--- trunk/iceiPaper/iceiPaper.tex	2004/09/15 19:06:05	1459
+++ trunk/iceiPaper/iceiPaper.tex	2004/09/15 21:44:27	1464
@@ -1,57 +1,50 @@
-
 %\documentclass[prb,aps,twocolumn,tabularx]{revtex4}
-\documentclass[preprint,aps,endfloats]{revtex4}
+\documentclass[11pt]{article}
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-%\usepackage{endfloat}
+\usepackage{endfloat}
 \usepackage{amsmath}
 \usepackage{epsf}
 \usepackage{berkeley}
-%\usepackage{setspace}
-%\usepackage{tabularx}
+\usepackage{setspace}
+\usepackage{tabularx}
 \usepackage{graphicx}
-%\usepackage[ref]{overcite}
-%\pagestyle{plain}
-%\pagenumbering{arabic}
-%\oddsidemargin 0.0cm \evensidemargin 0.0cm
-%\topmargin -21pt \headsep 10pt
-%\textheight 9.0in \textwidth 6.5in
-%\brokenpenalty=10000
+\usepackage[ref]{overcite}
+\pagestyle{plain}
+\pagenumbering{arabic}
+\oddsidemargin 0.0cm \evensidemargin 0.0cm
+\topmargin -21pt \headsep 10pt
+\textheight 9.0in \textwidth 6.5in
+\brokenpenalty=10000
+\renewcommand{\baselinestretch}{1.2}
+\renewcommand\citemid{\ } % no comma in optional reference note
 
-%\renewcommand\citemid{\ } % no comma in optional reference note
-
 \begin{document}
 
-\title{A Free Energy Study of Low Temperature and Anomalous Ice}
+\title{Ice-{\it i}: a novel ice polymorph predicted via computer simulation}
 
-\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 \\
+Department of Chemistry and Biochemistry\\ University of Notre Dame\\
 Notre Dame, Indiana 46556}
 
 \date{\today}
 
-%\maketitle
+\maketitle
 %\doublespacing
 
 \begin{abstract}
 The free energies of several ice polymorphs in the low pressure regime
-were calculated using thermodynamic integration of systems consisting
-of a variety of common water models. Ice-{\it i}, a recent
-computationally observed solid structure, was determined to be the
-stable state with the lowest free energy for all the water models
-investigated. Phase diagrams were generated, and melting and boiling
-points for all the models were determined and show relatively good
-agreement with experiment, although the solid phase is different
-between simulation and experiment. In addition, potential truncation
-was shown to have an effect on the calculated free energies, and may
-result in altered free energy landscapes.
+were calculated using thermodynamic integration.  These integrations
+were done for most of the common water models. Ice-{\it i}, a
+structure we recently observed to be stable in one of the single-point
+water models, was determined to be the stable crystalline state (at 1
+atm) for {\it all} the water models investigated.  Phase diagrams were
+generated, and phase coexistence lines were determined for all of the
+known low-pressure ice structures under all of the common water
+models.  Additionally, potential truncation was shown to have an
+effect on the calculated free energies, and can result in altered free
+energy landscapes.
 \end{abstract}
 
-\maketitle
-
-\newpage
-
 %\narrowtext 
 
 %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
@@ -60,11 +53,11 @@ Molecular dynamics has developed into a valuable tool 
 
 \section{Introduction}
 
-Molecular dynamics has developed into a valuable tool for studying the
-phase behavior of systems ranging from small or simple
-molecules\cite{smallStuff} to complex biological
-species.\cite{bigStuff} Many techniques have been developed in order
-to investigate the thermodynamic properites of model substances,
+Molecular dynamics is a valuable tool for studying the phase behavior
+of systems ranging from small or simple
+molecules\cite{Matsumoto02andOthers} to complex biological
+species.\cite{bigStuff} Many techniques have been developed to
+investigate the thermodynamic properites of model substances,
 providing both qualitative and quantitative comparisons between
 simulations and experiment.\cite{thermMethods} Investigation of these
 properties leads to the development of new and more accurate models,
@@ -72,24 +65,24 @@ simulations, and has resulted in a variety of models t
 and intricate molecular systems.
 
 Water has proven to be a challenging substance to depict in
-simulations, and has resulted in a variety of models that attempt to
-describe its behavior under a varying simulation
-conditions.\cite{lotsOfWaterPapers} Many of these models have been
-used to investigate important physical phenomena like phase
-transitions and the hydrophobic effect.\cite{evenMorePapers} With the
-advent of numerous differing models, it is only natural that attention
-is placed on the properties of the models themselves in an attempt to
-clarify their benefits and limitations when applied to a system of
-interest.\cite{modelProps} One important but challenging property to
-quantify is the free energy, particularly of the solid forms of
-water. Difficulty in these types of studies typically arises from the
-assortment of possible crystalline polymorphs that water that water
-adopts over a wide range of pressures and temperatures. There are
-currently 13 recognized forms of ice, and it is a challenging task to
-investigate the entire free energy landscape.\cite{Sanz04} Ideally,
-research is focused on the phases having the lowest free energy,
-because these phases will dictate the true transition temperatures and
-pressures for their respective model. 
+simulations, and a variety of models have been developed to describe
+its behavior under varying simulation
+conditions.\cite{Berendsen81,Jorgensen83,Bratko85,Berendsen87,Liu96,Mahoney00,Fennell04}
+These models have been used to investigate important physical
+phenomena like phase transitions and the hydrophobic
+effect.\cite{Yamada02} With the choice of models available, it
+is only natural to compare the models under interesting thermodynamic
+conditions in an attempt to clarify the limitations of each of the
+models.\cite{modelProps} Two important property to quantify are the
+Gibbs and Helmholtz free energies, particularly for the solid forms of
+water.  Difficulty in these types of studies typically arises from the
+assortment of possible crystalline polymorphs that water adopts over a
+wide range of pressures and temperatures. There are currently 13
+recognized forms of ice, and it is a challenging task to investigate
+the entire free energy landscape.\cite{Sanz04} Ideally, research is
+focused on the phases having the lowest free energy at a given state
+point, because these phases will dictate the true transition
+temperatures and pressures for their respective model.
 
 In this paper, standard reference state methods were applied to the
 study of crystalline water polymorphs in the low pressure regime. This
@@ -97,7 +90,7 @@ themselves\cite{nucleationStudies}; however, the cryst
 arrived at through crystallization of a computationally efficient
 water model under constant pressure and temperature
 conditions. Crystallization events are interesting in and of
-themselves\cite{nucleationStudies}; however, the crystal structure
+themselves\cite{Matsumoto02,Yamada02}; however, the crystal structure
 obtained in this case was different from any previously observed ice
 polymorphs, in experiment or simulation.\cite{Fennell04} This crystal
 was termed Ice-{\it i} in homage to its origin in computational
@@ -114,6 +107,21 @@ Results in the previous study indicated that Ice-{\it 
 diameter. This relatively open overall structure leads to crystals
 that are 0.07 g/cm$^3$ less dense on average than ice $I_h$.
 
+\begin{figure}
+\includegraphics[width=\linewidth]{unitCell.eps}
+\caption{Unit cells for (A) Ice-{\it i} and (B) Ice-2{\it i}, the elongated variant of Ice-{\it i}.  For Ice-{\it i}, the $a$ to $c$ relation is given by $a = 2.1214c$, while for Ice-2{\it i}, $a = 1.7850c$.}
+\label{iceiCell}
+\end{figure}
+
+\begin{figure}
+\includegraphics[width=\linewidth]{orderedIcei.eps}
+\caption{Image of a proton ordered crystal of Ice-{\it i} looking 
+down the (001) crystal face. The rows of water tetramers surrounded by
+octagonal pores leads to a crystal structure that is significantly
+less dense than ice $I_h$.}
+\label{protOrder}
+\end{figure}
+
 Results in the previous study indicated that Ice-{\it i} is the
 minimum energy crystal structure for the single point water models
 being studied (for discussions on these single point dipole models,
@@ -197,8 +205,9 @@ state.
 minimum potential energy of the ideal crystal. In the case of
 molecular liquids, the ideal vapor is chosen as the target reference
 state.
+
 \begin{figure}
-\includegraphics[scale=1.0]{rotSpring.eps}
+\includegraphics[width=\linewidth]{rotSpring.eps}
 \caption{Possible orientational motions for a restrained molecule. 
 $\theta$ angles correspond to displacement from the body-frame {\it
 z}-axis, while $\omega$ angles correspond to rotation about the
@@ -209,23 +218,25 @@ cubic switching between 100\% and 85\% of the cutoff v
 \end{figure}
 
 Charge, dipole, and Lennard-Jones interactions were modified by a
-cubic switching between 100\% and 85\% of the cutoff value (9 \AA ). By
-applying this function, these interactions are smoothly truncated,
-thereby avoiding poor energy conserving dynamics resulting from
-harsher truncation schemes. The effect of a long-range correction was
-also investigated on select model systems in a variety of manners. For
-the SSD/RF model, a reaction field with a fixed dielectric constant of
-80 was applied in all simulations.\cite{Onsager36} For a series of the
-least computationally expensive models (SSD/E, SSD/RF, and TIP3P),
-simulations were performed with longer cutoffs of 12 and 15 \AA\ to
-compare with the 9 \AA\ cutoff results. Finally, results from the use
-of an Ewald summation were estimated for TIP3P and SPC/E by performing
+cubic switching between 100\% and 85\% of the cutoff value (9 \AA
+). By applying this function, these interactions are smoothly
+truncated, thereby avoiding poor energy conserving dynamics resulting
+from harsher truncation schemes. The effect of a long-range correction
+was also investigated on select model systems in a variety of
+manners. For the SSD/RF model, a reaction field with a fixed
+dielectric constant of 80 was applied in all
+simulations.\cite{Onsager36} For a series of the least computationally
+expensive models (SSD/E, SSD/RF, and TIP3P), simulations were
+performed with longer cutoffs of 12 and 15 \AA\ to compare with the 9
+\AA\ cutoff results. Finally, results from the use of an Ewald
+summation were estimated for TIP3P and SPC/E by performing
 calculations with Particle-Mesh Ewald (PME) in the TINKER molecular
-mechanics software package. TINKER was chosen because it can also
-propagate the motion of rigid-bodies, and provides the most direct
-comparison to the results from OOPSE. The calculated energy difference
-in the presence and absence of PME was applied to the previous results
-in order to predict changes in the free energy landscape.
+mechanics software package.\cite{Tinker} TINKER was chosen because it
+can also propagate the motion of rigid-bodies, and provides the most
+direct comparison to the results from OOPSE. The calculated energy
+difference in the presence and absence of PME was applied to the
+previous results in order to predict changes in the free energy
+landscape.
 
 \section{Results and discussion}
 
@@ -254,9 +265,9 @@ kcal/mol. *Ice $I_c$ is unstable at 200 K using SSD/RF
 of 9 \AA\ and were performed at 200 K and $\sim$1 atm. Units are
 kcal/mol. *Ice $I_c$ is unstable at 200 K using SSD/RF.}
 \begin{tabular}{ l  c  c  c  c }
-\hline \\[-7mm]
+\hline 
 \ \quad \ Water Model\ \ & \ \quad \ \ \ \ $I_h$ \ \ & \ \quad \ \ \ \ $I_c$ \ \  & \ \quad \ \ \ \ B \ \  & \ \quad \ \ \ Ice-{\it i} \ \quad \ \\
-\hline \\[-3mm]
+\hline 
 \ \quad \ TIP3P  & \ \quad \ -11.41 & \ \quad \ -11.23 & \ \quad \ -11.82 & \quad -12.30\\
 \ \quad \ TIP4P  & \ \quad \ -11.84 & \ \quad \ -12.04 & \ \quad \ -12.08 & \quad -12.33\\
 \ \quad \ TIP5P  & \ \quad \ -11.85 & \ \quad \ -11.86 & \ \quad \ -11.96 & \quad -12.29\\
@@ -283,6 +294,7 @@ TIP4P in the high pressure regime.\cite{Sanz04} 
 representative of the dense ice polymorphs. A recent study by Sanz
 {\it et al.} goes into detail on the phase diagrams for SPC/E and
 TIP4P in the high pressure regime.\cite{Sanz04} 
+
 \begin{figure}
 \includegraphics[width=\linewidth]{tp3PhaseDia.eps}
 \caption{Phase diagram for the TIP3P water model in the low pressure 
@@ -292,6 +304,7 @@ higher in energy and don't appear in the phase diagram
 higher in energy and don't appear in the phase diagram.}
 \label{tp3phasedia}
 \end{figure}
+
 \begin{figure}
 \includegraphics[width=\linewidth]{ssdrfPhaseDia.eps}
 \caption{Phase diagram for the SSD/RF water model in the low pressure 
@@ -310,9 +323,9 @@ temperatures of several common water models compared w
 \caption{Melting ($T_m$), boiling ($T_b$), and sublimation ($T_s$) 
 temperatures of several common water models compared with experiment.}
 \begin{tabular}{ l  c  c  c  c  c  c  c }
-\hline \\[-7mm]
+\hline 
 \ \ Equilibria Point\ \ & \ \ \ \ \ TIP3P \ \ & \ \ \ \ \ TIP4P \ \ & \ \quad \ \ \ \ TIP5P \ \ & \ \ \ \ \ SPC/E \ \ & \ \ \ \ \ SSD/E \ \ & \ \ \ \ \ SSD/RF \ \ & \ \ \ \ \ Exp. \ \ \\
-\hline \\[-3mm]
+\hline 
 \ \ $T_m$ (K)  & \ \ 269 & \ \ 265 & \ \ 271 &  297 & \ \ - & \ \ 278 & \ \ 273\\
 \ \ $T_b$ (K)  & \ \ 357 & \ \ 354 & \ \ 337 &  396 & \ \ - & \ \ 349 & \ \ 373\\
 \ \ $T_s$ (K)  & \ \ - & \ \ - & \ \ - &  - & \ \ 355 & \ \ - & \ \ -\\
@@ -401,9 +414,9 @@ long-range interaction correction. Units are kcal/mol.
 the energy difference attributed to the inclusion of the PME
 long-range interaction correction. Units are kcal/mol.}
 \begin{tabular}{ l  c  c  c  c }
-\hline \\[-7mm]
+\hline 
 \ \ Water Model \ \ & \ \ \ \ \ $I_h$ \ \ & \ \ \ \ \ $I_c$ \ \ & \ \quad \ \ \ \ B \ \ & \ \ \ \ \ Ice-{\it i} \ \ \\
-\hline \\[-3mm]
+\hline 
 \ \ TIP3P  & \ \ -11.53 & \ \ -11.24 & \ \ -11.51 & \ \ -11.67\\
 \ \ SPC/E  & \ \ -12.77 & \ \ -12.92 & \ \ -12.96 & \ \ -13.02\\
 \end{tabular}
