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\usepackage{longtable} |
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\pagestyle{plain} |
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\pagenumbering{arabic} |
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\usepackage{floatrow} |
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\oddsidemargin 0.0cm |
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\evensidemargin 0.0cm |
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\topmargin -21pt |
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\usepackage[square, comma, sort&compress]{natbib} |
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\bibpunct{[}{]}{,}{n}{}{;} |
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\DeclareFloatFont{tiny}{\scriptsize}% "scriptsize" is defined by floatrow, "tiny" not |
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\floatsetup[table]{font=tiny} |
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|
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|
| 28 |
|
%\renewcommand\citemid{\ } % no comma in optional reference note |
| 29 |
< |
\lstset{language=C,frame=TB,basicstyle=\footnotesize,basicstyle=\ttfamily, % |
| 29 |
> |
\lstset{language=C,frame=TB,basicstyle=\footnotesize\ttfamily, % |
| 30 |
|
xleftmargin=0.25in, xrightmargin=0.25in,captionpos=b, % |
| 31 |
|
abovecaptionskip=0.5cm, belowcaptionskip=0.5cm, escapeinside={~}{~}} |
| 32 |
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\renewcommand{\lstlistingname}{Scheme} |
| 51 |
|
\newcolumntype{M}{p{1.55in}} |
| 52 |
|
|
| 53 |
|
|
| 54 |
< |
\title{{\sc OpenMD-2.1}: Molecular Dynamics in the Open} |
| 54 |
> |
\title{{\sc OpenMD-2.2}: Molecular Dynamics in the Open} |
| 55 |
|
|
| 56 |
|
\author{Joseph Michalka, James Marr, Kelsey Stocker, Madan Lamichhane, |
| 57 |
|
Patrick Louden, \\ |
| 843 |
|
|
| 844 |
|
\section{\label{section:frcFile}Force Field Files} |
| 845 |
|
|
| 846 |
< |
Force field files have a number of ``Blocks'' to demarkate different |
| 846 |
> |
Force field files have a number of ``Blocks'' to delineate different |
| 847 |
|
types of information. The blocks contain AtomType data, which provide |
| 848 |
|
properties belonging to a single AtomType, as well as interaction |
| 849 |
|
information which provides information about bonded or non-bonded |
| 850 |
|
interactions that cannot be deduced from AtomType information alone. |
| 851 |
|
A simple example of a forceField file is shown in scheme |
| 852 |
< |
\ref{sch:frcExample}. |
| 852 |
> |
\ref{sch:frcExample}. |
| 853 |
|
|
| 854 |
|
\begin{lstlisting}[float,caption={[An example of a complete OpenMD |
| 855 |
|
force field file for straight-chain united-atom alkanes.] An example |
| 856 |
|
showing a complete OpenMD force field for straight-chain united-atom |
| 857 |
|
alkanes.}, label={sch:frcExample}] |
| 858 |
|
begin Options |
| 859 |
< |
Name = "alkane" end |
| 860 |
< |
Options |
| 859 |
> |
Name = "alkane" |
| 860 |
> |
end Options |
| 861 |
|
|
| 862 |
|
begin BaseAtomTypes |
| 863 |
|
//name mass |
| 963 |
|
ability to print out the names of the base atom types for displaying |
| 964 |
|
simulations in Jmol or VMD. |
| 965 |
|
|
| 966 |
< |
\begin{lstlisting}[caption={[A simple example of a BaseAtomType |
| 967 |
< |
block.] A simple example of a BaseAtomType block.}, |
| 966 |
> |
\begin{lstlisting}[caption={[A simple example of a BaseAtomTypes |
| 967 |
> |
block.] A simple example of a BaseAtomTypes block.}, |
| 968 |
|
label={sch:baseAtomTypesBlock}] |
| 969 |
|
begin BaseAtomTypes |
| 970 |
|
//Name mass (amu) |
| 993 |
|
from the oxygen base type. |
| 994 |
|
|
| 995 |
|
\begin{lstlisting}[caption={[An example of a AtomTypes block.] A |
| 996 |
< |
simple example of an AtomType block which |
| 996 |
> |
simple example of an AtomTypes block which |
| 997 |
|
shows how multiple types can inherit from the same base type.}, |
| 998 |
|
label={sch:atomTypesBlock}] |
| 999 |
|
begin AtomTypes |
| 1022 |
|
\subsection{\label{section:ffDirectionalAtom}The DirectionalAtomTypes |
| 1023 |
|
block} |
| 1024 |
|
DirectionalAtoms have orientational degrees of freedom as well as |
| 1025 |
< |
translation, so they have moment of inertia tensors. |
| 1025 |
> |
translation, so moving these atoms requires information about the |
| 1026 |
> |
moments of inertias in the same way that translational motion requires |
| 1027 |
> |
mass. For DirectionalAtoms, OpenMD treats the mass distribution with |
| 1028 |
> |
higher priority than electrostatic distributions; the moment of |
| 1029 |
> |
inertia tensor, $\overleftrightarrow{\mathsf I}$, should be |
| 1030 |
> |
diagonalized to obtain body-fixed axes, and the three diagonal moments |
| 1031 |
> |
should correspond to rotational motion \textit{around} each of these |
| 1032 |
> |
body-fixed axes. Charge distributions may then result in dipole |
| 1033 |
> |
vectors that are oriented along a linear combination of the body-axes, |
| 1034 |
> |
and in quadrupole tensors that are not necessarily diagonal in the |
| 1035 |
> |
body frame. |
| 1036 |
|
|
| 1037 |
|
\begin{lstlisting}[caption={[An example of a DirectionalAtomTypes block.] A |
| 1038 |
|
simple example of a DirectionalAtomTypes block.}, |
| 1040 |
|
begin DirectionalAtomTypes |
| 1041 |
|
//Name I_xx I_yy I_zz (All moments in (amu*Ang^2) |
| 1042 |
|
SSD 1.7696 0.6145 1.1550 |
| 1029 |
– |
SSD_E 1.7696 0.6145 1.1550 |
| 1043 |
|
GBC6H6 88.781 88.781 177.561 |
| 1044 |
|
GBCH3OH 4.056 20.258 20.999 |
| 1045 |
|
GBH2O 1.777 0.581 1.196 |
| 1046 |
+ |
CO2 43.06 43.06 0.0 // single-site model for CO2 |
| 1047 |
|
end DirectionalAtomTypes |
| 1048 |
|
|
| 1049 |
|
\end{lstlisting} |
| 1050 |
|
|
| 1051 |
+ |
For a DirectionalAtom that represents a linear object, it is |
| 1052 |
+ |
appropriate for one of the moments of inertia to be zero. In this |
| 1053 |
+ |
case, OpenMD identifies that DirectionalAtom as having only 5 degrees |
| 1054 |
+ |
of freedom (three translations and two rotations), and will alter |
| 1055 |
+ |
calculation of temperatures to reflect this. |
| 1056 |
|
|
| 1057 |
|
\subsection{\label{section::ffAtomProperties}AtomType properties} |
| 1058 |
|
\subsubsection{\label{section:ffLJ}The LennardJonesAtomTypes block} |
| 1059 |
< |
The most basic interatomic interaction implemented in {\sc OpenMD} is |
| 1060 |
< |
the Lennard-Jones potential, which mimics the van der Waals |
| 1061 |
< |
interaction at long distances and uses an empirical repulsion at short |
| 1062 |
< |
distances. The Lennard-Jones potential is given by: |
| 1059 |
> |
One of the most basic interatomic interactions implemented in {\sc |
| 1060 |
> |
OpenMD} is the Lennard-Jones potential, which mimics the van der |
| 1061 |
> |
Waals interaction at long distances and uses an empirical repulsion at |
| 1062 |
> |
short distances. The Lennard-Jones potential is given by: |
| 1063 |
|
\begin{equation} |
| 1064 |
|
V_{\text{LJ}}(r_{ij}) = |
| 1065 |
|
4\epsilon_{ij} \biggl[ |
| 1074 |
|
|
| 1075 |
|
Interactions between dissimilar particles requires the generation of |
| 1076 |
|
cross term parameters for $\sigma$ and $\epsilon$. These parameters |
| 1077 |
< |
are determined using the Lorentz-Berthelot mixing |
| 1077 |
> |
are usually determined using the Lorentz-Berthelot mixing |
| 1078 |
|
rules:\cite{Allen87} |
| 1079 |
|
\begin{equation} |
| 1080 |
|
\sigma_{ij} = \frac{1}{2}[\sigma_{ii} + \sigma_{jj}], |
| 1086 |
|
\label{eq:epsilonMix} |
| 1087 |
|
\end{equation} |
| 1088 |
|
|
| 1089 |
< |
\subsubsection{\label{section:ffCharge}The ChargeAtomTypes block} |
| 1090 |
< |
\subsubsection{\label{section:ffMultipole}The MultipoleAtomTypes block} |
| 1091 |
< |
The dipole-dipole potential has the following form: |
| 1089 |
> |
The values of $\sigma_{ii}$ and $\epsilon_{ii}$ are properties of atom |
| 1090 |
> |
type $i$, and must be specified in a section of the force field file |
| 1091 |
> |
called the {\tt LennardJonesAtomTypes} block (see listing |
| 1092 |
> |
\ref{sch:LJatomTypesBlock}). Separate Lennard-Jones interactions |
| 1093 |
> |
which are not determined by the mixing rules can also be specified in |
| 1094 |
> |
the {\tt NonbondedInteractionTypes} block (see section |
| 1095 |
> |
\ref{section:ffNBinteraction}). |
| 1096 |
> |
|
| 1097 |
> |
\begin{lstlisting}[caption={[An example of a LennardJonesAtomTypes block.] A |
| 1098 |
> |
simple example of a LennardJonesAtomTypee block. Units for |
| 1099 |
> |
$\epsilon$ are kcal / mol and for $\sigma$ are \AA\ .}, |
| 1100 |
> |
label={sch:LJatomTypesBlock}] |
| 1101 |
> |
begin LennardJonesAtomTypes |
| 1102 |
> |
//Name epsilon sigma |
| 1103 |
> |
O_TIP4P 0.1550 3.15365 |
| 1104 |
> |
O_TIP4P-Ew 0.16275 3.16435 |
| 1105 |
> |
O_TIP5P 0.16 3.12 |
| 1106 |
> |
O_TIP5P-E 0.178 3.097 |
| 1107 |
> |
O_SPCE 0.15532 3.16549 |
| 1108 |
> |
O_SPC 0.15532 3.16549 |
| 1109 |
> |
CH4 0.279 3.73 |
| 1110 |
> |
CH3 0.185 3.75 |
| 1111 |
> |
CH2 0.0866 3.95 |
| 1112 |
> |
CH 0.0189 4.68 |
| 1113 |
> |
end LennardJonesAtomTypes |
| 1114 |
> |
\end{lstlisting} |
| 1115 |
> |
|
| 1116 |
> |
\subsubsection{\label{section:ffCharge}The ChargeAtomTypes block} |
| 1117 |
> |
|
| 1118 |
> |
In molecular simulations, proper accumulation of the electrostatic |
| 1119 |
> |
interactions is essential and is one of the most |
| 1120 |
> |
computationally-demanding tasks. Most common molecular mechanics |
| 1121 |
> |
force fields represent atomic sites with full or partial charges |
| 1122 |
> |
protected by Lennard-Jones (short range) interactions. Partial charge |
| 1123 |
> |
values, $q_i$ are empirical representations of the distribution of |
| 1124 |
> |
electronic charge in a molecule. This means that nearly every pair |
| 1125 |
> |
interaction involves a calculation of charge-charge forces. Coupled |
| 1126 |
> |
with relatively long-ranged $r^{-1}$ decay, the monopole interactions |
| 1127 |
> |
quickly become the most expensive part of molecular simulations. The |
| 1128 |
> |
interactions between point charges can be handled via a number of |
| 1129 |
> |
different algorithms, but Coulomb's law is the fundamental physical |
| 1130 |
> |
principle governing these interactions, |
| 1131 |
|
\begin{equation} |
| 1132 |
+ |
V_{\text{charge}}(r_{ij}) = \sum_{ij}\frac{q_iq_je^2}{4 \pi \epsilon_0 |
| 1133 |
+ |
r_{ij}}, |
| 1134 |
+ |
\end{equation} |
| 1135 |
+ |
where $q$ represents the charge on particle $i$ or $j$, and $e$ is the |
| 1136 |
+ |
charge of an electron in Coulombs. $\epsilon_0$ is the permittivity |
| 1137 |
+ |
of free space. |
| 1138 |
+ |
|
| 1139 |
+ |
\begin{lstlisting}[caption={[An example of a ChargeAtomTypes block.] A |
| 1140 |
+ |
simple example of a ChargeAtomTypes block. Units for |
| 1141 |
+ |
charge are in multiples of electron charge.}, |
| 1142 |
+ |
label={sch:ChargeAtomTypesBlock}] |
| 1143 |
+ |
begin ChargeAtomTypes |
| 1144 |
+ |
// Name charge |
| 1145 |
+ |
O_TIP3P -0.834 |
| 1146 |
+ |
O_SPCE -0.8476 |
| 1147 |
+ |
H_TIP3P 0.417 |
| 1148 |
+ |
H_TIP4P 0.520 |
| 1149 |
+ |
H_SPCE 0.4238 |
| 1150 |
+ |
EP_TIP4P -1.040 |
| 1151 |
+ |
Na+ 1.0 |
| 1152 |
+ |
Cl- -1.0 |
| 1153 |
+ |
end ChargeAtomTypes |
| 1154 |
+ |
\end{lstlisting} |
| 1155 |
+ |
|
| 1156 |
+ |
\subsubsection{\label{section:ffMultipole}The MultipoleAtomTypes |
| 1157 |
+ |
block} |
| 1158 |
+ |
For complex charge distributions that are centered on single sites, it |
| 1159 |
+ |
is convenient to write the total electrostatic potential in terms of |
| 1160 |
+ |
multipole moments, |
| 1161 |
+ |
\begin{equation} |
| 1162 |
+ |
U_{\bf{ab}}(r)=\hat{M}_{\bf a} \hat{M}_{\bf b} \frac{1}{r} \label{kernel}. |
| 1163 |
+ |
\end{equation} |
| 1164 |
+ |
where the multipole operator on site $\bf a$, |
| 1165 |
+ |
\begin{equation} |
| 1166 |
+ |
\hat{M}_{\bf a} = C_{\bf a} - D_{{\bf a}\alpha} \frac{\partial}{\partial r_{\alpha}} |
| 1167 |
+ |
+ Q_{{\bf a}\alpha\beta} |
| 1168 |
+ |
\frac{\partial^2}{\partial r_{\alpha} \partial r_{\beta}} + \dots |
| 1169 |
+ |
\end{equation} |
| 1170 |
+ |
Here, the point charge, dipole, and quadrupole for site $\bf a$ are |
| 1171 |
+ |
given by $C_{\bf a}$, $D_{{\bf a}\alpha}$, and $Q_{{\bf |
| 1172 |
+ |
a}\alpha\beta}$, respectively. These are the primitive |
| 1173 |
+ |
multipoles. If the site is representing a distribution of charges, |
| 1174 |
+ |
these can be expressed as, |
| 1175 |
+ |
\begin{align} |
| 1176 |
+ |
C_{\bf a} =&\sum_{k \, \text{in \bf a}} q_k , \label{eq:charge} \\ |
| 1177 |
+ |
D_{{\bf a}\alpha} =&\sum_{k \, \text{in \bf a}} q_k r_{k\alpha}, \label{eq:dipole}\\ |
| 1178 |
+ |
Q_{{\bf a}\alpha\beta} =& \frac{1}{2} \sum_{k \, \text{in \bf a}} q_k |
| 1179 |
+ |
r_{k\alpha} r_{k\beta} . \label{eq:quadrupole} |
| 1180 |
+ |
\end{align} |
| 1181 |
+ |
Note that the definition of the primitive quadrupole here differs from |
| 1182 |
+ |
the standard traceless form, and contains an additional Taylor-series |
| 1183 |
+ |
based factor of $1/2$. |
| 1184 |
+ |
|
| 1185 |
+ |
The details of the multipolar interactions will be given later, but |
| 1186 |
+ |
many readers are familiar with the dipole-dipole potential: |
| 1187 |
+ |
\begin{equation} |
| 1188 |
|
V_{\text{dipole}}(\mathbf{r}_{ij},\boldsymbol{\Omega}_{i}, |
| 1189 |
< |
\boldsymbol{\Omega}_{j}) = \frac{|\mu_i||\mu_j|}{4\pi\epsilon_{0}r_{ij}^{3}} \biggl[ |
| 1189 |
> |
\boldsymbol{\Omega}_{j}) = \frac{|{\bf D}_i||{\bf D}_j|}{4\pi\epsilon_{0}r_{ij}^{3}} \biggl[ |
| 1190 |
|
\boldsymbol{\hat{u}}_{i} \cdot \boldsymbol{\hat{u}}_{j} |
| 1191 |
|
- |
| 1192 |
|
3(\boldsymbol{\hat{u}}_i \cdot \hat{\mathbf{r}}_{ij}) % |
| 1196 |
|
Here $\mathbf{r}_{ij}$ is the vector starting at atom $i$ pointing |
| 1197 |
|
towards $j$, and $\boldsymbol{\Omega}_i$ and $\boldsymbol{\Omega}_j$ |
| 1198 |
|
are the orientational degrees of freedom for atoms $i$ and $j$ |
| 1199 |
< |
respectively. The magnitude of the dipole moment of atom $i$ is |
| 1200 |
< |
$|\mu_i|$, $\boldsymbol{\hat{u}}_i$ is the standard unit orientation |
| 1199 |
> |
respectively. The magnitude of the dipole moment of atom $i$ is $|{\bf |
| 1200 |
> |
D}_i|$, $\boldsymbol{\hat{u}}_i$ is the standard unit orientation |
| 1201 |
|
vector of $\boldsymbol{\Omega}_i$, and $\boldsymbol{\hat{r}}_{ij}$ is |
| 1202 |
|
the unit vector pointing along $\mathbf{r}_{ij}$ |
| 1203 |
|
($\boldsymbol{\hat{r}}_{ij}=\mathbf{r}_{ij}/|\mathbf{r}_{ij}|$). |
| 1204 |
|
|
| 1205 |
+ |
|
| 1206 |
+ |
\begin{lstlisting}[caption={[An example of a MultipoleAtomTypes block.] A |
| 1207 |
+ |
simple example of a MultipoleAtomTypes block. Dipoles are given in |
| 1208 |
+ |
units of Debyes, and Quadrupole moments are given in units of Debye |
| 1209 |
+ |
\AA~(or $10^{-26} \mathrm{~esu~cm}^2$)}, |
| 1210 |
+ |
label={sch:MultipoleAtomTypesBlock}] |
| 1211 |
+ |
begin MultipoleAtomTypes |
| 1212 |
+ |
// Euler angles are given in zxz convention in units of degrees. |
| 1213 |
+ |
// |
| 1214 |
+ |
// point dipoles: |
| 1215 |
+ |
// name d phi theta psi dipole_moment |
| 1216 |
+ |
DIP d 0.0 0.0 0.0 1.91 // dipole points along z-body axis |
| 1217 |
+ |
// |
| 1218 |
+ |
// point quadrupoles: |
| 1219 |
+ |
// name q phi theta psi Qxx Qyy Qzz |
| 1220 |
+ |
CO2 q 0.0 0.0 0.0 0.0 0.0 -0.430592 //quadrupole tensor has zz element |
| 1221 |
+ |
// |
| 1222 |
+ |
// Atoms with both dipole and quadrupole moments: |
| 1223 |
+ |
// name dq phi theta psi dipole_moment Qxx Qyy Qzz |
| 1224 |
+ |
SSD dq 0.0 0.0 0.0 2.35 -1.682 1.762 -0.08 |
| 1225 |
+ |
end MultipoleAtomTypes |
| 1226 |
+ |
\end{lstlisting} |
| 1227 |
+ |
|
| 1228 |
+ |
Specifying a MultipoleAtomType requires declaring how the |
| 1229 |
+ |
electrostatic frame for the site is rotated relative to the body-fixed |
| 1230 |
+ |
axes for that atom. The Euler angles $(\phi, \theta, \psi)$ for this |
| 1231 |
+ |
rotation must be given, and then the dipole, quadrupole, or all of |
| 1232 |
+ |
these moments are specified in the electrostatic frame. In OpenMD, |
| 1233 |
+ |
the Euler angles are specified in the $zxz$ convention and are entered |
| 1234 |
+ |
in units of degrees. Dipole moments are entered in units of Debye, |
| 1235 |
+ |
and Quadrupole moments in units of Debye \AA. |
| 1236 |
+ |
|
| 1237 |
|
\subsubsection{\label{section:ffGB}The FluctuatingChargeAtomTypes block} |
| 1238 |
|
\subsubsection{\label{section:ffPol}The PolarizableAtomTypes block} |
| 1239 |
|
\subsubsection{\label{section:ffGB}The GayBerneAtomTypes block} |
| 1240 |
+ |
|
| 1241 |
+ |
The Gay-Berne potential has been widely used in the liquid crystal |
| 1242 |
+ |
community to describe this anisotropic phase |
| 1243 |
+ |
behavior.~\cite{Gay:1981yu,Berne:1972pb,Kushick:1976xy,Luckhurst:1990fy,Cleaver:1996rt} |
| 1244 |
+ |
The form of the Gay-Berne potential implemented in OpenMD was |
| 1245 |
+ |
generalized by Cleaver {\it et al.} and is appropriate for dissimilar |
| 1246 |
+ |
uniaxial ellipsoids.\cite{Cleaver:1996rt} The potential is constructed in the |
| 1247 |
+ |
familiar form of the Lennard-Jones function using |
| 1248 |
+ |
orientation-dependent $\sigma$ and $\epsilon$ parameters, |
| 1249 |
+ |
\begin{equation*} |
| 1250 |
+ |
V_{ij}({{\bf \hat u}_i}, {{\bf \hat u}_j}, {{\bf \hat |
| 1251 |
+ |
r}_{ij}}) = 4\epsilon ({{\bf \hat u}_i}, {{\bf \hat u}_j}, |
| 1252 |
+ |
{{\bf \hat r}_{ij}})\left[\left(\frac{\sigma_0}{r_{ij}-\sigma({{\bf \hat u |
| 1253 |
+ |
}_i}, |
| 1254 |
+ |
{{\bf \hat u}_j}, {{\bf \hat r}_{ij}})+\sigma_0}\right)^{12} |
| 1255 |
+ |
-\left(\frac{\sigma_0}{r_{ij}-\sigma({{\bf \hat u}_i}, {{\bf \hat u}_j}, |
| 1256 |
+ |
{{\bf \hat r}_{ij}})+\sigma_0}\right)^6\right] |
| 1257 |
+ |
\label{eq:gb} |
| 1258 |
+ |
\end{equation*} |
| 1259 |
+ |
|
| 1260 |
+ |
The range $(\sigma({\bf \hat{u}}_{i},{\bf \hat{u}}_{j},{\bf |
| 1261 |
+ |
\hat{r}}_{ij}))$, and strength $(\epsilon({\bf \hat{u}}_{i},{\bf |
| 1262 |
+ |
\hat{u}}_{j},{\bf \hat{r}}_{ij}))$ parameters |
| 1263 |
+ |
are dependent on the relative orientations of the two ellipsoids (${\bf |
| 1264 |
+ |
\hat{u}}_{i},{\bf \hat{u}}_{j}$) as well as the direction of the |
| 1265 |
+ |
inter-ellipsoid separation (${\bf \hat{r}}_{ij}$). The shape and |
| 1266 |
+ |
attractiveness of each ellipsoid is governed by a relatively small set |
| 1267 |
+ |
of parameters: |
| 1268 |
+ |
\begin{itemize} |
| 1269 |
+ |
\item $d$: range parameter for the side-by-side (S) and cross (X) configurations |
| 1270 |
+ |
\item $l$: range parameter for the end-to-end (E) configuration |
| 1271 |
+ |
\item $\epsilon_X$: well-depth parameter for the cross (X) configuration |
| 1272 |
+ |
\item $\epsilon_S$: well-depth parameter for the side-by-side (S) configuration |
| 1273 |
+ |
\item $\epsilon_E$: well depth parameter for the end-to-end (E) configuration |
| 1274 |
+ |
\item $dw$: The ``softness'' of the potential |
| 1275 |
+ |
\end{itemize} |
| 1276 |
+ |
Additionally, there are two universal paramters to govern the overall |
| 1277 |
+ |
importance of the purely orientational ($\nu$) and the mixed |
| 1278 |
+ |
orientational / translational ($\mu$) parts of strength of the |
| 1279 |
+ |
interactions. These parameters have default or ``canonical'' values, |
| 1280 |
+ |
but may be changed as a force field option: |
| 1281 |
+ |
\begin{itemize} |
| 1282 |
+ |
\item $\nu$: purely orientational part : defaults to 1 |
| 1283 |
+ |
\item $\mu$: mixed orientational / translational part : defaults to |
| 1284 |
+ |
2 |
| 1285 |
+ |
\end{itemize} |
| 1286 |
+ |
Further details of the potential are given |
| 1287 |
+ |
elsewhere,\cite{Luckhurst:1990fy,Golubkov06,SunX._jp0762020} and an |
| 1288 |
+ |
excellent overview of the computational methods that can be used to |
| 1289 |
+ |
efficiently compute forces and torques for this potential can be found |
| 1290 |
+ |
in Ref. \citealp{Golubkov06} |
| 1291 |
+ |
|
| 1292 |
+ |
\begin{lstlisting}[caption={[An example of a GayBerneAtomTypes block.] A |
| 1293 |
+ |
simple example of a GayBerneAtomTypes block. Distances ($d$ and $l$) |
| 1294 |
+ |
are given in \AA\ and energies ($\epsilon_X, \epsilon_S, \epsilon_E$) |
| 1295 |
+ |
are in units of kcal/mol. $dw$ is unitless.}, |
| 1296 |
+ |
label={sch:GayBerneAtomTypes}] |
| 1297 |
+ |
begin GayBerneAtomTypes |
| 1298 |
+ |
//Name d l eps_X eps_S eps_E dw |
| 1299 |
+ |
GBlinear 2.8104 9.993 0.774729 0.774729 0.116839 1.0 |
| 1300 |
+ |
GBC6H6 4.65 2.03 0.540 0.540 1.9818 0.6 |
| 1301 |
+ |
GBCH3OH 2.55 3.18 0.542 0.542 0.55826 1.0 |
| 1302 |
+ |
end GayBerneAtomTypes |
| 1303 |
+ |
\end{lstlisting} |
| 1304 |
+ |
|
| 1305 |
|
\subsubsection{\label{section:ffSticky}The StickyAtomTypes block} |
| 1306 |
|
|
| 1307 |
< |
One of the solvents used by {\sc OpenMD} is the extended Soft Sticky |
| 1308 |
< |
Dipole (SSD/E) water model.\cite{fennell04} The original SSD was |
| 1309 |
< |
developed by Ichiye \emph{et al.}\cite{liu96:new_model} as a modified |
| 1310 |
< |
form of the hard-sphere water model proposed by Bratko, Blum, and |
| 1307 |
> |
One of the solvents that can be simulated by {\sc OpenMD} is the |
| 1308 |
> |
extended Soft Sticky Dipole (SSD/E) water model.\cite{fennell04} The |
| 1309 |
> |
original SSD was developed by Ichiye \emph{et |
| 1310 |
> |
al.}\cite{liu96:new_model} as a modified form of the hard-sphere |
| 1311 |
> |
water model proposed by Bratko, Blum, and |
| 1312 |
|
Luzar.\cite{Bratko85,Bratko95} It consists of a single point dipole |
| 1313 |
|
with a Lennard-Jones core and a sticky potential that directs the |
| 1314 |
|
particles to assume the proper hydrogen bond orientation in the first |
| 1391 |
|
|
| 1392 |
|
Recent constant pressure simulations revealed issues in the original |
| 1393 |
|
SSD model that led to lower than expected densities at all target |
| 1394 |
< |
pressures.\cite{Ichiye03,fennell04} The default model in {\sc OpenMD} |
| 1395 |
< |
is therefore SSD/E, a density corrected derivative of SSD that |
| 1396 |
< |
exhibits improved liquid structure and transport behavior. If the use |
| 1397 |
< |
of a reaction field long-range interaction correction is desired, it |
| 1398 |
< |
is recommended that the parameters be modified to those of the SSD/RF |
| 1399 |
< |
model (an SSD variant parameterized for reaction field). These solvent |
| 1188 |
< |
parameters are listed and can be easily modified in the {\sc duff} |
| 1189 |
< |
force field file ({\tt DUFF.frc}). A table of the parameter values |
| 1190 |
< |
and the drawbacks and benefits of the different density corrected SSD |
| 1191 |
< |
models can be found in reference~\cite{fennell04}. |
| 1394 |
> |
pressures,\cite{Ichiye03,fennell04} so variants on the sticky |
| 1395 |
> |
potential can be specified by using one of a number of substitute atom |
| 1396 |
> |
types (see listing \ref{sch:StickyAtomTypes}). A table of the |
| 1397 |
> |
parameter values and the drawbacks and benefits of the different |
| 1398 |
> |
density corrected SSD models can be found in |
| 1399 |
> |
reference~\citealp{fennell04}. |
| 1400 |
|
|
| 1401 |
< |
\subsection{\label{section::ffMetals}Metallic Atom Types} |
| 1402 |
< |
\subsubsection{\label{section:ffEAM}The EAMAtomTypes block} |
| 1403 |
< |
{\sc OpenMD} implements a potential that describes bonding in |
| 1404 |
< |
transition metal |
| 1405 |
< |
systems.~\cite{Finnis84,Ercolessi88,Chen90,Qi99,Ercolessi02} This |
| 1406 |
< |
potential has an attractive interaction which models ``Embedding'' a |
| 1407 |
< |
positively charged pseudo-atom core in the electron density due to the |
| 1408 |
< |
free valance ``sea'' of electrons created by the surrounding atoms in |
| 1409 |
< |
the system. A pairwise part of the potential (which is primarily |
| 1410 |
< |
repulsive) describes the interaction of the positively charged metal |
| 1411 |
< |
core ions with one another. The Embedded Atom Method ({\sc |
| 1412 |
< |
eam})~\cite{Daw84,FBD86,johnson89,Lu97} has been widely adopted in the |
| 1413 |
< |
materials science community and has been included in {\sc OpenMD}. A |
| 1206 |
< |
good review of {\sc eam} and other formulations of metallic potentials |
| 1207 |
< |
was given by Voter.\cite{Voter:95} |
| 1401 |
> |
\begin{lstlisting}[caption={[An example of a StickyAtomTypes block.] A |
| 1402 |
> |
simple example of a StickyAtomTypes block. Distances ($r_l$, $r_u$, |
| 1403 |
> |
$r_{l}'$ and $r_{u}'$) are given in \AA\ and energies ($v_0, v_{0}'$) |
| 1404 |
> |
are in units of kcal/mol. $w_0$ is unitless.}, |
| 1405 |
> |
label={sch:StickyAtomTypes}] |
| 1406 |
> |
begin StickyAtomTypes |
| 1407 |
> |
//name w0 v0 (kcal/mol) v0p rl (Ang) ru rlp rup |
| 1408 |
> |
SSD_E 0.07715 3.90 3.90 2.40 3.80 2.75 3.35 |
| 1409 |
> |
SSD_RF 0.07715 3.90 3.90 2.40 3.80 2.75 3.35 |
| 1410 |
> |
SSD 0.07715 3.7284 3.7284 2.75 3.35 2.75 4.0 |
| 1411 |
> |
SSD1 0.07715 3.6613 3.6613 2.75 3.35 2.75 4.0 |
| 1412 |
> |
end StickyAtomTypes |
| 1413 |
> |
\end{lstlisting} |
| 1414 |
|
|
| 1415 |
< |
The {\sc eam} potential has the form: |
| 1415 |
> |
\subsection{\label{section::ffMetals}Metallic Atom Types} |
| 1416 |
> |
|
| 1417 |
> |
{\sc OpenMD} implements a number of related potentials that describe |
| 1418 |
> |
bonding in transition metals. These potentials have an attractive |
| 1419 |
> |
interaction which models ``Embedding'' a positively charged |
| 1420 |
> |
pseudo-atom core in the electron density due to the free valance |
| 1421 |
> |
``sea'' of electrons created by the surrounding atoms in the system. |
| 1422 |
> |
A pairwise part of the potential (which is primarily repulsive) |
| 1423 |
> |
describes the interaction of the positively charged metal core ions |
| 1424 |
> |
with one another. These potentials have the form: |
| 1425 |
|
\begin{equation} |
| 1426 |
|
V = \sum_{i} F_{i}\left[\rho_{i}\right] + \sum_{i} \sum_{j \neq i} |
| 1427 |
|
\phi_{ij}({\bf r}_{ij}) |
| 1438 |
|
transition metal potentials require two loops through the atom pairs |
| 1439 |
|
to compute the inter-atomic forces. |
| 1440 |
|
|
| 1441 |
< |
The pairwise portion of the potential, $\phi_{ij}$, is a primarily |
| 1442 |
< |
repulsive interaction between atoms $i$ and $j$. In the original |
| 1228 |
< |
formulation of {\sc eam}\cite{Daw84}, $\phi_{ij}$ was an entirely |
| 1229 |
< |
repulsive term; however later refinements to {\sc eam} allowed for |
| 1230 |
< |
more general forms for $\phi$.\cite{Daw89} The effective cutoff |
| 1231 |
< |
distance, $r_{{\text cut}}$ is the distance at which the values of |
| 1232 |
< |
$f(r)$ and $\phi(r)$ drop to zero for all atoms present in the |
| 1233 |
< |
simulation. In practice, this distance is fairly small, limiting the |
| 1234 |
< |
summations in the {\sc eam} equation to the few dozen atoms |
| 1235 |
< |
surrounding atom $i$ for both the density $\rho$ and pairwise $\phi$ |
| 1236 |
< |
interactions. |
| 1441 |
> |
The pairwise portion of the potential, $\phi_{ij}$, is usually a |
| 1442 |
> |
repulsive interaction between atoms $i$ and $j$. |
| 1443 |
|
|
| 1444 |
< |
In computing forces for alloys, mixing rules as outlined by |
| 1445 |
< |
Johnson~\cite{johnson89} are used to compute the heterogenous pair |
| 1446 |
< |
potential, |
| 1444 |
> |
\subsubsection{\label{section:ffEAM}The EAMAtomTypes block} |
| 1445 |
> |
The Embedded Atom Method ({\sc eam}) is one of the most widely-used |
| 1446 |
> |
potentials for transition |
| 1447 |
> |
metals.~\cite{Finnis84,Ercolessi88,Chen90,Qi99,Ercolessi02,Daw84,FBD86,johnson89,Lu97} |
| 1448 |
> |
It has been widely adopted in the materials science community and a |
| 1449 |
> |
good review of {\sc eam} and other formulations of metallic potentials |
| 1450 |
> |
was given by Voter.\cite{Voter:95} |
| 1451 |
> |
|
| 1452 |
> |
In the original formulation of {\sc eam}\cite{Daw84}, the pair |
| 1453 |
> |
potential, $\phi_{ij}$ was an entirely repulsive term; however later |
| 1454 |
> |
refinements to {\sc eam} allowed for more general forms for |
| 1455 |
> |
$\phi$.\cite{Daw89} The effective cutoff distance, $r_{{\text cut}}$ |
| 1456 |
> |
is the distance at which the values of $f(r)$ and $\phi(r)$ drop to |
| 1457 |
> |
zero for all atoms present in the simulation. In practice, this |
| 1458 |
> |
distance is fairly small, limiting the summations in the {\sc eam} |
| 1459 |
> |
equation to the few dozen atoms surrounding atom $i$ for both the |
| 1460 |
> |
density $\rho$ and pairwise $\phi$ interactions. |
| 1461 |
> |
|
| 1462 |
> |
In computing forces for alloys, OpenMD uses mixing rules outlined by |
| 1463 |
> |
Johnson~\cite{johnson89} to compute the heterogenous pair potential, |
| 1464 |
|
\begin{equation} |
| 1465 |
|
\label{eq:johnson} |
| 1466 |
|
\phi_{ab}(r)=\frac{1}{2}\left( |
| 1491 |
|
should be noted that the energy units in these files are in eV, not |
| 1492 |
|
$\mbox{kcal mol}^{-1}$ as in the rest of the {\sc OpenMD} force field |
| 1493 |
|
files. |
| 1494 |
+ |
|
| 1495 |
+ |
\begin{lstlisting}[caption={[An example of a EAMAtomTypes block.] A |
| 1496 |
+ |
simple example of a EAMAtomTypes block. Here the only data provided is |
| 1497 |
+ |
the name of a {\tt funcfl} file which contains the raw data for spline |
| 1498 |
+ |
interpolations for the density, functional, and pair potential.}, |
| 1499 |
+ |
label={sch:EAMAtomTypes}] |
| 1500 |
+ |
begin EAMAtomTypes |
| 1501 |
+ |
Au Au.u3.funcfl |
| 1502 |
+ |
Ag Ag.u3.funcfl |
| 1503 |
+ |
Cu Cu.u3.funcfl |
| 1504 |
+ |
Ni Ni.u3.funcfl |
| 1505 |
+ |
Pd Pd.u3.funcfl |
| 1506 |
+ |
Pt Pt.u3.funcfl |
| 1507 |
+ |
end EAMAtomTypes |
| 1508 |
+ |
\end{lstlisting} |
| 1509 |
|
|
| 1510 |
+ |
|
| 1511 |
|
\subsubsection{\label{section:ffSC}The SuttonChenAtomTypes block} |
| 1512 |
|
|
| 1513 |
|
The Sutton-Chen ({\sc sc})~\cite{Chen90} potential has been used to |
| 1514 |
< |
study a wide range of phenomena in metals. Although it is similar in |
| 1515 |
< |
form to the {\sc eam} potential, the Sutton-Chen model takes on a |
| 1516 |
< |
simpler form, |
| 1514 |
> |
study a wide range of phenomena in metals. Although it has the same |
| 1515 |
> |
basic form as the {\sc eam} potential, the Sutton-Chen model takes on |
| 1516 |
> |
a simpler form, |
| 1517 |
|
\begin{equation} |
| 1518 |
|
\label{eq:SCP1} |
| 1519 |
|
U_{tot}=\sum _{i}\left[ \frac{1}{2}\sum _{j\neq |
| 1520 |
< |
i}D_{ij}V^{pair}_{ij}(r_{ij})-c_{i}D_{ii}\sqrt{\rho_{i}}\right] , |
| 1520 |
> |
i}\epsilon_{ij}V^{pair}_{ij}(r_{ij})-c_{i}\epsilon_{ii}\sqrt{\rho_{i}}\right] , |
| 1521 |
|
\end{equation} |
| 1522 |
|
where $V^{pair}_{ij}$ and $\rho_{i}$ are given by |
| 1523 |
|
\begin{equation} |
| 1524 |
|
\label{eq:SCP2} |
| 1525 |
|
V^{pair}_{ij}(r)=\left( |
| 1526 |
< |
\frac{\alpha_{ij}}{r_{ij}}\right)^{n_{ij}}, \rho_{i}=\sum_{j\neq i}\left( |
| 1526 |
> |
\frac{\alpha_{ij}}{r_{ij}}\right)^{n_{ij}} \hspace{1in} \rho_{i}=\sum_{j\neq i}\left( |
| 1527 |
|
\frac{\alpha_{ij}}{r_{ij}}\right) ^{m_{ij}} |
| 1528 |
|
\end{equation} |
| 1529 |
|
|
| 1531 |
|
interactions of the pseudo-atom cores. The $\sqrt{\rho_i}$ term in |
| 1532 |
|
Eq. (\ref{eq:SCP1}) is an attractive many-body potential that models |
| 1533 |
|
the interactions between the valence electrons and the cores of the |
| 1534 |
< |
pseudo-atoms. $D_{ij}$, $D_{ii}$, $c_i$ and $\alpha_{ij}$ are |
| 1535 |
< |
parameters used to tune the potential for different transition |
| 1536 |
< |
metals. |
| 1534 |
> |
pseudo-atoms. $\epsilon_{ij}$, $\epsilon_{ii}$, $c_i$ and |
| 1535 |
> |
$\alpha_{ij}$ are parameters used to tune the potential for different |
| 1536 |
> |
transition metals. |
| 1537 |
|
|
| 1538 |
|
The {\sc sc} potential form has also been parameterized by Qi {\it et |
| 1539 |
|
al.}\cite{Qi99} These parameters were obtained via empirical and {\it |
| 1540 |
|
ab initio} calculations to match structural features of the FCC |
| 1541 |
< |
crystal. To specify the original Sutton-Chen variant of the {\sc sc} |
| 1542 |
< |
force field, the user would add the {\tt forceFieldVariant = "SC";} |
| 1304 |
< |
line to the meta-data file, while specification of the Qi {\it et al.} |
| 1305 |
< |
quantum-adapted variant of the {\sc sc} potential, the user would add |
| 1306 |
< |
the {\tt forceFieldVariant = "QSC";} line to the meta-data file. |
| 1541 |
> |
crystal. Interested readers are encouraged to consult reference |
| 1542 |
> |
\citealp{Qi99} for further details. |
| 1543 |
|
|
| 1544 |
+ |
\begin{lstlisting}[caption={[An example of a SCAtomTypes block.] A |
| 1545 |
+ |
simple example of a SCAtomTypes block. Distances ($\alpha$) |
| 1546 |
+ |
are given in \AA\ and energies ($\epsilon$) are (by convention) given in |
| 1547 |
+ |
units of eV. These units must be specified in the {\tt Options} block |
| 1548 |
+ |
using the keyword {\tt MetallicEnergyUnitScaling}. Without this {\tt |
| 1549 |
+ |
Options} keyword, the default units for $\epsilon$ are kcal/mol. The |
| 1550 |
+ |
other parameters, $m$, $n$, and $c$ are unitless.}, |
| 1551 |
+ |
label={sch:SCAtomTypes}] |
| 1552 |
+ |
begin SCAtomTypes |
| 1553 |
+ |
// Name epsilon(eV) c m n alpha(angstroms) |
| 1554 |
+ |
Ni 0.0073767 84.745 5.0 10.0 3.5157 |
| 1555 |
+ |
Cu 0.0057921 84.843 5.0 10.0 3.6030 |
| 1556 |
+ |
Rh 0.0024612 305.499 5.0 13.0 3.7984 |
| 1557 |
+ |
Pd 0.0032864 148.205 6.0 12.0 3.8813 |
| 1558 |
+ |
Ag 0.0039450 96.524 6.0 11.0 4.0691 |
| 1559 |
+ |
Ir 0.0037674 224.815 6.0 13.0 3.8344 |
| 1560 |
+ |
Pt 0.0097894 71.336 7.0 11.0 3.9163 |
| 1561 |
+ |
Au 0.0078052 53.581 8.0 11.0 4.0651 |
| 1562 |
+ |
Au2 0.0078052 53.581 8.0 11.0 4.0651 |
| 1563 |
+ |
end SCAtomTypes |
| 1564 |
+ |
\end{lstlisting} |
| 1565 |
+ |
|
| 1566 |
|
\subsection{\label{section::ffShortRange}Short Range Interactions} |
| 1567 |
|
\subsubsection{\label{section:ffBond}The BondTypes block} |
| 1568 |
|
\subsubsection{\label{section:ffBend}The BendTypes block} |
| 1613 |
|
|
| 1614 |
|
\subsubsection{\label{section:ffInversion}The InversionTypes block} |
| 1615 |
|
\subsection{\label{section::ffLongRange}Long Range Interactions} |
| 1616 |
< |
\subsubsection{\label{section:ffInversion}The NonBondedInteraction block} |
| 1616 |
> |
\subsubsection{\label{section:ffNBinteraction}The NonBondedInteraction block} |
| 1617 |
|
|
| 1618 |
|
|
| 1619 |
|
|
