--- 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} %\documentclass[11pt]{article} -%\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}