ -595,22 +596,22 @@ strength of the sticky potential ($\nu_0$), and the st
 
 The parameters available for tuning include the $\sigma$ and
 $\epsilon$ Lennard-Jones parameters, the dipole strength ($\mu$), the
-strength of the sticky potential ($\nu_0$), and the sticky attractive
-and dipole repulsive cubic switching function cutoffs ($r_l$, $r_u$
-and $r_l^\prime$, $r_u^\prime$ respectively). The results of the
-reparameterizations are shown in table \ref{params}. We are calling
-these reparameterizations the Soft Sticky Dipole / Reaction Field
-(SSD/RF - for use with a reaction field) and Soft Sticky Dipole
-Extended (SSD/E - an attempt to improve the liquid structure in
-simulations without a long-range correction).
+strength of the sticky potential ($\nu_0$), and the cutoff distances
+for the sticky attractive and dipole repulsive cubic switching
+function cutoffs ($r_l$, $r_u$ and $r_l^\prime$, $r_u^\prime$
+respectively). The results of the reparameterizations are shown in
+table \ref{params}. We are calling these reparameterizations the Soft
+Sticky Dipole / Reaction Field ({\sc ssd/rf} - for use with a reaction
+field) and Soft Sticky Dipole Extended ({\sc 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  c } 
 \hline \\[-3mm]
-\ \ \ Parameters\ \ \  & \ \ \ SSD [Ref. \citen{Ichiye96}] \ \ \
-& \ SSD1 [Ref. \citen{Ichiye03}]\ \  & \ SSD/E\ \  & \ SSD/RF \\
+\ \ \ Parameters\ \ \  & \ \ \ {\sc ssd} [Ref. \citen{Ichiye96}] \ \ \
+& \ {\sc ssd1} [Ref. \citen{Ichiye03}]\ \  & \ {\sc ssd/e}\ \  & \ {\sc ssd/rf} \\
 \hline \\[-3mm]
 \ \ \ $\sigma$ (\AA)  & 3.051 & 3.016 & 3.035 & 3.019\\
 \ \ \ $\epsilon$ (kcal/mol) & 0.152 & 0.152 & 0.152 & 0.152\\
@@ -630,11 +631,11 @@ simulations without a long-range correction).
 \begin{center} 
 \epsfxsize=5in
 \epsfbox{GofRCompare.epsi} 
-\caption{Plots comparing experiment [Ref. \citen{Head-Gordon00_1}] with SSD/E 
-and SSD1 without reaction field (top), as well as SSD/RF and SSD1 with
+\caption{Plots comparing experiment [Ref. \citen{Head-Gordon00_1}] with {\sc ssd/e} 
+and {\sc ssd1} without reaction field (top), as well as {\sc ssd/rf} and {\sc ssd1} with
 reaction field turned on (bottom). The insets show the respective
 first peaks in detail. Note how the changes in parameters have lowered
-and broadened the first peak of SSD/E and SSD/RF.}
+and broadened the first peak of {\sc ssd/e} and {\sc ssd/rf}.}
 \label{grcompare} 
 \end{center}
 \end{figure} 
@@ -643,26 +644,26 @@ and broadened the first peak of SSD/E and SSD/RF.}
 \begin{center} 
 \epsfxsize=6in
 \epsfbox{dualsticky_bw.eps} 
-\caption{Isosurfaces of the sticky potential for SSD1 (left) and SSD/E \& 
-SSD/RF (right). Light areas correspond to the tetrahedral attractive
-component, and darker areas correspond to the dipolar repulsive
-component.}
+\caption{Positive and negative isosurfaces of the sticky potential for
+{\sc ssd1} (left) and {\sc ssd/e} \& {\sc ssd/rf} (right). Light areas correspond to the
+tetrahedral attractive component, and darker areas correspond to the
+dipolar repulsive component.}
 \label{isosurface} 
 \end{center}
 \end{figure} 
 
-In the original paper detailing the development of SSD, Liu and Ichiye
+In the original paper detailing the development of {\sc ssd}, Liu and Ichiye
 placed particular emphasis on an accurate description of the first
 solvation shell. This resulted in a somewhat tall and narrow first
 peak in $g(r)$ 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 our adjustments to SSD were
-made while taking into consideration the new experimental
+first peak in the g$_\mathrm{OO}(r)$, so our adjustments to {\sc ssd} were
+made after 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 $g(r)$ by comparing
-the revised SSD model (SSD1), SSD/E, and SSD/RF to the new
+the revised {\sc ssd} model ({\sc ssd1}), {\sc ssd/e}, and {\sc ssd/rf} to the new
 experimental results. Both modified water models have shorter peaks
 that match more closely to the experimental peak (as seen in the
 insets of figure \ref{grcompare}).  This structural alteration was
@@ -681,7 +682,7 @@ how SSD and SSD1 exclude preferred dipole alignments b
 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
+how {\sc ssd} and {\sc 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
@@ -692,9 +693,9 @@ both of our adjusted models. Since SSD is a dipole bas
 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 our adjusted models. Since SSD is a dipole based model, the
+both of our adjusted models. Since {\sc 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
+moment. The original {\sc 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 improves the dielectric properties of
@@ -702,15 +703,15 @@ increasing the dipole moments to 2.42 and 2.48 D for S
 liquid phase dipole moment ranging from 2.4 D 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,
+increasing the dipole moments to 2.42 and 2.48 D for {\sc ssd/e} and {\sc ssd/rf},
 respectively, leads to significant changes in the density and
 transport of the water models.
 
 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
+to the original {\sc ssd} model. This comparison involved full NPT melting
+sequences for both {\sc ssd/e} and {\sc ssd/rf}, as well as NVE transport
 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
@@ -725,218 +726,229 @@ collection times as stated previously.
 \begin{center} 
 \epsfxsize=6in
 \epsfbox{ssdeDense.epsi} 
-\caption{Comparison of densities calculated with SSD/E to SSD1 without a 
+\caption{Comparison of densities calculated with {\sc ssd/e} to {\sc ssd1} without a 
 reaction field, TIP3P [Ref. \citen{Jorgensen98b}], TIP5P
 [Ref. \citen{Jorgensen00}], SPC/E [Ref. \citen{Clancy94}] and
 experiment [Ref. \citen{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
+interest. Note that both {\sc ssd1} and {\sc ssd/e} show good agreement with
 experiment when the long-range correction is neglected.}
 \label{ssdedense} 
 \end{center}
 \end{figure} 
 
-Fig. \ref{ssdedense} shows the density profile for the SSD/E model
-in comparison to SSD1 without a reaction field, other common water
+Fig. \ref{ssdedense} shows the density profile for the {\sc ssd/e} model
+in comparison to {\sc 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
+{\sc ssd/e} and {\sc ssd1} have increased significantly over the original {\sc ssd}
 model (see fig. \ref{dense1}) and are in better agreement with the
-experimental values. At 298 K, the densities of SSD/E and SSD1 without
+experimental values. At 298 K, the densities of {\sc ssd/e} and {\sc 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$. The changes to
+better than the {\sc ssd} value of 0.967$\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
+character. However, this increasing disorder in the {\sc ssd/e} model has
 little effect on the melting transition. By monitoring $C_p$
-throughout these simulations, the melting transition for SSD/E was
+throughout these simulations, the melting transition for {\sc ssd/e} was
 shown to occur at 235 K.  The same transition temperature observed
-with SSD and SSD1.
+with {\sc ssd} and {\sc ssd1}.
 
 \begin{figure}
 \begin{center} 
 \epsfxsize=6in
 \epsfbox{ssdrfDense.epsi} 
-\caption{Comparison of densities calculated with SSD/RF to SSD1 with a 
+\caption{Comparison of densities calculated with {\sc ssd/rf} to {\sc ssd1} with a 
 reaction field, TIP3P [Ref. \citen{Jorgensen98b}], TIP5P
 [Ref. \citen{Jorgensen00}], SPC/E [Ref. \citen{Clancy94}], and
 experiment [Ref. \citen{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.}
+correction - {\sc ssd/rf} provides significantly more accurate densities
+than {\sc ssd1} when performing room temperature simulations.}
 \label{ssdrfdense} 
 \end{center}
 \end{figure} 
 
 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
+{\sc ssd/rf} and {\sc 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
+field, the densities of {\sc ssd/rf} and {\sc ssd1} show a dramatic increase over
+normal {\sc ssd} (see figure \ref{dense1}). At 298 K, {\sc ssd/rf} has a density
 of 0.997$\pm$0.001 g/cm$^3$, directly in line with experiment and
-considerably better than the original SSD value of 0.941$\pm$0.001
-g/cm$^3$ and the SSD1 value of 0.972$\pm$0.002 g/cm$^3$. These results
+considerably better than the original {\sc ssd} value of 0.941$\pm$0.001
+g/cm$^3$ and the {\sc 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
+which observed at 245 K for {\sc ssd/rf}, is identical to {\sc ssd} and only 5 K
+lower than {\sc ssd1} with a reaction field. Additionally, the difference in
+density maxima is not as extreme, with {\sc 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.
+K, shown by {\sc ssd} and {\sc ssd1} respectively.
 
 \begin{figure}
 \begin{center} 
 \epsfxsize=6in
 \epsfbox{ssdeDiffuse.epsi} 
-\caption{The diffusion constants calculated from SSD/E and SSD1,
- both without a reaction field, along with experimental results
- [Refs. \citen{Gillen72} and \citen{Holz00}]. 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 mobile
- than experiment at all of the temperatures, but it is closer to
- experiment at biologically relevant temperatures than SSD1 without a
- long-range correction.}
+\caption{The diffusion constants calculated from {\sc ssd/e} and {\sc ssd1} (both
+without a reaction field) along with experimental results
+[Refs. \citen{Gillen72} and \citen{Holz00}]. The NVE calculations were
+performed at the average densities observed in the 1 atm NPT
+simulations for the respective models. {\sc ssd/e} is slightly more mobile
+than experiment at all of the temperatures, but it is closer to
+experiment at biologically relevant temperatures than {\sc ssd1} without a
+long-range correction.}
 \label{ssdediffuse} 
 \end{center}
 \end{figure} 
 
-The reparameterization of the SSD water model, both for use with and
+The reparameterization of the {\sc 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 the excellent diffusive behavior
-of SSD be maintained or improved. Figure \ref{ssdediffuse} compares
-the temperature dependence of the diffusion constant of SSD/E to SSD1
+the densities, it is important that the diffusive behavior of {\sc ssd} be
+maintained or improved. Figure \ref{ssdediffuse} compares the
+temperature dependence of the diffusion constant of {\sc ssd/e} to {\sc ssd1}
 without an active reaction field at the densities calculated from
 their respective NPT simulations at 1 atm. The diffusion constant for
-SSD/E is consistently higher than experiment, while SSD1 remains lower
+{\sc ssd/e} is consistently higher than experiment, while {\sc ssd1} remains lower
 than experiment until relatively high temperatures (around 360
 K). Both models follow the shape of the experimental curve well below
 300 K but tend to diffuse too rapidly at higher temperatures, as seen
-in SSD1's crossing above 360 K.  This increasing diffusion relative to
+in {\sc ssd1}'s crossing above 360 K.  This increasing diffusion relative to
 the experimental values is caused by the rapidly decreasing system
-density with increasing temperature.  Both SSD1 and SSD/E show this
+density with increasing temperature.  Both {\sc ssd1} and {\sc ssd/e} show this
 deviation in particle mobility, but this trend has different
-implications on the diffusive behavior of the models.  While SSD1
+implications on the diffusive behavior of the models.  While {\sc ssd1}
 shows more experimentally accurate diffusive behavior in the high
-temperature regimes, SSD/E shows more accurate behavior in the
+temperature regimes, {\sc ssd/e} shows more accurate behavior in the
 supercooled and biologically relevant temperature ranges.  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 under the most commonly simulated
+of {\sc ssd/e} relative to {\sc ssd1} under the most commonly simulated
 conditions.
 
 \begin{figure}
 \begin{center} 
 \epsfxsize=6in
 \epsfbox{ssdrfDiffuse.epsi} 
-\caption{The diffusion constants calculated from SSD/RF and SSD1,
- both with an active reaction field, along with experimental results
- [Refs. \citen{Gillen72} and \citen{Holz00}]. 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 lower calculated
- densities than those observed in experiment.}
+\caption{The diffusion constants calculated from {\sc ssd/rf} and {\sc ssd1} (both
+with an active reaction field) along with experimental results
+[Refs. \citen{Gillen72} and \citen{Holz00}]. The NVE calculations were
+performed at the average densities observed in the 1 atm NPT
+simulations for both of the models. {\sc ssd/rf} simulates the diffusion of
+water throughout this temperature range very well. The rapidly
+increasing diffusion constants at high temperatures for both models
+can be attributed to lower calculated densities than those observed in
+experiment.}
 \label{ssdrfdiffuse} 
 \end{center}
 \end{figure} 
 
-In figure \ref{ssdrfdiffuse}, the diffusion constants for SSD/RF are
-compared to SSD1 with an active reaction field. Note that SSD/RF
+In figure \ref{ssdrfdiffuse}, the diffusion constants for {\sc ssd/rf} are
+compared to {\sc ssd1} with an active reaction field. Note that {\sc ssd/rf}
 tracks the experimental results quantitatively, identical within error
 throughout most of the temperature range shown and exhibiting only a
-slight increasing trend at higher temperatures. SSD1 tends to diffuse
+slight increasing trend at higher temperatures. {\sc ssd1} tends to diffuse
 more slowly at low temperatures and deviates to diffuse too rapidly at
 temperatures greater than 330 K.  As stated above, 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
+temperatures. {\sc ssd/rf} does not suffer from this problem as much as {\sc ssd1}
 because the calculated densities are closer to the experimental
 values. These results again emphasize the importance of careful
 reparameterization when using an altered long-range correction.
 
 \begin{table}
+\begin{minipage}{\linewidth}
+\renewcommand{\thefootnote}{\thempfootnote}
 \begin{center}
-\caption{Calculated and experimental properties of the single point waters and liquid water at 298 K and 1 atm. (a) Ref. [\citen{Mills73}]. (b) Calculated by integrating the data in ref. \citen{Head-Gordon00_1}. (c) Calculated by integrating the data in ref. \citen{Soper86}. (d) Calculated for 298 K from data in ref. [\citen{Eisenberg69}]. (e) Calculated for 298 K from data in ref. \citen{Krynicki66}.}
+\caption{Properties of the single-point water models compared with
+experimental data at ambient conditions} 
 \begin{tabular}{ l  c  c  c  c  c } 
 \hline \\[-3mm]
-\ \ \ \ \ \  & \ \ \ SSD1 \ \ \ & \ SSD/E \ \ \ & \ SSD1 (RF) \ \ 
-\ & \ SSD/RF \ \ \ & \ Expt. \\
+\ \ \ \ \ \  & \ \ \ {\sc ssd1} \ \ \ & \ {\sc ssd/e} \ \ \ & \ {\sc ssd1} (RF) \ \ 
+\ & \ {\sc ssd/rf} \ \ \ & \ Expt. \\
  \hline \\[-3mm]
 \ \ \ $\rho$ (g/cm$^3$) & 0.999 $\pm$0.001 & 0.996 $\pm$0.001 & 0.972 $\pm$0.002 & 0.997 $\pm$0.001 & 0.997 \\
 \ \ \ $C_p$ (cal/mol K) & 28.80 $\pm$0.11 & 25.45 $\pm$0.09 & 28.28 $\pm$0.06 & 23.83 $\pm$0.16 & 17.98 \\
-\ \ \ $D$ ($10^{-5}$ cm$^2$/s) & 1.78 $\pm$0.07 & 2.51 $\pm$0.18 & 2.00 $\pm$0.17 & 2.32 $\pm$0.06 & 2.299$^\text{a}$ \\
-\ \ \ Coordination Number & 3.9 & 4.3 & 3.8 & 4.4 & 4.7$^\text{b}$ \\
-\ \ \ H-bonds per particle & 3.7 & 3.6 & 3.7 & 3.7 & 3.5$^\text{c}$ \\
-\ \ \ $\tau_1$ (ps) & 10.9 $\pm$0.6 & 7.3 $\pm$0.4 & 7.5 $\pm$0.7 & 7.2 $\pm$0.4 & 5.7$^\text{d}$ \\
-\ \ \ $\tau_2$ (ps) & 4.7 $\pm$0.4 & 3.1 $\pm$0.2 & 3.5 $\pm$0.3 & 3.2 $\pm$0.2 & 2.3$^\text{e}$ \\
+\ \ \ $D$ ($10^{-5}$ cm$^2$/s) & 1.78 $\pm$0.07 & 2.51 $\pm$0.18 &
+2.00 $\pm$0.17 & 2.32 $\pm$0.06 & 2.299\cite{Mills73} \\
+\ \ \ Coordination Number ($n_C$) & 3.9 & 4.3 & 3.8 & 4.4 &
+4.7\footnote{Calculated by integrating $g_{\text{OO}}(r)$ in
+Ref. \citen{Head-Gordon00_1}} \\ 
+\ \ \ H-bonds per particle ($n_H$) & 3.7 & 3.6 & 3.7 & 3.7 &
+3.5\footnote{Calculated by integrating $g_{\text{OH}}(r)$ in
+Ref. \citen{Soper86}}  \\
+\ \ \ $\tau_1$ (ps) & 10.9 $\pm$0.6 & 7.3 $\pm$0.4 & 7.5 $\pm$0.7 &
+7.2 $\pm$0.4 & 5.7\footnote{Calculated for 298 K from data in Ref. \citen{Eisenberg69}} \\
+\ \ \ $\tau_2$ (ps) & 4.7 $\pm$0.4 & 3.1 $\pm$0.2 & 3.5 $\pm$0.3 & 3.2
+$\pm$0.2 & 2.3\footnote{Calculated for 298 K from data in
+Ref. \citen{Krynicki66}}
 \end{tabular}
 \label{liquidproperties}
 \end{center}
+\end{minipage}
 \end{table}
 
 Table \ref{liquidproperties} gives a synopsis of the liquid state
 properties of the water models compared in this study along with the
 experimental values for liquid water at ambient conditions. The
-coordination number ($N_C$) and hydrogen bonds per particle ($N_H$)
-were calculated by integrating the following relations:
+coordination number ($n_C$) and number of hydrogen bonds per particle
+($n_H$) were calculated by integrating the following relations:
 \begin{equation}
-N_C = 4\pi\rho_{\text{OO}}\int_{0}^{a}r^2\text{g}_{\text{OO}}(r)dr,
+n_C = 4\pi\rho_{\text{OO}}\int_{0}^{a}r^2\text{g}_{\text{OO}}(r)dr,
 \end{equation}
 \begin{equation}
-N_H = 4\pi\rho_{\text{OH}}\int_{0}^{b}r^2\text{g}_{\text{OH}}(r)dr,
+n_H = 4\pi\rho_{\text{OH}}\int_{0}^{b}r^2\text{g}_{\text{OH}}(r)dr,
 \end{equation}
 where $\rho$ is the number density of the specified pair interactions,
 $a$ and $b$ are the radial locations of the minima following the first
-solvation shell peak in g$_\text{OO}(r)$ or g$_\text{OH}(r)$
-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
+peak in g$_\text{OO}(r)$ or g$_\text{OH}(r)$ respectively. The number
+of hydrogen bonds stays relatively constant across all of the models,
+but the coordination numbers of {\sc ssd/e} and {\sc ssd/rf} show an improvement
+over {\sc ssd1}.  This improvement is primarily due to extension of the
+first solvation shell in the new parameter sets.  Because $n_H$ and
+$n_C$ are nearly identical in {\sc ssd1}, it appears that all molecules in
+the first solvation shell are involved in hydrogen bonds.  Since $n_H$
+and $n_C$ differ in the newly parameterized models, the orientations
+in the first solvation shell are a bit more ``fluid''.  Therefore {\sc ssd1}
+overstructures the first solvation shell and our reparameterizations
+have returned this shell to more realistic liquid-like behavior.
+
+The time constants for the orientational autocorrelation functions
 are also displayed in Table \ref{liquidproperties}. The dipolar
-orientational time correlation function ($\Gamma_{l}$) is described
+orientational time correlation functions ($C_{l}$) are described
 by:
 \begin{equation}
-\Gamma_{l}(t) = \langle P_l[\mathbf{u}_j(0)\cdot\mathbf{u}_j(t)]\rangle,
+C_{l}(t) = \langle P_l[\hat{\mathbf{u}}_j(0)\cdot\hat{\mathbf{u}}_j(t)]\rangle,
 \end{equation}
-where $P_l$ is a Legendre polynomial of order $l$ and $\mathbf{u}_j$
-is the unit vector of the particle dipole.\cite{Rahman71} From these
-correlation functions, the orientational relaxation time of the dipole
-vector can be calculated from an exponential fit in the long-time
-regime ($t > \tau_l$).\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. 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{Rahman71} 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
+where $P_l$ are Legendre polynomials of order $l$ and
+$\hat{\mathbf{u}}_j$ is the unit vector pointing along the molecular
+dipole.\cite{Rahman71} From these correlation functions, the
+orientational relaxation time of the dipole vector can be calculated
+from an exponential fit in the long-time regime ($t >
+\tau_l$).\cite{Rothschild84} Calculation of these time constants were
+averaged over five detailed NVE simulations performed at the ambient
+conditions for each of the respective models. It should be noted that
+the commonly cited value of 1.9 ps for $\tau_2$ was determined from
+the NMR data in Ref. \citen{Krynicki66} at a temperature near
+34$^\circ$C.\cite{Rahman71} 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}. Similarly, $\tau_1$
-was recomputed for 298 K from the data in ref \citen{Eisenberg69}.
-Again, SSD/E and SSD/RF show improved behavior over SSD1, both with
+fashion described in Ref. \citen{Krynicki66}. Similarly, $\tau_1$ was
+recomputed for 298 K from the data in Ref. \citen{Eisenberg69}.
+Again, {\sc ssd/e} and {\sc ssd/rf} show improved behavior over {\sc 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 are shorter than the
-values observed here, and this difference can be attributed to the use
-of the Ewald sum technique versus a reaction field.\cite{Ichiye99}
+leads to much improved time constants for {\sc ssd1}; however, these results
+also include a corresponding decrease in system density.
+Orientational relaxation times published in the original {\sc ssd} dynamics
+papers are smaller than the values observed here, and this difference
+can be attributed to the use of the Ewald sum.\cite{Ichiye99}
 
 \subsection{Additional Observations}
 
@@ -944,17 +956,16 @@ of the Ewald sum technique versus a reaction field.\ci
 \begin{center}
 \epsfxsize=6in
 \epsfbox{icei_bw.eps} 
-\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-{\it i} to
-emphasize its simulation origins. This image was taken of the (001)
-face of the crystal.}
+\caption{The most stable crystal structure assumed by the {\sc ssd} family
+of water models.  We refer to this structure as Ice-{\it i} to
+indicate its origins in computer simulation.  This image was taken of
+the (001) face of the crystal.}
 \label{weirdice} 
 \end{center}
 \end{figure}
 
 While performing a series of melting simulations on an early iteration
-of SSD/E not discussed in this paper, we observed recrystallization
+of {\sc ssd/e} not discussed in this paper, we observed recrystallization
 into a novel structure not previously known for water.  After melting
 at 235 K, two of five systems underwent crystallization events near
 245 K.  The two systems remained crystalline up to 320 and 330 K,
@@ -962,9 +973,9 @@ Ice-$\sqrt{\smash[b]{-\text{I}}}$ (ice-{\it i}).  A la
 that does not correspond to any known form of ice.  This appears to be
 an artifact of the point dipolar models, so to distinguish it from the
 experimentally observed forms of ice, we have denoted the structure
-Ice-$\sqrt{\smash[b]{-\text{I}}}$ (ice-{\it i}).  A large enough
+Ice-$\sqrt{\smash[b]{-\text{I}}}$ (Ice-{\it i}).  A large enough
 portion of the sample crystallized that we have been able to obtain a
-near ideal crystal structure of ice-{\it i}. Figure \ref{weirdice}
+near ideal crystal structure of Ice-{\it i}. 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 bent rather than perfectly straight. This results
@@ -975,60 +986,64 @@ Initial simulations indicated that ice-{\it i} is the 
 configuration. Though not ideal, these flexed hydrogen bonds are
 favorable enough to stabilize an entire crystal generated around them.
 
-Initial simulations indicated that ice-{\it 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-{\it i} 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 enthalpies of each were compared using all three water
-models. With every model in the SSD family, ice-{\it i} had the lowest
-calculated enthalpy: 5\% lower than $I_h$ with SSD1, 6.5\% lower with
-SSD/E, and 7.5\% lower with SSD/RF.  The enthalpy data is summarized
-in Table \ref{iceenthalpy}.
+Initial simulations indicated that Ice-{\it i} is the preferred ice
+structure for at least the {\sc ssd/e} model. To verify this, a
+comparison was made between near ideal crystals of ice~$I_h$,
+ice~$I_c$, and Ice-{\it i} at constant pressure with {\sc ssd/e}, {\sc
+ssd/rf}, and {\sc ssd1}. Near-ideal versions of the three types of
+crystals were cooled to 1 K, and enthalpies of formation of each were
+compared using all three water models.  Enthalpies were estimated from
+the isobaric-isothermal simulations using $H=U+P_{\text ext}V$ where
+$P_{\text ext}$ is the applied pressure.  A constant value of
+-60.158 kcal / mol has been added to place our zero for the
+enthalpies of formation for these systems at the traditional state
+(elemental forms at standard temperature and pressure).  With every
+model in the {\sc ssd} family, Ice-{\it i} had the lowest calculated
+enthalpy of formation.
 
 \begin{table}
 \begin{center}
-\caption{Enthalpies (in kcal / mol) of the three crystal structures (at 1
-K) exhibited by the SSD family of water models}
+\caption{Enthalpies of Formation (in kcal / mol) of the three crystal
+structures (at 1 K) exhibited by the {\sc ssd} family of water models} 
 \begin{tabular}{ l  c  c  c  } 
 \hline \\[-3mm]
 \ \ \ Water Model \ \ \  & \ \ \ Ice-$I_h$ \ \ \ & \ Ice-$I_c$\ \  & \
 Ice-{\it i} \\
 \hline \\[-3mm]
-\ \ \ SSD/E & -12.286 & -12.292 & -13.590 \\
-\ \ \ SSD/RF & -12.935 & -12.917 & -14.022 \\
-\ \ \ SSD1 & -12.496 & -12.411 & -13.417 \\
-\ \ \ SSD1 (RF) & -12.504 & -12.411 & -13.134 \\
+\ \ \ {\sc ssd/e} & -12.286 & -12.292 & -13.590 \\
+\ \ \ {\sc ssd/rf} & -12.935 & -12.917 & -14.022 \\
+\ \ \ {\sc ssd1} & -12.496 & -12.411 & -13.417 \\
+\ \ \ {\sc ssd1} (RF) & -12.504 & -12.411 & -13.134 \\
 \end{tabular}
 \label{iceenthalpy}
 \end{center}
 \end{table}
 
 In addition to these energetic comparisons, melting simulations were
-performed with ice-{\it 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 reaction field occurred at
-temperature in excess of 375~K.  SSD/RF and SSD1 with a reaction field
+performed with ice-{\it i} as the initial configuration using {\sc ssd/e},
+{\sc ssd/rf}, and {\sc ssd1} both with and without a reaction field. The melting
+transitions for both {\sc ssd/e} and {\sc ssd1} without reaction field occurred at
+temperature in excess of 375~K.  {\sc ssd/rf} and {\sc ssd1} with a reaction field
 showed more reasonable melting transitions near 325~K.  These melting
-point observations clearly show that all of the SSD-derived models
+point observations clearly show that all of the {\sc ssd}-derived models
 prefer the ice-{\it i} structure.
 
 \section{Conclusions}
 
 The density maximum and temperature dependence of the self-diffusion
-constant were studied for the SSD water model, both with and without
+constant were studied for the {\sc ssd} water model, both with and without
 the use of reaction field, via a series of NPT and NVE
 simulations. The constant pressure simulations showed a density
 maximum near 260 K. In most cases, the calculated densities were
 significantly lower than the densities obtained from other water
-models (and experiment). Analysis of self-diffusion showed SSD to
+models (and experiment). Analysis of self-diffusion showed {\sc ssd} to
 capture the transport properties of water well in both the liquid and
 supercooled 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 comparisons were made with SSD1, Ichiye's density
-corrected version of SSD. Both models improve the liquid structure,
+In order to correct the density behavior, the original {\sc ssd} model was
+reparameterized for use both with and without a reaction field ({\sc ssd/rf}
+and {\sc ssd/e}), and comparisons were made with {\sc ssd1}, Ichiye's density
+corrected version of {\sc ssd}. Both models improve the liquid structure,
 densities, and diffusive properties under their respective simulation
 conditions, indicating the necessity of reparameterization when
 changing the method of calculating long-range electrostatic
@@ -1037,7 +1052,7 @@ by the SSD family of water models is somewhat troublin
 simulations of biochemical systems.
 
 The existence of a novel low-density ice structure that is preferred
-by the SSD family of water models is somewhat troubling, since liquid
+by the {\sc ssd} family of water models is somewhat troubling, since liquid
 simulations on this family of water models at room temperature are
 effectively simulations of supercooled or metastable liquids.  One
 way to destabilize this unphysical ice structure would be to make the
@@ -1046,7 +1061,7 @@ Additionally, our initial calculations show that the i
 reparameterization to maintain the same level of agreement with the
 experiments.
 
-Additionally, our initial calculations show that the ice-{\it i}
+Additionally, our initial calculations show that the Ice-{\it i}
 structure may also be a preferred crystal structure for at least one
 other popular multi-point water model (TIP3P), and that much of the
 simulation work being done using this popular model could also be at
