| 10 |
|
\pagestyle{plain} |
| 11 |
|
\pagenumbering{arabic} |
| 12 |
|
\usepackage{floatrow} |
| 13 |
+ |
\usepackage[margin=0.5cm,font=small,format=hang]{caption} |
| 14 |
+ |
|
| 15 |
|
\oddsidemargin 0.0cm |
| 16 |
|
\evensidemargin 0.0cm |
| 17 |
|
\topmargin -21pt |
| 31 |
|
\lstset{language=C,frame=TB,basicstyle=\footnotesize\ttfamily, % |
| 32 |
|
xleftmargin=0.25in, xrightmargin=0.25in,captionpos=b, % |
| 33 |
|
abovecaptionskip=0.5cm, belowcaptionskip=0.5cm, escapeinside={~}{~}} |
| 34 |
< |
\renewcommand{\lstlistingname}{Scheme} |
| 34 |
> |
\renewcommand{\lstlistingname}{Example} |
| 35 |
|
|
| 36 |
+ |
\lstnewenvironment{code}[1][]% |
| 37 |
+ |
{\noindent\minipage{\linewidth}\vspace{0.5\baselineskip} |
| 38 |
+ |
\lstset{language=C,basicstyle=\footnotesize\ttfamily,% |
| 39 |
+ |
captionpos=b,aboveskip=0.5cm,belowskip=0.5cm,abovecaptionskip=0.5cm,% |
| 40 |
+ |
belowcaptionskip=0.5cm,% |
| 41 |
+ |
escapeinside={~}{~},frame=single,#1}} |
| 42 |
+ |
{\endminipage} |
| 43 |
+ |
|
| 44 |
+ |
|
| 45 |
+ |
|
| 46 |
|
\begin{document} |
| 47 |
|
|
| 48 |
|
\newcolumntype{A}{p{1.5in}} |
| 197 |
|
$<$Snapshot$>$} block. Both the {\tt $<$MetaData$>$} and {\tt $<$Snapshot$>$} |
| 198 |
|
formats are described in the following sections. |
| 199 |
|
|
| 200 |
< |
\begin{lstlisting}[float,caption={[The structure of an {\sc OpenMD} file] |
| 200 |
> |
\begin{code}[caption={[The structure of an {\sc OpenMD} file] |
| 201 |
|
The basic structure of an {\sc OpenMD} file contains HTML-like tags to |
| 202 |
|
define simulation meta-data and subsequent instantaneous configuration |
| 203 |
< |
information. A well-formed {\sc OpenMD} file must contain one $<$MetaData$>$ |
| 204 |
< |
block and {\it at least one} $<$Snapshot$>$ block. Each |
| 205 |
< |
$<$Snapshot$>$ is further divided into $<$FrameData$>$ and |
| 206 |
< |
$<$StuntDoubles$>$ sections.}, |
| 195 |
< |
label=sch:mdFormat] |
| 203 |
> |
information. A well-formed {\sc OpenMD} file must contain one {\tt <MetaData>} |
| 204 |
> |
block and {\it at least one} {\tt <Snapshot>} block. Each |
| 205 |
> |
{\tt <Snapshot>} is further divided into {\tt <FrameData>} and |
| 206 |
> |
{\tt <StuntDoubles>} sections.},label={sch:mdFormat}] |
| 207 |
|
<OpenMD> |
| 208 |
|
<MetaData> |
| 209 |
|
// see section ~\ref{sec:miscConcepts}~ for details on the formatting |
| 229 |
|
<Snapshot> // Further information on <Snapshot> blocks |
| 230 |
|
</Snapshot> // can be found in section ~\ref{section:coordFiles}~. |
| 231 |
|
</OpenMD> |
| 232 |
< |
\end{lstlisting} |
| 232 |
> |
\end{code} |
| 233 |
|
|
| 234 |
|
|
| 235 |
|
\section{OpenMD Files and $<$MetaData$>$ blocks} |
| 245 |
|
shown in Scheme~\ref{sch:mdFormat} and example file is shown in |
| 246 |
|
Scheme~\ref{sch:mdExample}. |
| 247 |
|
|
| 248 |
< |
\begin{lstlisting}[float,caption={[An example of a complete OpenMD |
| 248 |
> |
\begin{code}[caption={[An example of a complete OpenMD |
| 249 |
|
file] An example showing a complete OpenMD file.}, |
| 250 |
|
label={sch:mdExample}] |
| 251 |
|
<OpenMD> |
| 284 |
|
</StuntDoubles> |
| 285 |
|
</Snapshot> |
| 286 |
|
</OpenMD> |
| 287 |
< |
\end{lstlisting} |
| 287 |
> |
\end{code} |
| 288 |
|
|
| 289 |
|
Within the {\tt $<$MetaData$>$} block it is necessary to provide a |
| 290 |
|
complete description of the molecule before it is actually placed in |
| 298 |
|
Scheme~\ref{sch:mdIncludeExample}, and the new {\sc OpenMD} file would |
| 299 |
|
become Scheme~\ref{sch:mdExPrime}. |
| 300 |
|
|
| 301 |
< |
\begin{lstlisting}[float,caption={An example molecule definition in an |
| 301 |
> |
\begin{code}[caption={An example molecule definition in an |
| 302 |
|
include file.},label={sch:mdIncludeExample}] |
| 303 |
|
molecule{ |
| 304 |
|
name = "Ar"; |
| 307 |
|
position( 0.0, 0.0, 0.0 ); |
| 308 |
|
} |
| 309 |
|
} |
| 310 |
< |
\end{lstlisting} |
| 310 |
> |
\end{code} |
| 311 |
|
|
| 312 |
< |
\begin{lstlisting}[float,caption={Revised OpenMD input file |
| 312 |
> |
\begin{code}[caption={Revised OpenMD input file |
| 313 |
|
example.},label={sch:mdExPrime}] |
| 314 |
|
<OpenMD> |
| 315 |
|
<MetaData> |
| 342 |
|
</StuntDoubles> |
| 343 |
|
</Snapshot> |
| 344 |
|
</OpenMD> |
| 345 |
< |
\end{lstlisting} |
| 345 |
> |
\end{code} |
| 346 |
|
|
| 347 |
|
\section{\label{section:atomsMolecules}Atoms, Molecules, and other |
| 348 |
|
ways of grouping atoms} |
| 413 |
|
rigid body can be seen in Scheme |
| 414 |
|
\ref{sch:rigidBody}. |
| 415 |
|
|
| 416 |
< |
\begin{lstlisting}[float,caption={[Defining rigid bodies]A sample |
| 416 |
> |
\begin{code}[caption={[Defining rigid bodies]A sample |
| 417 |
|
definition of a molecule containing a rigid body and a cutoff |
| 418 |
|
group},label={sch:rigidBody}] |
| 419 |
|
molecule{ |
| 439 |
|
members(0, 1, 2); |
| 440 |
|
} |
| 441 |
|
} |
| 442 |
< |
\end{lstlisting} |
| 442 |
> |
\end{code} |
| 443 |
|
|
| 444 |
|
\section{\label{sec:miscConcepts}Creating a $<$MetaData$>$ block} |
| 445 |
|
|
| 647 |
|
complete rotation matrix, directional entities are written out using |
| 648 |
|
quaternions to save space in the output files. |
| 649 |
|
|
| 650 |
< |
\begin{lstlisting}[float,caption={[The format of the {\tt $<$Snapshot$>$} block] |
| 650 |
> |
\begin{code}[caption={[The format of the {\tt $<$Snapshot$>$} block] |
| 651 |
|
An example of the format of the {\tt $<$Snapshot$>$} block. There is an |
| 652 |
|
initial sub-block called {\tt $<$FrameData$>$} which contains the time |
| 653 |
|
stamp, the three column vectors of $\mathsf{H}$, and optional extra |
| 656 |
|
configuration of each integrable object. For each integrable object, |
| 657 |
|
the global index is followed by a short string describing what |
| 658 |
|
additional information is present on the line. Atoms with only |
| 659 |
< |
position and velocity information use the ``pv'' string which must |
| 659 |
> |
position and velocity information use the {\tt pv} string which must |
| 660 |
|
then be followed by the position and velocity vectors for that atom. |
| 661 |
< |
Directional atoms and Rigid Bodies typically use the ``pvqj'' string |
| 661 |
> |
Directional atoms and Rigid Bodies typically use the {\tt pvqj} string |
| 662 |
|
which is followed by position, velocity, quaternions, and |
| 663 |
< |
lastly, body fixed angular momentum for that integrable object.}, |
| 653 |
< |
label=sch:dumpFormat] |
| 663 |
> |
lastly, body fixed angular momentum for that integrable object.},label={sch:dumpFormat}] |
| 664 |
|
<Snapshot> |
| 665 |
|
<FrameData> |
| 666 |
|
Time: 0 |
| 675 |
|
3 pvqj x y z vx vy vz qw qx qy qz jx jy jz |
| 676 |
|
</StuntDoubles> |
| 677 |
|
</Snapshot> |
| 678 |
< |
\end{lstlisting} |
| 678 |
> |
\end{code} |
| 679 |
|
|
| 680 |
|
There are three {\sc OpenMD} files that are written using the combined |
| 681 |
|
format. They are: the initial startup file (\texttt{.md}), the |
| 726 |
|
\end{enumerate} |
| 727 |
|
An example is given in the {\sc OpenMD} file in Scheme~\ref{sch:initEx1}. |
| 728 |
|
|
| 729 |
< |
\begin{lstlisting}[float,caption={Example declaration of the |
| 730 |
< |
$\text{I}_2$ molecule and the HCl molecule in $<$MetaData$>$ and |
| 731 |
< |
$<$Snapshot$>$ blocks. Note that even though $\text{I}_2$ is |
| 732 |
< |
declared before HCl, the $<$Snapshot$>$ block follows the order {\it in |
| 729 |
> |
\begin{code}[caption={Example declaration of the |
| 730 |
> |
$\text{I}_2$ molecule and the HCl molecule in {\tt <MetaData>} and |
| 731 |
> |
{\tt <Snapshot>} blocks. Note that even though $\text{I}_2$ is |
| 732 |
> |
declared before HCl, the {\tt <Snapshot>} block follows the order {\it in |
| 733 |
|
which the components were included}.}, label=sch:initEx1] |
| 734 |
|
<OpenMD> |
| 735 |
|
<MetaData> |
| 773 |
|
</StuntDoubles> |
| 774 |
|
</Snapshot> |
| 775 |
|
</OpenMD> |
| 776 |
< |
\end{lstlisting} |
| 776 |
> |
\end{code} |
| 777 |
|
|
| 778 |
|
\section{The Statistics File} |
| 779 |
|
|
| 836 |
|
A simple example of a forceField file is shown in scheme |
| 837 |
|
\ref{sch:frcExample}. |
| 838 |
|
|
| 839 |
< |
\begin{lstlisting}[float,caption={[An example of a complete OpenMD |
| 839 |
> |
\begin{code}[caption={[An example of a complete OpenMD |
| 840 |
|
force field file for straight-chain united-atom alkanes.] An example |
| 841 |
|
showing a complete OpenMD force field for straight-chain united-atom |
| 842 |
|
alkanes.}, label={sch:frcExample}] |
| 883 |
|
CH3 CH2 CH2 CH2 Trappe 0.0 0.70544 -0.13549 1.5723 |
| 884 |
|
CH2 CH2 CH2 CH2 Trappe 0.0 0.70544 -0.13549 1.5723 |
| 885 |
|
end TorsionTypes |
| 886 |
< |
\end{lstlisting} |
| 886 |
> |
\end{code} |
| 887 |
|
|
| 888 |
|
\section{\label{section:ffOptions}The Options block} |
| 889 |
|
|
| 894 |
|
the various keywords and their possible values are given in Scheme |
| 895 |
|
\ref{sch:optionsBlock}. |
| 896 |
|
|
| 897 |
< |
\begin{lstlisting}[caption={[A force field Options block showing default values |
| 897 |
> |
\begin{code}[caption={[A force field Options block showing default values |
| 898 |
|
for many force field options.] A force field Options block showing default values |
| 899 |
|
for many force field options. Most of these options do not need to be |
| 900 |
|
specified if the default values are working.}, |
| 920 |
|
GayBerneNu = 1.0 |
| 921 |
|
EAMMixingMethod = "Johnson" // can also be "Daw" |
| 922 |
|
end Options |
| 923 |
< |
\end{lstlisting} |
| 923 |
> |
\end{code} |
| 924 |
|
|
| 925 |
|
\section{\label{section:ffBase}The BaseAtomTypes block} |
| 926 |
|
|
| 948 |
|
ability to print out the names of the base atom types for displaying |
| 949 |
|
simulations in Jmol or VMD. |
| 950 |
|
|
| 951 |
< |
\begin{lstlisting}[caption={[A simple example of a BaseAtomTypes |
| 951 |
> |
\begin{code}[caption={[A simple example of a BaseAtomTypes |
| 952 |
|
block.] A simple example of a BaseAtomTypes block.}, |
| 953 |
|
label={sch:baseAtomTypesBlock}] |
| 954 |
|
begin BaseAtomTypes |
| 968 |
|
Ba 137.327 |
| 969 |
|
Cl 35.453 |
| 970 |
|
end BaseAtomTypes |
| 971 |
< |
\end{lstlisting} |
| 971 |
> |
\end{code} |
| 972 |
|
|
| 973 |
|
\section{\label{section:ffAtom}The AtomTypes block} |
| 974 |
|
|
| 977 |
|
shows an example where multiple types of oxygen atoms can inherit mass |
| 978 |
|
from the oxygen base type. |
| 979 |
|
|
| 980 |
< |
\begin{lstlisting}[caption={[An example of a AtomTypes block.] A |
| 980 |
> |
\begin{code}[caption={[An example of a AtomTypes block.] A |
| 981 |
|
simple example of an AtomTypes block which |
| 982 |
|
shows how multiple types can inherit from the same base type.}, |
| 983 |
|
label={sch:atomTypesBlock}] |
| 1002 |
|
feo Fe |
| 1003 |
|
lio Li |
| 1004 |
|
end AtomTypes |
| 1005 |
< |
\end{lstlisting} |
| 1005 |
> |
\end{code} |
| 1006 |
|
|
| 1007 |
|
\section{\label{section:ffDirectionalAtom}The DirectionalAtomTypes |
| 1008 |
|
block} |
| 1019 |
|
and in quadrupole tensors that are not necessarily diagonal in the |
| 1020 |
|
body frame. |
| 1021 |
|
|
| 1022 |
< |
\begin{lstlisting}[caption={[An example of a DirectionalAtomTypes block.] A |
| 1022 |
> |
\begin{code}[caption={[An example of a DirectionalAtomTypes block.] A |
| 1023 |
|
simple example of a DirectionalAtomTypes block.}, |
| 1024 |
|
label={sch:datomTypesBlock}] |
| 1025 |
|
begin DirectionalAtomTypes |
| 1031 |
|
CO2 43.06 43.06 0.0 // single-site model for CO2 |
| 1032 |
|
end DirectionalAtomTypes |
| 1033 |
|
|
| 1034 |
< |
\end{lstlisting} |
| 1034 |
> |
\end{code} |
| 1035 |
|
|
| 1036 |
|
For a DirectionalAtom that represents a linear object, it is |
| 1037 |
|
appropriate for one of the moments of inertia to be zero. In this |
| 1079 |
|
the {\tt NonbondedInteractionTypes} block (see section |
| 1080 |
|
\ref{section:ffNBinteraction}). |
| 1081 |
|
|
| 1082 |
< |
\begin{lstlisting}[caption={[An example of a LennardJonesAtomTypes block.] A |
| 1082 |
> |
\begin{code}[caption={[An example of a LennardJonesAtomTypes block.] A |
| 1083 |
|
simple example of a LennardJonesAtomTypee block. Units for |
| 1084 |
|
$\epsilon$ are kcal / mol and for $\sigma$ are \AA\ .}, |
| 1085 |
|
label={sch:LJatomTypesBlock}] |
| 1096 |
|
CH2 0.0866 3.95 |
| 1097 |
|
CH 0.0189 4.68 |
| 1098 |
|
end LennardJonesAtomTypes |
| 1099 |
< |
\end{lstlisting} |
| 1099 |
> |
\end{code} |
| 1100 |
|
|
| 1101 |
|
\subsection{\label{section:ffCharge}The ChargeAtomTypes block} |
| 1102 |
|
|
| 1121 |
|
charge of an electron in Coulombs. $\epsilon_0$ is the permittivity |
| 1122 |
|
of free space. |
| 1123 |
|
|
| 1124 |
< |
\begin{lstlisting}[caption={[An example of a ChargeAtomTypes block.] A |
| 1124 |
> |
\begin{code}[caption={[An example of a ChargeAtomTypes block.] A |
| 1125 |
|
simple example of a ChargeAtomTypes block. Units for |
| 1126 |
|
charge are in multiples of electron charge.}, |
| 1127 |
|
label={sch:ChargeAtomTypesBlock}] |
| 1136 |
|
Na+ 1.0 |
| 1137 |
|
Cl- -1.0 |
| 1138 |
|
end ChargeAtomTypes |
| 1139 |
< |
\end{lstlisting} |
| 1139 |
> |
\end{code} |
| 1140 |
|
|
| 1141 |
|
\subsection{\label{section:ffMultipole}The MultipoleAtomTypes |
| 1142 |
|
block} |
| 1188 |
|
($\boldsymbol{\hat{r}}_{ij}=\mathbf{r}_{ij}/|\mathbf{r}_{ij}|$). |
| 1189 |
|
|
| 1190 |
|
|
| 1191 |
< |
\begin{lstlisting}[caption={[An example of a MultipoleAtomTypes block.] A |
| 1191 |
> |
\begin{code}[caption={[An example of a MultipoleAtomTypes block.] A |
| 1192 |
|
simple example of a MultipoleAtomTypes block. Dipoles are given in |
| 1193 |
|
units of Debyes, and Quadrupole moments are given in units of Debye |
| 1194 |
|
\AA~(or $10^{-26} \mathrm{~esu~cm}^2$)}, |
| 1208 |
|
// name dq phi theta psi dipole_moment Qxx Qyy Qzz |
| 1209 |
|
SSD dq 0.0 0.0 0.0 2.35 -1.682 1.762 -0.08 |
| 1210 |
|
end MultipoleAtomTypes |
| 1211 |
< |
\end{lstlisting} |
| 1211 |
> |
\end{code} |
| 1212 |
|
|
| 1213 |
|
Specifying a MultipoleAtomType requires declaring how the |
| 1214 |
|
electrostatic frame for the site is rotated relative to the body-fixed |
| 1275 |
|
efficiently compute forces and torques for this potential can be found |
| 1276 |
|
in Ref. \citealp{Golubkov06} |
| 1277 |
|
|
| 1278 |
< |
\begin{lstlisting}[caption={[An example of a GayBerneAtomTypes block.] A |
| 1278 |
> |
\begin{code}[caption={[An example of a GayBerneAtomTypes block.] A |
| 1279 |
|
simple example of a GayBerneAtomTypes block. Distances ($d$ and $l$) |
| 1280 |
|
are given in \AA\ and energies ($\epsilon_X, \epsilon_S, \epsilon_E$) |
| 1281 |
|
are in units of kcal/mol. $dw$ is unitless.}, |
| 1286 |
|
GBC6H6 4.65 2.03 0.540 0.540 1.9818 0.6 |
| 1287 |
|
GBCH3OH 2.55 3.18 0.542 0.542 0.55826 1.0 |
| 1288 |
|
end GayBerneAtomTypes |
| 1289 |
< |
\end{lstlisting} |
| 1289 |
> |
\end{code} |
| 1290 |
|
|
| 1291 |
|
\subsection{\label{section:ffSticky}The StickyAtomTypes block} |
| 1292 |
|
|
| 1384 |
|
density corrected SSD models can be found in |
| 1385 |
|
reference~\citealp{fennell04}. |
| 1386 |
|
|
| 1387 |
< |
\begin{lstlisting}[caption={[An example of a StickyAtomTypes block.] A |
| 1387 |
> |
\begin{code}[caption={[An example of a StickyAtomTypes block.] A |
| 1388 |
|
simple example of a StickyAtomTypes block. Distances ($r_l$, $r_u$, |
| 1389 |
|
$r_{l}'$ and $r_{u}'$) are given in \AA\ and energies ($v_0, v_{0}'$) |
| 1390 |
|
are in units of kcal/mol. $w_0$ is unitless.}, |
| 1396 |
|
SSD 0.07715 3.7284 3.7284 2.75 3.35 2.75 4.0 |
| 1397 |
|
SSD1 0.07715 3.6613 3.6613 2.75 3.35 2.75 4.0 |
| 1398 |
|
end StickyAtomTypes |
| 1399 |
< |
\end{lstlisting} |
| 1399 |
> |
\end{code} |
| 1400 |
|
|
| 1401 |
|
\section{\label{section::ffMetals}Metallic Atom Types} |
| 1402 |
|
|
| 1478 |
|
$\mbox{kcal mol}^{-1}$ as in the rest of the {\sc OpenMD} force field |
| 1479 |
|
files. |
| 1480 |
|
|
| 1481 |
< |
\begin{lstlisting}[caption={[An example of a EAMAtomTypes block.] A |
| 1481 |
> |
\begin{code}[caption={[An example of a EAMAtomTypes block.] A |
| 1482 |
|
simple example of a EAMAtomTypes block. Here the only data provided is |
| 1483 |
|
the name of a {\tt funcfl} file which contains the raw data for spline |
| 1484 |
|
interpolations for the density, functional, and pair potential.}, |
| 1491 |
|
Pd Pd.u3.funcfl |
| 1492 |
|
Pt Pt.u3.funcfl |
| 1493 |
|
end EAMAtomTypes |
| 1494 |
< |
\end{lstlisting} |
| 1494 |
> |
\end{code} |
| 1495 |
|
|
| 1496 |
|
\subsection{\label{section:ffSC}The SuttonChenAtomTypes block} |
| 1497 |
|
|
| 1526 |
|
crystal. Interested readers are encouraged to consult reference |
| 1527 |
|
\citealp{Qi99} for further details. |
| 1528 |
|
|
| 1529 |
< |
\begin{lstlisting}[caption={[An example of a SCAtomTypes block.] A |
| 1529 |
> |
\begin{code}[caption={[An example of a SCAtomTypes block.] A |
| 1530 |
|
simple example of a SCAtomTypes block. Distances ($\alpha$) |
| 1531 |
|
are given in \AA\ and energies ($\epsilon$) are (by convention) given in |
| 1532 |
|
units of eV. These units must be specified in the {\tt Options} block |
| 1546 |
|
Au 0.0078052 53.581 8.0 11.0 4.0651 |
| 1547 |
|
Au2 0.0078052 53.581 8.0 11.0 4.0651 |
| 1548 |
|
end SCAtomTypes |
| 1549 |
< |
\end{lstlisting} |
| 1549 |
> |
\end{code} |
| 1550 |
|
|
| 1551 |
|
\section{\label{section::ffShortRange}Short Range Interactions} |
| 1552 |
|
The internal structure of a molecule is usually specified in terms of |
| 1613 |
|
\begin{equation} |
| 1614 |
|
V_{\text{bond}}(b) = D_{ij} \left[ 1 - e^{-\beta_{ij} (b - b_{ij}^0)} \right]^2 |
| 1615 |
|
\end{equation} |
| 1616 |
+ |
|
| 1617 |
+ |
\begin{figure}[h] |
| 1618 |
+ |
\centering |
| 1619 |
+ |
\includegraphics[width=2.5in]{bond.pdf} |
| 1620 |
+ |
\caption[Bond coordinates]{The coordinate describing a |
| 1621 |
+ |
a bond between atoms $i$ and $j$ is $|r_{ij}|$, the length of the |
| 1622 |
+ |
$\vec{r}_{ij}$ vector. } |
| 1623 |
+ |
\label{fig:bond} |
| 1624 |
+ |
\end{figure} |
| 1625 |
|
|
| 1626 |
|
OpenMD can also simulate some less common types of bond potentials, |
| 1627 |
|
including {\tt Fixed} bonds (which are constrained to be at a |
| 1660 |
|
\item any other parameters required by the {\tt BondType} |
| 1661 |
|
\end{itemize} |
| 1662 |
|
|
| 1663 |
< |
\begin{lstlisting}[caption={[An example of a BondTypes block.] A |
| 1663 |
> |
\begin{code}[caption={[An example of a BondTypes block.] A |
| 1664 |
|
simple example of a BondTypes block. Distances ($b_0$) |
| 1665 |
|
are given in \AA\ and force constants are given in |
| 1666 |
|
units so that when multiplied by the correct power of distance they |
| 1678 |
|
//Atom1 Atom2 Quartic b0 K4 K3 K2 K1 K0 |
| 1679 |
|
//Atom1 Atom2 Polynomial b0 n Kn [m Km] |
| 1680 |
|
end BondTypes |
| 1681 |
< |
\end{lstlisting} |
| 1681 |
> |
\end{code} |
| 1682 |
|
|
| 1683 |
|
There are advantages and disadvantages of all of the different types |
| 1684 |
|
of bonds, but specific simulation tasks may call for specific |
| 1694 |
|
The bending potential energy functions used in most force fields are |
| 1695 |
|
often simple functions of the angle between two bonds, |
| 1696 |
|
\begin{equation} |
| 1697 |
< |
\theta_{ijk} = \cos^{-1} \left(\frac{\vec{r}_{ij} \cdot |
| 1698 |
< |
\vec{r}_{jk}}{\left| \vec{r}_{ij} \right| \left| \vec{r}_{ij} |
| 1697 |
> |
\theta_{ijk} = \cos^{-1} \left(\frac{\vec{r}_{ji} \cdot |
| 1698 |
> |
\vec{r}_{jk}}{\left| \vec{r}_{ji} \right| \left| \vec{r}_{jk} |
| 1699 |
|
\right|} \right) |
| 1700 |
|
\end{equation} |
| 1701 |
|
Here atom $j$ is the central atom that is bonded to two partners $i$ |
| 1702 |
|
and $k$. |
| 1703 |
|
|
| 1704 |
+ |
\begin{figure}[h] |
| 1705 |
+ |
\centering |
| 1706 |
+ |
\includegraphics[width=3.5in]{bend.pdf} |
| 1707 |
+ |
\caption[Bend angle coordinates]{The coordinate describing a bend |
| 1708 |
+ |
between atoms $i$, $j$, and $k$ is the angle $\theta_{ijk} = |
| 1709 |
+ |
\cos^{-1} \left(\hat{r}_{ji} \cdot \hat{r}_{jk}\right)$ where $\hat{r}_{ji}$ is |
| 1710 |
+ |
the unit vector between atoms $j$ and $i$. } |
| 1711 |
+ |
\label{fig:bend} |
| 1712 |
+ |
\end{figure} |
| 1713 |
+ |
|
| 1714 |
+ |
|
| 1715 |
|
All BendTypes must specify three AtomType names ($i$, $j$ and $k$) |
| 1716 |
|
that describe when that bend potential should be applied, as well as |
| 1717 |
|
an equilibrium bending angle, $\theta_{ijk}^0$, in units of |
| 1771 |
|
\item any other parameters required by the {\tt BendType} |
| 1772 |
|
\end{itemize} |
| 1773 |
|
|
| 1774 |
< |
\begin{lstlisting}[caption={[An example of a BendTypes block.] A |
| 1774 |
> |
\begin{code}[caption={[An example of a BendTypes block.] A |
| 1775 |
|
simple example of a BendTypes block. By convention, equilibrium angles |
| 1776 |
|
($\theta_0$) are given in degrees but force constants are given in |
| 1777 |
|
units so that when multiplied by the correct power of angle (in |
| 1794 |
|
//Polynomial |
| 1795 |
|
//Atom1 Atom2 Atom3 Polynomial theta0 n Kn [m Km] |
| 1796 |
|
end BendTypes |
| 1797 |
< |
\end{lstlisting} |
| 1797 |
> |
\end{code} |
| 1798 |
|
|
| 1799 |
|
Note that the parameters for a particular bend type are the same for |
| 1800 |
|
any bending triplet of the same atomic types (in the same or reversed |
| 1833 |
|
\label{eq:torsPhi} |
| 1834 |
|
\end{equation} |
| 1835 |
|
Here, $\hat{\mathbf{r}}_{\alpha\beta}$ are the set of unit bond |
| 1836 |
< |
vectors between atoms $i$, $j$, $k$, and $l$. |
| 1836 |
> |
vectors between atoms $i$, $j$, $k$, and $l$. Note that some force |
| 1837 |
> |
fields define the zero of the $\phi_{ijkl}$ angle when atoms $i$ and |
| 1838 |
> |
$l$ are in the {\em trans} configuration, while most define the zero |
| 1839 |
> |
angle for when $i$ and $l$ are in the fully eclipsed orientation. The |
| 1840 |
> |
behavior of the torsion parser can be altered with the {\tt |
| 1841 |
> |
TorsionAngleConvention} keyword in the Options block. The default |
| 1842 |
> |
behavior is {\tt "180\_is\_trans"} while the opposite behavior can be |
| 1843 |
> |
invoked by setting this keyword to {\tt "0\_is\_trans"}. |
| 1844 |
> |
|
| 1845 |
> |
\begin{figure}[h] |
| 1846 |
> |
\centering |
| 1847 |
> |
\includegraphics[width=4.5in]{torsion.pdf} |
| 1848 |
> |
\caption[Torsion or dihedral angle coordinates]{The coordinate |
| 1849 |
> |
describing a torsion between atoms $i$, $j$, $k$, and $l$ is the |
| 1850 |
> |
dihedral angle $\phi_{ijkl}$ which measures the relative rotation of |
| 1851 |
> |
the two terminal atoms around the axis defined by the middle bond. } |
| 1852 |
> |
\label{fig:torsion} |
| 1853 |
> |
\end{figure} |
| 1854 |
|
|
| 1855 |
|
For computational efficiency, OpenMD recasts torsion potential in the |
| 1856 |
|
method of {\sc charmm},\cite{Brooks83} in which the angle series is |
| 1919 |
|
kcal/mol/degrees$^2$. All other torsion parameters are measured in |
| 1920 |
|
units of kcal/mol. |
| 1921 |
|
|
| 1922 |
< |
\begin{lstlisting}[caption={[An example of a TorsionTypes block.] A |
| 1922 |
> |
\begin{code}[caption={[An example of a TorsionTypes block.] A |
| 1923 |
|
simple example of a TorsionTypes block. Energy constants are given in |
| 1924 |
|
kcal / mol, and when required by the form, $\delta$ angles are given |
| 1925 |
|
in degrees.}, |
| 1943 |
|
//Atom1 Atom2 Atom3 Atom4 Polynomial n Kn [m Km] |
| 1944 |
|
S CH2 CH2 C Polynomial 0 2.218 1 2.905 2 -3.136 3 -0.7313 4 6.272 5 -7.528 |
| 1945 |
|
end TorsionTypes |
| 1946 |
< |
\end{lstlisting} |
| 1946 |
> |
\end{code} |
| 1947 |
|
|
| 1948 |
|
Note that the parameters for a particular torsion type are the same |
| 1949 |
|
for any torsional quartet of the same atomic types (in the same or |
| 1997 |
|
V_{\text{torsion}}(\omega) = \frac{d}{2} \left(\omega - \omega_0\right). |
| 1998 |
|
\end{equation*} |
| 1999 |
|
\end{itemize} |
| 2000 |
< |
\begin{lstlisting}[caption={[An example of an InversionTypes block.] A |
| 2000 |
> |
\begin{code}[caption={[An example of an InversionTypes block.] A |
| 2001 |
|
simple example of a InversionTypes block. Angles ($\delta_n$ and |
| 2002 |
|
$\omega_0$) angles are given in degrees, while energy parameters ($v, |
| 2003 |
|
K_n$) are given in kcal / mol. The Harmonic Inversion type has a |
| 2014 |
|
//ImproperCosine |
| 2015 |
|
//Atom1 Atom2 Atom3 Atom4 ImproperCosine Kn n delta_n [Kn n delta_n] |
| 2016 |
|
end InversionTypes |
| 2017 |
< |
\end{lstlisting} |
| 2017 |
> |
\end{code} |
| 2018 |
|
|
| 2019 |
|
\section{\label{section::ffLongRange}Long Range Interactions} |
| 2020 |
|
|
| 2057 |
|
\end{equation*} |
| 2058 |
|
\end{itemize} |
| 2059 |
|
|
| 2060 |
< |
\begin{lstlisting}[caption={[An example of a NonBondedInteractions block.] A |
| 2060 |
> |
\begin{code}[caption={[An example of a NonBondedInteractions block.] A |
| 2061 |
|
simple example of a NonBondedInteractions block. Distances ($\sigma, |
| 2062 |
|
r_0$) are given in \AA, while energies ($\epsilon, D0$) are in |
| 2063 |
|
kcal/mol. The Morse potentials have an additional parameter $\beta_0$ |
| 2085 |
|
Au ON RepulsivePower 3.47005 0.186208 11 |
| 2086 |
|
Au NO RepulsivePower 3.53955 0.168629 11 |
| 2087 |
|
end NonBondedInteractions |
| 2088 |
< |
\end{lstlisting} |
| 2088 |
> |
\end{code} |
| 2089 |
|
|
| 2090 |
|
\section{\label{section:electrostatics}Electrostatics} |
| 2091 |
|
|
| 2092 |
< |
To aid in performing simulations in more traditional force fields, we |
| 2093 |
< |
have added routines to carry out electrostatic interactions using a |
| 2094 |
< |
number of different electrostatic summation methods. These methods |
| 2095 |
< |
are extended from the damped and cutoff-neutralized Coulombic sum |
| 2096 |
< |
originally proposed by Wolf, {\it et al.}\cite{Wolf99} One of these, |
| 2097 |
< |
the damped shifted force method, shows a remarkable ability to |
| 2098 |
< |
reproduce the energetic and dynamic characteristics exhibited by |
| 2099 |
< |
simulations employing lattice summation techniques. The basic idea is |
| 2100 |
< |
to construct well-behaved real-space summation methods using two tricks: |
| 2092 |
> |
Because nearly all force fields involve electrostatic interactions in |
| 2093 |
> |
one form or another, OpenMD implements a number of different |
| 2094 |
> |
electrostatic summation methods. These methods are extended from the |
| 2095 |
> |
damped and cutoff-neutralized Coulombic sum originally proposed by |
| 2096 |
> |
Wolf, {\it et al.}\cite{Wolf99} One of these, the damped shifted force |
| 2097 |
> |
method, shows a remarkable ability to reproduce the energetic and |
| 2098 |
> |
dynamic characteristics exhibited by simulations employing lattice |
| 2099 |
> |
summation techniques. The basic idea is to construct well-behaved |
| 2100 |
> |
real-space summation methods using two tricks: |
| 2101 |
|
\begin{enumerate} |
| 2102 |
|
\item shifting through the use of image charges, and |
| 2103 |
|
\item damping the electrostatic interaction. |
| 2264 |
|
|
| 2265 |
|
\section{\label{section:cutoffGroups}Switching Functions} |
| 2266 |
|
|
| 2267 |
< |
If done poorly, calculating the the long-range interactions for $N$ |
| 2268 |
< |
atoms would involve $N(N-1)/2$ evaluations of atomic distances. To |
| 2269 |
< |
reduce the number of distance evaluations between pairs of atoms, {\sc |
| 2270 |
< |
OpenMD} allows the use of switched cutoffs with Verlet neighbor |
| 2271 |
< |
lists.\cite{Allen87} Neutral groups which contain charges will exhibit |
| 2272 |
< |
pathological forces unless the cutoff is applied to the neutral groups |
| 2273 |
< |
evenly instead of to the individual atoms.\cite{leach01:mm} {\sc |
| 2274 |
< |
OpenMD} allows users to specify cutoff groups which may contain an |
| 2275 |
< |
arbitrary number of atoms in the molecule. Atoms in a cutoff group |
| 2276 |
< |
are treated as a single unit for the evaluation of the switching |
| 2277 |
< |
function: |
| 2267 |
> |
Calculating the the long-range interactions for $N$ atoms involves |
| 2268 |
> |
$N(N-1)/2$ evaluations of atomic distances if it is done in a brute |
| 2269 |
> |
force manner. To reduce the number of distance evaluations between |
| 2270 |
> |
pairs of atoms, {\sc OpenMD} allows the use of hard or switched |
| 2271 |
> |
cutoffs with Verlet neighbor lists.\cite{Allen87} Neutral groups which |
| 2272 |
> |
contain charges can exhibit pathological forces unless the cutoff is |
| 2273 |
> |
applied to the neutral groups evenly instead of to the individual |
| 2274 |
> |
atoms.\cite{leach01:mm} {\sc OpenMD} allows users to specify cutoff |
| 2275 |
> |
groups which may contain an arbitrary number of atoms in the molecule. |
| 2276 |
> |
Atoms in a cutoff group are treated as a single unit for the |
| 2277 |
> |
evaluation of the switching function: |
| 2278 |
|
\begin{equation} |
| 2279 |
|
V_{\mathrm{long-range}} = \sum_{a} \sum_{b>a} s(r_{ab}) \sum_{i \in a} \sum_{j \in b} V_{ij}(r_{ij}), |
| 2280 |
|
\end{equation} |
| 2300 |
|
Here, $r_{\text{sw}}$ is the {\tt switchingRadius}, or the distance |
| 2301 |
|
beyond which interactions are reduced, and $r_{\text{cut}}$ is the |
| 2302 |
|
{\tt cutoffRadius}, or the distance at which interactions are |
| 2303 |
< |
truncated. |
| 2303 |
> |
truncated. |
| 2304 |
|
|
| 2305 |
|
Users of {\sc OpenMD} do not need to specify the {\tt cutoffRadius} or |
| 2306 |
< |
{\tt switchingRadius}. In simulations containing only Lennard-Jones |
| 2307 |
< |
atoms, the cutoff radius has a default value of $2.5\sigma_{ii}$, |
| 2308 |
< |
where $\sigma_{ii}$ is the largest Lennard-Jones length parameter |
| 2309 |
< |
present in the simulation. In simulations containing charged or |
| 2310 |
< |
dipolar atoms, the default cutoff radius is $15 \mbox{\AA}$. |
| 2306 |
> |
{\tt switchingRadius}. |
| 2307 |
> |
If the {\tt cutoffRadius} was not explicitly set, OpenMD will attempt |
| 2308 |
> |
to guess an appropriate choice. If the system contains electrostatic |
| 2309 |
> |
atoms, the default cutoff radius is 12 \AA. In systems without |
| 2310 |
> |
electrostatic (charge or multipolar) atoms, the atom types present in the simulation will be |
| 2311 |
> |
polled for suggested cutoff values (e.g. $2.5 max(\left\{ \sigma |
| 2312 |
> |
\right\})$ for Lennard-Jones atoms. The largest suggested value |
| 2313 |
> |
that was found will be used. |
| 2314 |
|
|
| 2315 |
+ |
By default, OpenMD uses shifted force potentials to force the |
| 2316 |
+ |
potential energy and forces to smoothly approach zero at the cutoff |
| 2317 |
+ |
radius. If the user would like to use another cutoff method |
| 2318 |
+ |
they may do so by setting the {\tt cutoffMethod} parameter to: |
| 2319 |
+ |
\begin{itemize} |
| 2320 |
+ |
\item {\tt HARD} |
| 2321 |
+ |
\item {\tt SWITCHED} |
| 2322 |
+ |
\item {\tt SHIFTED\_FORCE} (default): |
| 2323 |
+ |
\item {\tt TAYLOR\_SHIFTED} |
| 2324 |
+ |
\item {\tt SHIFTED\_POTENTIAL} |
| 2325 |
+ |
\end{itemize} |
| 2326 |
+ |
|
| 2327 |
|
The {\tt switchingRadius} is set to a default value of 95\% of the |
| 2328 |
|
{\tt cutoffRadius}. In the special case of a simulation containing |
| 2329 |
|
{\it only} Lennard-Jones atoms, the default switching radius takes the |
| 2332 |
|
Both radii may be specified in the meta-data file. |
| 2333 |
|
|
| 2334 |
|
|
| 2273 |
– |
\section{\label{section:WATER}The {\sc water} Force Field} |
| 2274 |
– |
|
| 2275 |
– |
In addition to the {\sc duff} force field's solvent description, a |
| 2276 |
– |
separate {\sc water} force field has been included for simulating most |
| 2277 |
– |
of the common rigid-body water models. This force field includes the |
| 2278 |
– |
simple and point-dipolar models (SSD, SSD1, SSD/E, SSD/RF, and DPD |
| 2279 |
– |
water), as well as the common charge-based models (SPC, SPC/E, TIP3P, |
| 2280 |
– |
TIP4P, and |
| 2281 |
– |
TIP5P).\cite{liu96:new_model,Ichiye03,fennell04,Marrink01,Berendsen81,Berendsen87,Jorgensen83,Mahoney00} |
| 2282 |
– |
In order to handle these models, charge-charge interactions were |
| 2283 |
– |
included in the force-loop: |
| 2284 |
– |
\begin{equation} |
| 2285 |
– |
V_{\text{charge}}(r_{ij}) = \sum_{ij}\frac{q_iq_je^2}{r_{ij}}, |
| 2286 |
– |
\end{equation} |
| 2287 |
– |
where $q$ represents the charge on particle $i$ or $j$, and $e$ is the |
| 2288 |
– |
charge of an electron in Coulombs. The charge-charge interaction |
| 2289 |
– |
support is rudimentary in the current version of {\sc OpenMD}. As with |
| 2290 |
– |
the other pair interactions, charges can be simulated with a pure |
| 2291 |
– |
cutoff or a reaction field. The various methods for performing the |
| 2292 |
– |
Ewald summation have not yet been included. The {\sc water} force |
| 2293 |
– |
field can be easily expanded through modification of the {\sc water} |
| 2294 |
– |
force field file ({\tt WATER.frc}). By adding atom types and inserting |
| 2295 |
– |
the appropriate parameters, it is possible to extend the force field |
| 2296 |
– |
to handle rigid molecules other than water. |
| 2297 |
– |
|
| 2298 |
– |
|
| 2299 |
– |
|
| 2335 |
|
\section{\label{section:pbc}Periodic Boundary Conditions} |
| 2336 |
|
|
| 2337 |
|
\newcommand{\roundme}{\operatorname{round}} |
