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<H2>
LAMMPS</H2>
<P>
LAMMPS = Large-scale Atomic/Molecular Massively Parallel Simulator</P>
<P>
This is the documentation for the LAMMPS 2001 version, written in F90,
which has been superceded by more current versions. See the <A
HREF="http://www.cs.sandia.gov/~sjplimp/lammps.html">LAMMPS WWW
Site</A> for more information.
<P>
LAMMPS is a classical molecular dynamics code designed for simulating
molecular and atomic systems on parallel computers using
spatial-decomposition techniques. It runs on any parallel platform that
supports F90 and the MPI message-passing library or on single-processor
workstations.</P>
<P>
LAMMPS 2001 is copyrighted code that is distributed freely as
open-source software under the GNU Public License (GPL). See the
LICENSE file or <A HREF="http://www.gnu.org">www.gnu.org</A> for more
details. Basically the GPL allows you as a user to use, modify, or
distribute LAMMPS however you wish, so long as any software you
distribute remains under the GPL.
<P>
Features of LAMMPS 2001 include:</P>
<UL>
<LI>
short-range pairwise Lennard-Jones and Coulombic interactions
<LI>
long-range Coulombic interactions via Ewald or PPPM (particle-mesh
Ewald)
<LI>
short-range harmonic bond potentials (bond, angle, torsion, improper)
<LI>
short-range class II (cross-term) molecular potentials
<LI>
NVE, NVT, NPT dynamics
<LI>
constraints on atoms or groups of atoms
<LI>
rRESPA long-timescale integrator
<LI>
energy minimizer (Hessian-free truncated Newton method)
</UL>
<P>
For users of LAMMPS 99, this version is written in F90 to take
advantage of dynamic memory allocation. This means the user does not
have to fiddle with parameter settings and re-compile the code so
often for different problems. This enhancment means there are new
rules for the ordering of commands in a LAMMPS input script, as well
as a few new commands to guide the memory allocator. Users should read
the beginning sections of the <A
HREF="input_commands.html">input_commands</A> file for an
explanation.</P>
<P>
More details about the code can be found <A
HREF="#_cch3_930958294">here</A>, in the HTML- or text-based
documentation. The LAMMPS Web page is at <A
HREF="http://www.cs.sandia.gov/~sjplimp/lammps.html">www.cs.sandia.gov/~sjplimp/lammps.html</A>
, which includes benchmark timings and a list of papers written using
LAMMPS results. They illustrate the kinds of scientific problems that
can be modeled with LAMMPS. These two papers describe the parallel
algorithms used in the code. Please cite these if you incorporate
LAMMPS results in your work. And if you send me citations for your
papers, I'll be pleased to add them to the LAMMPS WWW page.
</P>
<P>
S. J. Plimpton, R. Pollock, M. Stevens, &quot;Particle-Mesh Ewald and
rRESPA for Parallel Molecular Dynamics Simulations&quot;, in Proc of
the Eighth SIAM Conference on Parallel Processing for Scientific
Computing, Minneapolis, MN, March 1997.</P>
<P>
S. J. Plimpton, "Fast Parallel Algorithms for Short-Range Molecular Dynamics", J Comp Phys, 117, 1-19 (1995).</P>
<P>
LAMMPS was originally developed as part of a 5-way CRADA collaboration
between 3 industrial partners (Cray Research, Bristol-Myers Squibb, and
Dupont) and 2 DoE laboratories (Sandia National Laboratories and
Lawrence Livermore National Laboratories).</P>
<P>
The primary author of LAMMPS is Steve Plimpton, but others have written
or worked on significant portions of the code:</P>
<UL>
<LI>
Roy Pollock (LLNL): Ewald, PPPM solvers
<LI>
Mark Stevens (Sandia): rRESPA, NPT integrators
<LI>
Eric Simon (Cray Research): class II force fields
<LI>
Todd Plantenga (Sandia): energy minimizer
<LI>
Steve Lustig (Dupont): msi2lmp tool
<LI>
Mike Peachey (Cray Research): msi2lmp tool
</UL>
<P>
Other CRADA partners involved in the design and testing of LAMMPS are </P>
<UL>
<LI>
John Carpenter (Cray Research)
<LI>
Terry Stouch (Bristol-Myers Squibb)
<LI>
Jim Belak (LLNL)
</UL>
<P>
If you have questions about LAMMPS, please contact me:
</P>
<DL>
<DT>
Steve Plimpton
<DD>
sjplimp@sandia.gov
<DD>
www.cs.sandia.gov/~sjplimp
<DD>
Sandia National Labs
<DD>
Albuquerque, NM 87185
</DL>
<HR>
<H3>
<A NAME="_cch3_930958294">More Information about LAMMPS</A></H3>
<DIR>
<LI>
<A HREF="basics.html">Basics</A>
<DIR>
<LI>
how to make, run, and test LAMMPS with the example problems
</DIR>
<LI>
<A HREF="input_commands.html">Input Commands</A>
<DIR>
<LI>
a complete listing of input commands used by LAMMPS
</DIR>
<LI>
<A HREF="data_format.html">Data Format</A>
<DIR>
<LI>
the data file format used by LAMMPS
</DIR>
<LI>
<A HREF="force_fields.html">Force Fields</A>
<DIR>
<LI>
the equations LAMMPS uses to compute force-fields
</DIR>
<LI>
<A HREF="units.html">Units</A>
<DIR>
<LI>
the input/output and internal units for LAMMPS variables
</DIR>
<LI>
<A HREF="history.html">History</A>
<DIR>
<LI>
a brief timeline of features added to LAMMPS
</DIR>
<LI>
<A HREF="deficiencies.html">Deficiencies</A>
<DIR>
<LI>
features LAMMPS does not (yet) have
</DIR>
</DIR>
</BODY>
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<H2>
Basics of Using LAMMPS</H2>
<P>
<A HREF="README.html">Return</A> to top-level of LAMMPS documentation.</P>
<UL>
<LI>
<A HREF="#_cch3_931273040">Distribution</A>
<LI>
<A HREF="#_cch3_930327142">Making LAMMPS</A>
<LI>
<A HREF="#_cch3_930327155">Running LAMMPS</A>
<LI>
<A HREF="#_cch3_930759879">Examples</A>
<LI>
<A HREF="#_cch3_931282515">Other Tools</A>
<LI>
<A HREF="#_cch3_931282000">Extending LAMMPS</A>
</UL>
<HR>
<H3>
<A NAME="_cch3_931273040">Distribution</A></H3>
<P>
When you unzip/untar the LAMMPS distribution you should have several
directories: </P>
<UL>
<LI>
src = source files for LAMMPS
<LI>
doc = HTML documentation
<LI>
examples = sample problems with inputs and outputs
<LI>
tools = serial program for creating and massaging LAMMPS data files
<LI>
converters = msi2lmp, lmp2arc, amber = codes & scripts for converting
between MSI/Discover, AMBER, and LAMMPS formats
</UL>
<HR>
<H3>
<A NAME="_cch3_930327142">Making LAMMPS</A></H3>
<P>
The src directory contains the F90 and C source files for LAMMPS as
well as several sample Makefiles for different machines. To make LAMMPS
for a specfic machine, you simply type</P>
<P>
make machine</P>
<P>
from within the src directoy. E.g. "make sgi" or "make t3e". This
should create an executable such as lmp_sgi or lmp_t3e. For optimal
performance you'll want to use a good F90 compiler to make LAMMPS; on
Linux boxes I've been told the Leahy F90 compiler is a good choice.
(If you don't have an F90 compiler, I can give you an older F77-based
version of LAMMPS 99, but you'll lose the dynamic memory and some
other new features in LAMMPS 2001.)</P>
<P>
In the src directory, there is one top-level Makefile and several
low-level machine-specific files named Makefile.xxx where xxx = the
machine name. If a low-level Makefile exists for your platform, you do
not need to edit the top-level Makefile. However you should check the
system-specific section of the low-level Makefile to insure the
various paths are correct for your environment. If a low-level
Makefile does not exist for your platform, you will need to add a
suitable target to the top-level Makefile. You will also need to
create a new low-level Makefile using one of the existing ones as a
template. If you wish to make LAMMPS for a single-processor
workstation that doesn't have an installed MPI library, you can
specify the "serial" target which uses a directory of MPI stubs to
link against - e.g. &quot;make serial&quot;. You will need to make the
stub library (type &quot;make&quot; in STUBS directory) for your
workstation before doing this.</P>
<P>
Note that the two-level Makefile system allows you to make LAMMPS for
multiple platforms. Each target creates its own object directory for
separate storage of its *.o files.</P>
<P>
There are a few compiler switches of interest which can be specified
in the low-level Makefiles. If you use a F90FLAGS switch of -DSYNC
then synchronization calls will be made before the timing routines in
integrate.f. This may slow down the code slightly, but will make the
individual timings reported at the end of a run more accurate. The
F90FLAGS setting of -DSENDRECV will use MPI_Sendrecv calls for data
exchange between processors instead of MPI_Irecv, MPI_Send,
MPI_Wait. Sendrecv is often slower, but on some platforms can be
faster, so it is worth trying, particularly if your communication
timings seem slow.</P>
<P>
The CCFLAGS setting in the low-level Makefiles requires a FFT setting,
for example -DFFT_SGI or -DFFT_T3E. This is for inclusion of the
appropriate machine-specific native 1-d FFT libraries on various
platforms. Currently, the supported machines and switches (used in
fft_3d.c) are FFT_SGI, FFT_DEC, FFT_INTEL, FFT_T3E, and FFT_FFTW. The
latter is a publicly available portable FFT library, <A
HREF="http://www.fftw.org">FFTW</A>, which you can install on any
machine. If none of these options is suitable for your machine, please
contact me, and we'll discuss how to add the capability to call your
machine's native FFT library. You can also use FFT_NONE if you have no
need to use the PPPM option in LAMMPS.</P>
<P>
For Linux and T3E compilation, there is a also a CCFLAGS setting for KLUDGE
needed (see Makefile.linux and Makefile.t3e). This is to enable F90 to
call C with appropriate underscores added to C function names.
<HR>
<H3>
<A NAME="_cch3_930327155">Running LAMMPS</A></H3>
<P>
LAMMPS is run by redirecting a text file (script) of input commands into it.</P>
<P>
lmp_sgi &lt; in.lj</P>
<P>
lmp_t3e &lt; in.lj</P>
<P>
The script file contains commands that specify the parameters for the
simulation as well as to read other necessary files such as a data file
that describes the initial atom positions, molecular topology, and
force-field parameters. The <A HREF="input_commands.html">input_commands</A>
page describes all the possible commands that can be used. The <A
HREF="data_format.html">data_format</A> page describes the format of
the data file. </P>
<P>
LAMMPS can be run on any number of processors, including a single
processor. In principle you should get identical answers on any number
of processors and on any machine. In practice, numerical round-off can
cause slight differences and eventual divergence of dynamical
trajectories. </P>
<P>
When LAMMPS runs, it estimates the array sizes it should allocate based
on the problem you are simulating and the number of processors you
are running on. If you run out of physical memory, you will get a F90
allocation error and the code should hang or crash. The only thing you
can do about this is run on more processors or run a smaller problem. If
you get an error message to the screen about &quot;boosting&quot;
something, it means LAMMPS under-estimated the size needed for one (or
more) data arrays. The &quot;extra memory&quot; command can be used in
the input script to augment these sizes at run time. A few arrays are
hard-wired to sizes that should be sufficient for most users. These are
specified with parameter settings in the global.f file. If you get a
message to &quot;boost&quot; one of these parameters you will have to
change it and re-compile LAMMPS.</P>
<P>
Some LAMMPS errors are detected at setup; others like neighbor list
overflow may not occur until the middle of a run. Except for F90
allocation errors which may cause the code to hang (with an error
message) since only one processor may incur the error, LAMMPS should
always print a message to the screen and exit gracefully when it
encounters a fatal error. If the code ever crashes or hangs without
spitting out an error message first, it's probably a bug, so let me
know about it. Of course this applies to algorithmic or parallelism
issues, not to physics mistakes, like specifying too big a timestep or
putting 2 atoms on top of each other! One exception is that different
MPI implementations handle buffering of messages differently. If the
code hangs without an error message, it may be that you need to
specify an MPI setting or two (usually via an environment variable) to
enable buffering or boost the sizes of messages that can be
buffered.</P>
<HR>
<H3>
<A NAME="_cch3_930759879">Examples</A></H3>
<P>
There are several directories of sample problems in the examples
directory. All of them use an input file (in.*) of commands and a data
file (data.*) of initial atomic coordinates and produce one or more
output files. Sample outputs on different machines and numbers of
processors are included to compare your answers to. See the README
file in the examples sub-directory for more information on what LAMMPS
features the examples illustrate.</P>
<P>
(1) lj = atomic simulations of Lennard-Jones systems.
<P>
(2) class2 = phenyalanine molecule using the DISCOVER cff95 class 2
force field.
<P>
(3) lc = liquid crystal molecules with various Coulombic options and
periodicity settings.
<P>
(4) flow = 2d flow of Lennard-Jones atoms in a channel using various
constraint options.
<P>
(5) polymer = bead-spring polymer models with one or two chain types.
</P>
<HR>
<H3>
<A NAME="_cch3_931282515">Other Tools</A></H3>
<P>
The converters directory has source code and scripts for tools that
perform input/output file conversions between MSI Discover, AMBER, and
LAMMPS formats. See the README files for the individual tools for
additional information.
<P>
The tools directory has several serial programs that create and
massage LAMMPS data files.
<P>
(1) setup_chain.f = create a data file of polymer bead-spring chains
<P>
(2) setup_lj.f = create a data file of an atomic LJ mixture of species
<P>
(3) setup_flow_2d.f = create a 2d data file of LJ particles with walls for
a flow simulation
<P>
(4) replicate.c = replicate or scale an existing data file into a new one
<P>
(5) peek_restart.f = print-out info from a binary LAMMPS restart file
<P>
(6) restart2data.f = convert a binary LAMMPS restart file into a text data file
<P>
See the comments at the top of each source file for information on how
to use the tool.
<HR>
<H3>
<A NAME="_cch3_931282000">Extending LAMMPS</A></H3>
<P>
User-written routines can be compiled and linked with LAMMPS, then
invoked with the "diagnostic" command as LAMMPS runs. These routines
can be used for on-the-fly diagnostics or a variety of other purposes.
The examples/lc directory shows an example of using the diagnostic
command with the in.lc.big.fixes input script. A sample diagnostic
routine is given there also: diagnostic_temp_molecules.f.
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<H2>
LAMMPS Data Format</H2>
<P>
<A HREF="README.html">Return</A> to top-level of LAMMPS documentation</P>
<P>
This file describes the format of the data file read into LAMMPS with
the &quot;read data&quot; command. The data file contains basic
information about the size of the problem to be run, the initial atomic
coordinates, molecular topology, and (optionally) force-field
coefficients. It will be easiest to understand this file if you read it
while looking at a sample data file from the examples.</P>
<P>
This page has 2 sections:</P>
<UL>
<LI>
<A HREF="#_cch3_930958962">Rules for formatting the Data File</A>
<LI>
<A HREF="#_cch3_930958969">Sample file with Annotations</A>
</UL>
<HR>
<H3>
<A NAME="_cch3_930958962">Rules for formatting the Data File: </A></H3>
<P>
Blank lines are important. After the header section, new entries are
separated by blank lines. </P>
<P>
Indentation and space between words/numbers on one line is not
important except that keywords (e.g. Masses, Bond Coeffs) must be
left-justified and capitalized as shown. </P>
<P>
The header section (thru box bounds) must appear first in the file, the
remaining entries (Masses, various Coeffs, Atoms, Bonds, etc) can come
in any order. </P>
<P>
These entries must be in the file: header section, Masses, Atoms. </P>
<P>
These entries must be in the file if there are a non-zero number of
them: Bonds, Angles, Dihedrals, Impropers. Force field coefficients
can be specified in the input script, so do not have to appear in the
data file. The one exception to this is class 2 force field
coefficients which can only be specified in the data file.
<P>
The Nonbond Coeffs entry contains one line for each atom type. These
are the coefficients for an interaction between 2 atoms of the same
type. The cross-type coeffs are computed by the appropriate class I or
class II mixing rules, or can be specified explicitly using the
&quot;nonbond coeff&quot; command in the input command script. See the <A
HREF="force_fields.html">force_fields</A> page for more information. </P>
<P>
In the Atoms entry, the atoms can be in any order so long as there are
N entries. The 1st number on the line is the atom-tag (number from 1 to
N) which is used to identify the atom throughout the simulation. The
molecule-tag is a second identifier which is attached to the atom; it
can be 0, or a counter for the molecule the atom is part of, or any
other number you wish. The q value is the charge of the atom in
electron units (e.g. +1 for a proton). The xyz values are the initial
position of the atom. For 2-d simulations specify z as 0.0.</P>
<P>
The final 3 nx,ny,nz values on a line of the Atoms entry are optional.
LAMMPS only reads them if the &quot;true flag&quot; command is
specified in the input command script. Otherwise they are initialized
to 0 by LAMMPS. Their meaning, for each dimension, is that
&quot;n&quot; box-lengths are added to xyz to get the atom's
&quot;true&quot; un-remapped position. This can be useful in pre- or
post-processing to enable the unwrapping of long-chained molecules
which wind thru the periodic box one or more times. The value of
&quot;n&quot; can be positive, negative, or zero. For 2-d simulations
specify nz as 0. </P>
<P>
Atom velocities are initialized to 0.0 if there is no Velocities entry.
In the Velocities entry, the atoms can be in any order so long as there
are N entries. The 1st number on the line is the atom-tag (number from
1 to N) which is used to identify the atom which the given velocity
will be assigned to.</P>
<P>
Entries for Velocities, Bonds, Angles, Dihedrals, Impropers must appear
in the file after an Atoms entry.</P>
<P>
For simulations with periodic boundary conditions, xyz coords are
remapped into the periodic box (from as far away as needed), so the
initial coordinates need not be inside the box. The nx,ny,nz values
(as read in or as set to zero by LAMMPS) are appropriately adjusted by
this remapping. </P>
<P>
The number of coefficients specified on each line of coefficient
entries (Nonbond Coeffs, Bond Coeffs, etc) depends on the
&quot;style&quot; of interaction. This must be specified in the input
command script before the "read data" command is issued, unless the
default is used. See the <A
HREF="input_commands.html">input_commands</A> page for a description
of the various style options. The <A HREF="input_commands.html">input_commands</A>
and <A HREF="force_fields.html">force_fields</A> pages explain the
meaning and valid values for each of the coefficients. </P>
<HR>
<H3>
<A NAME="_cch3_930958969">Sample file with Annotations</A></H3>
<P>
Here is a sample file with annotations in parenthesis and lengthy
sections replaced by dots (...). Note that the blank lines are
important in this example.</P>
<PRE>
LAMMPS Description (1st line of file)
100 atoms (this must be the 3rd line, 1st 2 lines are ignored)
95 bonds (# of bonds to be simulated)
50 angles (include these lines even if number = 0)
30 dihedrals
20 impropers
5 atom types (# of nonbond atom types)
10 bond types (# of bond types = sets of bond coefficients)
18 angle types
20 dihedral types (do not include a bond,angle,dihedral,improper type
2 improper types line if number of bonds,angles,etc is 0)
-0.5 0.5 xlo xhi (for periodic systems this is box size,
-0.5 0.5 ylo yhi for non-periodic it is min/max extent of atoms)
-0.5 0.5 zlo zhi (do not include this line for 2-d simulations)
Masses
1 mass
...
N mass (N = # of atom types)
Nonbond Coeffs
1 coeff1 coeff2 ...
...
N coeff1 coeff2 ... (N = # of atom types)
Bond Coeffs
1 coeff1 coeff2 ...
...
N coeff1 coeff2 ... (N = # of bond types)
Angle Coeffs
1 coeff1 coeff2 ...
...
N coeff1 coeff2 ... (N = # of angle types)
Dihedral Coeffs
1 coeff1 coeff2 ...
...
N coeff1 coeff2 ... (N = # of dihedral types)
Improper Coeffs
1 coeff1 coeff2 ...
...
N coeff1 coeff2 ... (N = # of improper types)
BondBond Coeffs
1 coeff1 coeff2 ...
...
N coeff1 coeff2 ... (N = # of angle types)
BondAngle Coeffs
1 coeff1 coeff2 ...
...
N coeff1 coeff2 ... (N = # of angle types)
MiddleBondTorsion Coeffs
1 coeff1 coeff2 ...
...
N coeff1 coeff2 ... (N = # of dihedral types)
EndBondTorsion Coeffs
1 coeff1 coeff2 ...
...
N coeff1 coeff2 ... (N = # of dihedral types)
AngleTorsion Coeffs
1 coeff1 coeff2 ...
...
N coeff1 coeff2 ... (N = # of dihedral types)
AngleAngleTorsion Coeffs
1 coeff1 coeff2 ...
...
N coeff1 coeff2 ... (N = # of dihedral types)
BondBond13 Coeffs
1 coeff1 coeff2 ...
...
N coeff1 coeff2 ... (N = # of dihedral types)
AngleAngle Coeffs
1 coeff1 coeff2 ...
...
N coeff1 coeff2 ... (N = # of improper types)
Atoms
1 molecule-tag atom-type q x y z nx ny nz (nx,ny,nz are optional -
... see &quot;true flag&quot; input command)
...
N molecule-tag atom-type q x y z nx ny nz (N = # of atoms)
Velocities
1 vx vy vz
...
...
N vx vy vz (N = # of atoms)
Bonds
1 bond-type atom-1 atom-2
...
N bond-type atom-1 atom-2 (N = # of bonds)
Angles
1 angle-type atom-1 atom-2 atom-3 (atom-2 is the center atom in angle)
...
N angle-type atom-1 atom-2 atom-3 (N = # of angles)
Dihedrals
1 dihedral-type atom-1 atom-2 atom-3 atom-4 (atoms 2-3 form central bond)
...
N dihedral-type atom-1 atom-2 atom-3 atom-4 (N = # of dihedrals)
Impropers
1 improper-type atom-1 atom-2 atom-3 atom-4 (atom-2 is central atom)
...
N improper-type atom-1 atom-2 atom-3 atom-4 (N = # of impropers)
</PRE>
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<H2>
LAMMPS Deficiencies</H2>
<P>
<A HREF="README.html">Return</A> to top-level of LAMMPS documentation.</P>
<P>
This is a brief list of features lacking in the current version of
LAMMPS. Some of these deficiencies are because of lack of
time/interest; others are just hard!</P>
<UL>
<LI>
The calculation of pressure does not include a long-range Van der Waals
correction. This would be a constant for constant volume simulations
but is a source of error for constant pressure simulations where
the box-size varies dynamically.
<LI>
The smoothed Coulomb style cannot be used with class 2 force fields.
<LI>
The minimizer does not work with constant pressure conditions, nor
for some kinds of fixes (constraints).
<LI>
No support for non-rectilinear boxes (e.g. Parinello-Rahman
pressure control).
<LI>
SHAKE fixes cannot be combined with rREPSA.
<LI>
In the current F90 version of LAMMPS, Ewald computations are 2x slower
on some machines than they were in the earlier F77 version. This is
probably because of F90 compiler treatment of allocatable arrays. This
slowdown is not an issue with PPPM, which is more commonly used anyway.
<LI>
LAMMPS uses a spatial-decomposition of the simulation domain, but no
other load-balancing -- thus some geometries or density fluctuations can
lead to load imbalance on a parallel machine.
</UL>
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<H2>
LAMMPS Force Fields</H2>
<P>
<A HREF="README.html">Return</A> to top-level of LAMMPS documentation</P>
<P>
This file outlines the force-field formulas used in LAMMPS. Read this
file in conjunction with the <A HREF="data_format.html">data_format</A>
and <A HREF="units.html">units</A> files.</P>
<P>
The sections of this page are as follows:</P>
<UL>
<LI>
<A HREF="#_cch3_930957465">Nonbond Coulomb</A>
<LI>
<A HREF="#_cch3_930957471">Nonbond Lennard-Jones</A>
<LI>
<A HREF="#_cch3_930957478">Mixing Rules for Lennard-Jones</A>
<LI>
<A HREF="#_cch3_930957482">Bonds</A>
<LI>
<A HREF="#_cch3_930957488">Angles</A>
<LI>
<A HREF="#_cch3_930957509">Dihedrals</A>
<LI>
<A HREF="#_cch3_930957513">Impropers</A>
<LI>
<A HREF="#_cch3_930957527">Class 2 Force Field</A>
</UL>
<HR>
<H3>
<A NAME="_cch3_930957465">Nonbond Coulomb</A></H3>
<P>
Whatever Coulomb style is specified in the input command file, the
short-range Coulombic interactions are computed by this formula,
modified by an appropriate smoother for the smooth, Ewald, PPPM,
charmm, and debye styles.</P>
<PRE>
E = C q1 q2 / (epsilon * r)
r = distance (computed by LAMMPS)
C = hardwired constant to convert to energy units
q1,q2 = charge of each atom in electron units (proton = +1),
specified in &quot;Atoms&quot; entry in data file
epsilon = dielectric constant (vacuum = 1.0),
set by user in input command file
</PRE>
For the debye style, the smoother is exp(-kappa*r) where kappa is an
input parameter.
<HR>
<H3>
<A NAME="_cch3_930957471">Nonbond Lennard-Jones </A></H3>
<P>
The style of nonbond potential is specified in the input command file. </P>
<H4>
(1) lj/cutoff </H4>
<PRE>
E = 4 epsilon [ (sigma/r)^12 - (sigma/r)^6 ]
standard Lennard Jones potential
r = distance (computed by LAMMPS)
coeff1 = epsilon (energy)
coeff2 = sigma (distance)
2 coeffs are listed in data file or set in input script
1 cutoff is set in input script
</PRE>
<H4>
(2) lj/switch </H4>
<PRE>
E = 4 epsilon [ (sigma/r)^12 - (sigma/r)^6 ] for r &lt; r_inner
= spline fit for r_inner &lt; r &lt; cutoff
= 0 for r &gt; cutoff
switching function (spline fit) is applied to standard LJ
within a switching region (from r_inner to cutoff) so that
energy and force go smoothly to zero
spline coefficients are computed by LAMMPS
so that at inner cutoff (r_inner) the potential, force,
and 1st-derivative of force are all continuous,
and at outer cutoff (cutoff) the potential and force
both go to zero
r = distance (computed by LAMMPS)
coeff1 = epsilon (energy)
coeff2 = sigma (distance)
2 coeffs are listed in data file or set in input script
2 cutoffs (r_inner and cutoff) are set in input script
</PRE>
<H4>
(3) lj/shift </H4>
<PRE>
E = 4 epsilon [ (sigma/(r - delta))^12 - (sigma/(r - delta))^6 ]
same as lj/cutoff except that r is shifted by delta
r = distance (computed by LAMMPS)
coeff1 = epsilon (energy)
coeff2 = sigma (distance)
coeff3 = delta (distance)
3 coeffs are listed in data file or set in input script
1 cutoff is set in input script
</PRE>
<H4>
(4) soft </H4>
<PRE>
E = A * [ 1 + cos( pi * r / cutoff ) ]
useful for pushing apart overlapping atoms by ramping A over time
r = distance (computed by LAMMPS)
coeff1 = prefactor A at start of run (energy)
coeff2 = prefactor A at end of run (energy)
2 coeffs are listed in data file or set in input script
1 cutoff is set in input script
</PRE>
<H4>
(5) class2/cutoff </H4>
<PRE>
E = epsilon [ 2 (sigma/r)^9 - 3 (sigma/r)^6 ]
used with class2 bonded force field
r = distance (computed by LAMMPS)
coeff1 = epsilon (energy)
coeff2 = sigma (distance)
2 coeffs are listed in data file or set in input script
1 cutoff is set in input script
</PRE>
<H4>
6) lj/charmm </H4>
<PRE>
E = 4 epsilon [ (sigma/r)^12 - (sigma/r)^6 ] for r &lt; r_inner
= switch * E for r_inner &lt; r &lt; cutoff
= 0 for r &gt; cutoff
where
switch = [(cutoff^2 - r^2)^2 * (cutoff^2 + 2*r^2 - 3*r_inner)] /
[(cutoff^2 - r_inner^2)^3]
switching function is applied to standard LJ
within a switching region (from r_inner to cutoff) so that
energy and force go smoothly to zero
switching function causes that at inner cutoff (r_inner)
the potential and force are continuous,
and at outer cutoff (cutoff) the potential and force
both go to zero
r = distance (computed by LAMMPS)
coeff1 = epsilon (energy)
coeff2 = sigma (distance)
coeff3 = epsilon for 1-4 interactions (energy)
coeff4 = sigma for 1-4 interactions (distance)
4 coeffs are listed in data file or set in input script
2 cutoffs (r_inner and cutoff) are set in input script
</PRE>
<HR>
<H3>
<A NAME="_cch3_930957478">Mixing Rules for Lennard-Jones</A></H3>
<P>
The coefficients for each nonbond style are input in either the data
file by the &quot;read data&quot; command or in the input script using
the &quot;nonbond coeff&quot; command. In the former case, only one set
of coefficients is input for each atom type. The cross-type coeffs are
computed using one of three possible mixing rules: </P>
<PRE>
geometric: epsilon_ij = sqrt(epsilon_i * epsilon_j)
sigma_ij = sqrt(sigma_i * sigma_j)
arithmetic: epsilon_ij = sqrt(epsilon_i * epsilon_j)
sigma_ij = (sigma_i + sigma_j) / 2
sixthpower: epsilon_ij =
(2 * sqrt(epsilon_i*epsilon_j) * sigma_i^3 * sigma_j^3) /
(sigma_i^6 + sigma_j^6)
sigma_ij= ((sigma_i**6 + sigma_j**6) / 2) ^ (1/6)
</PRE>
<P>
The default mixing rule for nonbond styles lj/cutoff, lj/switch,
lj/shift, and soft is &quot;geometric&quot;. The default for nonbond
style class2/cutoff is &quot;sixthpower&quot;. </P>
<P>
The default can be overridden using the &quot;mixing style&quot;
command. Two exceptions to this are for the nonbond style soft, for
which only an epsilon prefactor is input. This is always mixed
geometrically. Also, for nonbond style lj/shift, the delta
coefficient is always mixed using the rule </P>
<UL>
<LI>
delta_ij = (delta_i + delta_j) / 2
</UL>
<HR>
<H3>
<A NAME="_cch3_930957482">Bonds</A></H3>
<P>
The style of bond potential is specified in the input command file.</P>
<H4>
(1) harmonic </H4>
<PRE>
E = K (r - r0)^2
standard harmonic spring
r = distance (computed by LAMMPS)
coeff1 = K (energy/distance^2) (the usual 1/2 is included in the K)
coeff2 = r0 (distance)
2 coeffs are listed in data file or set in input script
</PRE>
<H4>
(2) FENE/standard </H4>
<PRE>
E = -0.5 K R0^2 * ln[1 - (r/R0)^2] +
4 epsilon [(sigma/r)^12 - (sigma/r)^6] + epsilon
finite extensible nonlinear elastic (FENE) potential for
polymer bead-spring models
see Kremer, Grest, J Chem Phys, 92, p 5057 (1990)
r = distance (computed by LAMMPS)
coeff1 = K (energy/distance^2)
coeff2 = R0 (distance)
coeff3 = epsilon (energy)
coeff4 = sigma (distance)
1st term is attraction, 2nd term is repulsion (shifted LJ)
1st term extends to R0
2nd term only extends to the minimum of the LJ potential,
a cutoff distance computed by LAMMPS (2^(1/6) * sigma)
4 coeffs are listed in data file or set in input script
</PRE>
<H4>
(3) FENE/shift </H4>
<PRE>
E = -0.5 K R0^2 * ln[1 - ((r - delta)/R0)^2] +
4 epsilon [(sigma/(r - delta))^12 - (sigma/(r - delta))^6] + epsilon
same as FENE/standard expect that r is shifted by delta
r = distance (computed by LAMMPS)
coeff1 = K (energy/distance^2)
coeff2 = R0 (distance)
coeff3 = epsilon (energy)
coeff4 = sigma (distance)
coeff5 = delta (distance)
1st term is attraction, 2nd term is repulsion (shifted LJ)
1st term extends to R0
2nd term only extends to the minimum of the LJ potential,
a cutoff distance computed by LAMMPS (2^(1/6) * sigma + delta)
5 coeffs are listed in data file or set in input script
</PRE>
<H4>
(4) nonlinear </H4>
<PRE>
E = epsilon (r - r0)^2 / [ lamda^2 - (r - r0)^2 ]
non-harmonic spring of equilibrium length r0
with finite extension of lamda
see Rector, Van Swol, Henderson, Molecular Physics, 82, p 1009 (1994)
r = distance (computed by LAMMPS)
coeff1 = epsilon (energy)
coeff2 = r0 (distance)
coeff3 = lamda (distance)
3 coeffs are listed in data file or set in input script
</PRE>
<H4>
(5) class2 </H4>
<PRE>
E = K2 (r - r0)^2 + K3 (r - r0)^3 + K4 (r - r0)^4
r = distance (computed by LAMMPS)
coeff1 = r0 (distance)
coeff2 = K2 (energy/distance^2)
coeff3 = K3 (energy/distance^3)
coeff4 = K4 (energy/distance^4)
4 coeffs are listed in data file - cannot be set in input script
</PRE>
<HR>
<H3>
<A NAME="_cch3_930957488">Angles </A></H3>
<P>
The style of angle potential is specified in the input command file. </P>
<H4>
(1) harmonic </H4>
<PRE>
E = K (theta - theta0)^2
theta = radians (computed by LAMMPS)
coeff1 = K (energy/radian^2) (the usual 1/2 is included in the K)
coeff2 = theta0 (degrees) (converted to radians within LAMMPS)
2 coeffs are listed in data file or set in input script
</PRE>
<H4>
(2) class2 </H4>
<PRE>
E = K2 (theta - theta0)^2 + K3 (theta - theta0)^3 +
K4 (theta - theta0)^4
theta = radians (computed by LAMMPS)
coeff1 = theta0 (degrees) (converted to radians within LAMMPS)
coeff2 = K2 (energy/radian^2)
coeff3 = K3 (energy/radian^3)
coeff4 = K4 (energy/radian^4)
4 coeffs are listed in data file - cannot be set in input script
</PRE>
<H4>
(3) charmm </H4>
<PRE>
(harmonic + Urey-Bradley)
E = K (theta - theta0)^2 + K_UB (r_13 - r_UB)^2
theta = radians (computed by LAMMPS)
r_13 = distance (computed by LAMMPS)
coeff1 = K (energy/radian^2) (the usual 1/2 is included in the K)
coeff2 = theta0 (degrees) (converted to radians within LAMMPS)
coeff3 = K_UB (energy/distance^2)
coeff4 = r_UB (distance)
4 coeffs are listed in data file or set in input script
</PRE>
<H4>
(4) cosine </H4>
<PRE>
E = K (1 + cos(theta))
theta = radians (computed by LAMMPS)
coeff1 = K (energy)
1 coeff is listed in data file or set in input script
</PRE>
<H3>
<A NAME="_cch3_930957509">Dihedrals </A></H3>
<P>
The style of dihedral potential is specified in the input command
file. IMPORTANT NOTE for all these dihedral styles: in the LAMMPS
force field the trans position = 180 degrees, while in some force
fields trans = 0 degrees. </P>
<H4>
(1) harmonic </H4>
<PRE>
E = K [1 + d * cos (n*phi) ]
phi = radians (computed by LAMMPS)
coeff1 = K (energy)
coeff2 = d (+1 or -1)
coeff3 = n (1,2,3,4,6)
Additional cautions when comparing to other force fields:
some force fields reverse the sign convention on d so that
E = K [1 - d * cos(n*phi)]
some force fields divide/multiply K by the number of multiple
torsions that contain the j-k bond in an i-j-k-l torsion
some force fields let n be positive or negative which
corresponds to d = 1,-1
3 coeffs are listed in data file or set in input script
</PRE>
<H4>
(2) class2 </H4>
<PRE>
E = SUM(n=1,3) { K_n [ 1 - cos( n*Phi - Phi0_n ) ] }
phi = radians (computed by LAMMPS)
coeff1 = K_1 (energy)
coeff2 = Phi0_1 (degrees) (converted to radians within LAMMPS)
coeff3 = K_2 (energy)
coeff4 = Phi0_2 (degrees) (converted to radians within LAMMPS)
coeff5 = K_3 (energy)
coeff6 = Phi0_3 (degrees) (converted to radians within LAMMPS)
6 coeffs are listed in data file - cannot be set in input script
</PRE>
<H4>
(3) multiharmonic </H4>
<PRE>
E = SUM(n=1,5) { A_n * cos(Phi)^(n-1) }
phi = radians (computed by LAMMPS)
coeff1 = A_1
coeff2 = A_2
coeff3 = A_3
coeff4 = A_4
coeff5 = A_5
5 coeffs are listed in data file or set in input script
</PRE>
<H4>
(4) charmm </H4>
<PRE>
(harmonic + 1-4 interactions)
E = K [1 + cos (n*phi + d) ]
phi = radians (computed by LAMMPS)
coeff1 = K (energy)
coeff2 = n (1,2,3,4,6)
coeff3 = d (0 or 180 degrees) (converted to radians within LAMMPS)
coeff4 = weighting factor to turn on/off 1-4 neighbor nonbond interactions
coeff4 weight values are from 0.0 to 1.0 and are used to multiply the
energy and force interaction (both Coulombic and LJ) between the 2 atoms
weight of 0.0 means no interaction
weight of 1.0 means full interaction
must be used with the special bonds charmm command
"special bonds 0 0 0") which shuts off the uniform special bonds and
allows pair-specific special bonds for the 1-4 interactions to be
defined in the data file
LAMMPS assumes that all 1-4 interaction distances, which are
generally less than 6 Angstroms, are less than the smallest of the
inner LJ and Coulombic cutoffs, which are generally at least 8
Angstroms.
4 coeffs are listed in data file or set in input script
</PRE>
<HR>
<H3>
<A NAME="_cch3_930957513">Impropers</A></H3>
<P>
The style of improper potential is specified in the input command file. </P>
<H4>
(1) harmonic </H4>
<PRE>
E = K (chi - chi0)^2
chi = radians (computed by LAMMPS)
coeff1 = K (energy/radian^2) (the usual 1/2 is included in the K)
coeff2 = chi0 (degrees) (converted to radians within LAMMPS)
2 coeffs are listed in data file or set in input script
</PRE>
<H4>
(2) cvff </H4>
<PRE>
E = K [1 + d * cos (n*chi) ]
chi = radians (computed by LAMMPS)
coeff1 = K (energy)
coeff2 = d (+1 or -1)
coeff3 = n (0,1,2,3,4,6)
3 coeffs are listed in data file or set in input script
</PRE>
<H4>
(3) class2 </H4>
<PRE>
same formula, coeffs, and meaning as &quot;harmonic&quot; except that LAMMPS
averages all 3 angle-contributions to chi
in class 2 this is called a Wilson out-of-plane interaction
2 coeffs are listed in data file - cannot be set in input script
</PRE>
<HR>
<H3>
<A NAME="_cch3_930957527">Class 2 Force Field</A></H3>
<P>
If class 2 force fields are selected in the input command file,
additional cross terms are computed as part of the force field. All
class 2 coefficients must be set in the data file; they cannot be set
in the input script.</P>
<H4>
Bond-Bond (computed within class 2 angles) </H4>
<PRE>
E = K (r - r0) * (r' - r0')
r,r' = distance (computed by LAMMPS)
coeff1 = K (energy/distance^2)
coeff2 = r0 (distance)
coeff3 = r0' (distance)
3 coeffs are input in data file
</PRE>
<H4>
Bond-Angle (computed within class 2 angles for each of 2 bonds) </H4>
<PRE>
E = K_n (r - r0_n) * (theta - theta0)
r = distance (computed by LAMMPS)
theta = radians (computed by LAMMPS)
coeff1 = K_1 (energy/distance-radians)
coeff2 = K_2 (energy/distance-radians)
coeff3 = r0_1 (distance)
coeff4 = r0_2 (distance)
Note: theta0 is known from angle coeffs so don't need it specified here
4 coeffs are listed in data file
</PRE>
<H4>
Middle-Bond-Torsion (computed within class 2 dihedral) </H4>
<PRE>
E = (r - r0) * [ F1*cos(phi) + F2*cos(2*phi) + F3*cos(3*phi) ]
r = distance (computed by LAMMPS)
phi = radians (computed by LAMMPS)
coeff1 = F1 (energy/distance)
coeff2 = F2 (energy/distance)
coeff3 = F3 (energy/distance)
coeff4 = r0 (distance)
4 coeffs are listed in data file
</PRE>
<H4>
End-Bond-Torsion (computed within class 2 dihedral for each of 2 bonds) </H4>
<PRE>
E = (r - r0_n) * [ F1_n*cos(phi) + F2_n*cos(2*phi) + F3_n*cos(3*phi) ]
r = distance (computed by LAMMPS)
phi = radians (computed by LAMMPS)
coeff1 = F1_1 (energy/distance)
coeff2 = F2_1 (energy/distance)
coeff3 = F3_1 (energy/distance)
coeff4 = F1_2 (energy/distance)
coeff5 = F2_3 (energy/distance)
coeff6 = F3_3 (energy/distance)
coeff7 = r0_1 (distance)
coeff8 = r0_2 (distance)
8 coeffs are listed in data file
</PRE>
<H4>
Angle-Torsion (computed within class 2 dihedral for each of 2 angles) </H4>
<PRE>
E = (theta - theta0) * [ F1_n*cos(phi) + F2_n*cos(2*phi) + F3_n*cos(3*phi) ]
theta = radians (computed by LAMMPS)
phi = radians (computed by LAMMPS)
coeff1 = F1_1 (energy/radians)
coeff2 = F2_1 (energy/radians)
coeff3 = F3_1 (energy/radians)
coeff4 = F1_2 (energy/radians)
coeff5 = F2_3 (energy/radians)
coeff6 = F3_3 (energy/radians)
coeff7 = theta0_1 (degrees) (converted to radians within LAMMPS)
coeff8 = theta0_2 (degrees) (converted to radians within LAMMPS)
8 coeffs are listed in data file
</PRE>
<H4>
Angle-Angle-Torsion (computed within class 2 dihedral) </H4>
<PRE>
E = K (theta - theta0) * (theta' - theta0') * (phi - phi0)
theta,theta' = radians (computed by LAMMPS)
phi = radians (computed by LAMMPS)
coeff1 = K (energy/radians^3)
coeff2 = theta0 (degrees) (converted to radians within LAMMPS)
coeff3 = theta0' (degrees) (converted to radians within LAMMPS)
Note: phi0 is known from dihedral coeffs so don't need it specified here
3 coeffs are listed in data file
</PRE>
<H4>
Bond-Bond-13-Torsion (computed within class 2 dihedral) </H4>
<PRE>
E = K * (r1 - r10)*(r3 - r30)
r1,r3 = bond lengths of bonds 1 and 3 (computed by LAMMPS)
coeff1 = K (energy/distance^2)
coeff2 = r10 (distance) = equilibrium bond length for bond 1
coeff3 = r30 (distance) = equilibrium bond length for bond 3
K is only non-zero for aromatic rings
3 coeffs are listed in data file
</PRE>
<H4>
Angle-Angle (computed within class 2 improper for each of 3 pairs of
angles) </H4>
<PRE>
E = K_n (theta - theta0_n) * (theta' - theta0_n')
theta,theta' = radians (computed by LAMMPS)
coeff1 = K_1 (energy/radians^2)
coeff2 = K_2 (energy/radians^2)
coeff3 = K_3 (energy/radians^2)
coeff4 = theta0_1 (degrees) (converted to radians within LAMMPS)
coeff5 = theta0_2 (degrees) (converted to radians within LAMMPS)
coeff6 = theta0_3 (degrees) (converted to radians within LAMMPS)
6 coeffs are listed in data file
</PRE>
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<H2>
History of LAMMPS</H2>
<P>
<A HREF="README.html">Return</A> to top-level of LAMMPS documentation.</P>
<P>
This is a brief history of features added to each version of LAMMPS.</P>
<HR>
<H3>
LAMMPS 2001 - November 2001</H3>
<UL>
<LI>
F90 + MPI version of code
<LI>
dynamic memory, no param.h file settings to twiddle, see "extra memory"
command
<LI>
changed required ordering of some input script commands (see discussion in
<A HREF="input_commands.html">input_commands</A>) file
<LI>
new commands: "extra memory", "maximum cutoff", "restart version",
"angle coeff", "dihedral coeff", "improper coeff",
"volume control", "slab volume", "rotation zero"
<LI>
changed meaning or syntax of commands:
"special bonds", "fix style rescale", "fix style hoover/drag",
"temp control rescale", "press control", "restart"
<LI>
deleted commands: "log file", "press_x control" (and y,z)
<LI>
better match to CHARMM force fields via "nonbond style lj/charmm",
"coulomb style charmm/switch", "angle style charmm", dihedral style charmm"
(due to Mark Stevens and Paul Crozier)
<LI>
changed "special bonds" default to 0.0 weighting on 1-4 interactions for
CHARMM compatibility, added "special bonds amber" option for AMBER
compatibility
<LI>
ghost atoms and new treatment of periodic boundary conditions,
this allows for cutoffs &gt; box-size and faster neighbor binning,
binned neighbor list construction is now the default as it is almost
always faster
<LI>
perform blocked-input from data and restart files, faster for many MPI
implementations (due to Mathias Puetz)
<LI>
added Velocities option to data file to initialize each atom's
velocity (see <A HREF="data_format.html">data_format</A> file)
<LI>
pressure control was decoupled from temperature control, so that
constant NPH simulations can be run (not just NPT), temperature
controls such as rescale or Langevin can now be used with constant P
simulations (due to Mark Stevens)
<LI>
temperature rescaling (either in "temp control" or "fix style rescale")
has an added fractional parameter which allows it to be applied
in a lightweight or heavy-handed way to induce the desired temperature
<LI>
got rid of crib.html file, see global.f for documentation of all
variables
<LI>
2-d slab Ewald and PPPM option, (see "slab volume" in
<A HREF="input_commands.html">input commands</A>) (due to Paul Crozier)
<LI>
new multiharmonic dihedral and cvff improper force-field options
(due to Mathias Puetz)
<LI>
SHAKE constraint for small clusters of atoms, see "fix style shake"
and "assign fix bondtype" commands
<LI>
added option to output restart files with timestep stamp or to toggle
between 2 files, see "restart" command
<LI>
tools for converting to/from other MD program formats:
msi2lmp (updated by John Carpenter),
lmp2arc (due to John Carpenter),
amber2lammps & dump2trj (Python scripts due to Keir Novik)
<LI>
tools for creating and massaging LAMMPS data and restart files:
setup_lj, setup_flow_2d, setup_chain, peek_restart, restart2data,
replicate
</UL>
<HR>
<H3>
LAMMPS 99 - June 99 </H3>
<UL>
<LI>
all-MPI version of code (F77 + C + MPI) for maximum portablility
<LI>
only one PPPM choice now, the better of the two earlier ones
<LI>
PPPM uses portable FFTs and data remapping routines, written in C w/
MPI, can now use non-power-of-2 processors and grid sizes
<LI>
auto-mapping of simulation box to processors
<LI>
removed a few unused/unneeded commands (bdump, log file, id string,
limit)
<LI>
changed syntax of some commands for simplicity &amp; consistency (see <A
HREF="input_commands.html">input commands</A>)
<LI>
changed method of calling/writing user diagnostic routines to be
simpler
<LI>
documentation in HTML format
</UL>
<HR>
<H3>
Version 5.0 - Oct 1997 </H3>
<UL>
<LI>
final version of class II force fields (due to Eric Simon)
<LI>
new formulation of NVE, NVT, NPT and rRESPA integrators (due to
Mark Stevens)
<LI>
new version of msi2lmp pre-processing tool, does not require DISCOVER
to run, only DISCOVER force field files (due to Steve Lustig)
<LI>
energy minimizer, Hessian-free truncated Newton method
(due to Todd Plantenga)
<LI>
new pressure controllers and constraints (due to Mark Stevens)
<LI>
replicate tool for generating new data files from old ones
</UL>
<HR ALIGN="LEFT">
<H3>
Version 4.0 - March 1997 </H3>
<UL>
<LI>
1st version of class II force fields (due to Eric Simon)
<LI>
new, faster PPPM solver (newpppm, due to Roy Pollock)
<LI>
rRESPA (due to Mark Stevens)
<LI>
new data file format
<LI>
new constraints, diagnostics
<LI>
msi2lmp pre-processing tool (due to Steve Lustig)
</UL>
<HR>
<H3>
Version 3.0 - March 1996 </H3>
<UL>
<LI>
more general force-field formulation
<LI>
atom/group constraints
<LI>
LJ units and bond potentials
<LI>
smoothed LJ potential option
<LI>
Langevin thermostat
<LI>
Newton's 3rd law option
<LI>
hook for user-supplied diagnostic routines
</UL>
<HR>
<H3>
Version 2.0 - October 1995 </H3>
<UL>
<LI>
bug fix of velocity initialization which caused drift
<LI>
PPPM for long-range Coulombic (due to Roy Pollock)
<LI>
constant NPT (due to Mark Stevens)
</UL>
<HR>
<H3>
Version 1.1 - February 1995 </H3>
<UL>
<LI>
Ewald for long-range Coulombic (due to Roy Pollock)
<LI>
full Newton's 3rd law (doubled communication)
<LI>
dumping of atom positions and velocities
<LI>
restart files
</UL>
<HR>
<H3>
Version 1.0 - January 1995 </H3>
<UL>
<LI>
short-range bonded and non-bonded forces
<LI>
partial Newton's 3rd law
<LI>
velocity-Verlet integrator
</UL>
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<H2>
LAMMPS Units</H2>
<P>
<A HREF="README.html">Return</A> to top-level LAMMPS documentation.</P>
<P>
This file describes the units associated with many of the key variables
and equations used inside the LAMMPS code. Units used for input command
parameters are described in the input_commands file. The input command
&quot;units&quot; selects between conventional and Lennard-Jones units.
See the force_fields file for more information on units for the force
field parameters that are input from data files or input scripts. </P>
<P>
Conventional units: </P>
<UL>
<LI>
distance = Angstroms
<LI>
time = femtoseconds
<LI>
mass = grams/mole
<LI>
temperature = degrees K
<LI>
pressure = atmospheres
<LI>
energy = Kcal/mole
<LI>
velocity = Angstroms/femtosecond
<LI>
force = grams/mole * Angstroms/femtosecond^2
<LI>
charge = +/- 1.0 is proton/electron
</UL>
<P>
LJ reduced units: </P>
<UL>
<LI>
distance = sigmas
<LI>
time = reduced LJ tau
<LI>
mass = ratio to unitless 1.0
<LI>
temperature = reduced LJ temp
<LI>
pressure = reduced LJ pressure
<LI>
energy = epsilons
<LI>
velocity = sigmas/tau
<LI>
force = reduced LJ force (sigmas/tau^2)
<LI>
charge = ratio to unitless 1.0
</UL>
<HR>
<P>
This listing of variables assumes conventional units; to convert to LJ
reduced units, simply substitute the appropriate term from the list
above. E.g. x is in sigmas in LJ units. Per-mole in any of the units
simply means for 6.023 x 10^23 atoms.</P>
<P>
</P>
<PRE>
Meaning Variable Units
positions x Angstroms
velocities v Angstroms / click (see below)
forces f Kcal / (mole - Angstrom)
masses mass gram / mole
charges q electron units (-1 for an electron)
(1 e.u. = 1.602 x 10^-19 coul)
time --- clicks (1 click = 48.88821 fmsec)
timestep dt clicks
input timestep dt_in fmsec
time convert dtfactor 48.88821 fmsec / click
temperature t_current degrees K
t_start
t_stop
input damping t_freq_in inverse fmsec
internal temp t_freq inverse clicks
damping
dielec const dielectric 1.0 (unitless)
Boltmann const boltz 0.001987191 Kcal / (mole - degree K)
virial virial[xyz] Kcal/mole = r dot F
pressure factor pfactor 68589.796 (convert internal to atmospheres)
internal p_current Kcal / (mole - Angs^3)
pressure p_start
p_stop
input press p_start_in atmospheres
p_stop_in
output press log file atmospheres
input damping p_freq_in inverse time
internal press p_freq inverse clicks
damping
pot eng e_potential Kcal/mole
kin eng e_kinetic Kcal/mole
eng convert efactor 332.0636 (Kcal - Ang) / (q^2 - mole)
(convert Coulomb eng to Kcal/mole)
LJ coeffs lja,ljb Kcal-Angs^(6,12)/mole
bond various see force_fields file
parameters 2,3,4-body
terms
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<H2>
LAMMPS</H2>
<P>
LAMMPS = Large-scale Atomic/Molecular Massively Parallel Simulator</P>
<P>
This is the documentation for the LAMMPS 99 version, written in F77,
which has been superceded by more current versions. See the <A
HREF="http://www.cs.sandia.gov/~sjplimp/lammps.html">LAMMPS WWW
Site</A> for more information.
<P>
LAMMPS is a classical molecular dynamics code designed for simulating
molecular and atomic systems on parallel computers using
spatial-decomposition techniques. It runs on any parallel platform that
supports the MPI message-passing library or on single-processor
workstations.</P>
<P>
LAMMPS 99 is copyrighted code that is distributed freely as
open-source software under the GNU Public License (GPL). See the
LICENSE file or <A HREF="http://www.gnu.org">www.gnu.org</A> for more
details. Basically the GPL allows you as a user to use, modify, or
distribute LAMMPS however you wish, so long as any software you
distribute remains under the GPL.
<P>
Features of LAMMPS 99 include:</P>
<UL>
<LI>
short-range pairwise Lennard-Jones and Coulombic interactions
<LI>
long-range Coulombic interactions via Ewald or PPPM (particle-mesh
Ewald)
<LI>
short-range harmonic bond potentials (bond, angle, torsion, improper)
<LI>
short-range class II (cross-term) molecular potentials
<LI>
NVE, NVT, NPT dynamics
<LI>
constraints on atoms or groups of atoms
<LI>
rRESPA long-timescale integrator
<LI>
energy minimizer (Hessian-free truncated Newton method)
</UL>
<P>
More details about the code can be found <A HREF="#_cch3_930958294">here</A>,
in the HTML-based documentation. There is also a conference paper
describing the parallel algorithms used in the code:</P>
<P>
S. J. Plimpton, R. Pollock, M. Stevens, &quot;Particle-Mesh Ewald and
rRESPA for Parallel Molecular Dynamics Simulations&quot;, in Proc of
the Eighth SIAM Conference on Parallel Processing for Scientific
Computing, Minneapolis, MN, March 1997.</P>
<P>
LAMMPS was originally developed as part of a 5-way CRADA collaboration
between 3 industrial partners (Cray Research, Bristol-Myers Squibb, and
Dupont) and 2 DoE laboratories (Sandia National Laboratories and
Lawrence Livermore National Laboratories).</P>
<P>
The primary author of LAMMPS is Steve Plimpton, but others have written
or worked on significant portions of the code:</P>
<UL>
<LI>
Roy Pollock (LLNL): Ewald, PPPM solvers
<LI>
Mark Stevens (Sandia): rRESPA, NPT integrators
<LI>
Eric Simon (Cray Research): class II force fields
<LI>
Todd Plantenga (Sandia): energy minimizer
<LI>
Steve Lustig (Dupont): msi2lmp tool
<LI>
Mike Peachey (Cray Research): msi2lmp tool
</UL>
<P>
Other CRADA partners involved in the design and testing of LAMMPS are </P>
<UL>
<LI>
John Carpenter (Cray Research)
<LI>
Terry Stouch (Bristol-Myers Squibb)
<LI>
Jim Belak (LLNL)
</UL>
<P>
LAMMPS is copyrighted code that is distributed freely as open-source
software under the GNU Public License (GPL). See the LICENSE file or
<A HREF="http://www.gnu.org">www.gnu.org</A> for more details.
Basically the GPL allows you as a user to use, modify, or distribute
LAMMPS however you wish, so long as any software you distribute
remains under the GPL.
<P>
If you have questions about LAMMPS, please contact me:
</P>
<DL>
<DT>
Steve Plimpton
<DD>
sjplimp@sandia.gov
<DD>
www.cs.sandia.gov/~sjplimp
<DD>
Sandia National Labs
<DD>
Albuquerque, NM 87185
</DL>
<HR>
<H3>
<A NAME="_cch3_930958294">More Information about LAMMPS</A></H3>
<DIR>
<LI>
<A HREF="basics.html">Basics</A>
<DIR>
<LI>
how to make, run, and test LAMMPS with the example problems
</DIR>
<LI>
<A HREF="input_commands.html">Input Commands</A>
<DIR>
<LI>
a complete listing of input commands used by LAMMPS
</DIR>
<LI>
<A HREF="data_format.html">Data Format</A>
<DIR>
<LI>
the data file format used by LAMMPS
</DIR>
<LI>
<A HREF="force_fields.html">Force Fields</A>
<DIR>
<LI>
the equations LAMMPS uses to compute force-fields
</DIR>
<LI>
<A HREF="units.html">Units</A>
<DIR>
<LI>
the input/output and internal units for LAMMPS variables
</DIR>
<LI>
<A HREF="crib.html">Crib</A>
<DIR>
<LI>
a one-line description of the variables used in LAMMPS
</DIR>
<LI>
<A HREF="history.html">History</A>
<DIR>
<LI>
a brief timeline of features added to LAMMPS
</DIR>
</DIR>
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<H2>
Basics of Using LAMMPS</H2>
<P>
<A HREF="README.html">Return</A> to top-level of LAMMPS documentation.</P>
<UL>
<LI>
<A HREF="#_cch3_931273040">Distribution</A>
<LI>
<A HREF="#_cch3_930327142">Making LAMMPS</A>
<LI>
<A HREF="#_cch3_930327155">Running LAMMPS</A>
<LI>
<A HREF="#_cch3_930759879">Examples</A>
<LI>
<A HREF="#_cch3_931282515">Other Tools</A>
</UL>
<HR>
<H3>
<A NAME="_cch3_931273040">Distribution</A></H3>
<P>
When you unzip/untar the LAMMPS distribution you should have 5
directories: </P>
<UL>
<LI>
src = source files for LAMMPS
<LI>
doc = HTML documentation
<LI>
examples = sample problems with inputs and outputs
<LI>
msi2lmp = tool for converting files from DISCOVER to LAMMPS format
(this requires that you have DISCOVER force field files)
<LI>
tools = serial program for replicating data files
</UL>
<HR>
<H3>
<A NAME="_cch3_930327142">Making LAMMPS</A></H3>
<P>
The src directory contains the F77 and C source files for LAMMPS as
well as several sample Makefiles for different machines. To make LAMMPS
for a specfic machine, you simply type</P>
<P>
make machine</P>
<P>
from within the src directoy. E.g. &quot;make sgi&quot; or &quot;make
t3e&quot;. This should create an executable named lmp_sgi or lmp_t3e.</P>
<P>
In the src directory, there is one top-level Makefile and several
low-level machine-specific files named Makefile.xxx where xxx = the
machine name. If a low-level Makefile exists for your platform, you do
not need to edit the top-level Makefile. However you should check the
system-specific section of the low-level Makefile to make sure the
various paths are correct for your environment. If a low-level Makefile
does not exist for your platform, you will need to add a suitable
target to the top-level Makefile. You will also need to create a new
low-level Makefile using one of the existing ones as a template. If you
wish to make LAMMPS for a single-processor workstation that doesn't
have an installed MPI library, you can specify the serial target which
uses a directory of MPI stubs to link against - e.g. &quot;make
serial&quot;. You will need to make the stub library (see STUBS
directory) on your workstation before doing this.</P>
<P>
Note that the two-level Makefile system allows you to make LAMMPS for
multiple platforms. Each target creates its own object directory for
separate storage of its *.o files.</P>
<P>
There are a couple compiler switches of interest which can be specified
in the low-level Makefiles. If you use a F77FLAGS switch of -DSYNC then
synchronization calls will be made before the timing routines in
integrate.f. This may slow down the code slightly, but will make the
reported timings at the end of a run more accurate. The CCFLAGS setting
in the low-level Makefiles requires a FFT setting, for example
-DFFT_SGI or -DFFT_T3E. This is for inclusion of the appropriate
machine-specific native 1-d FFT libraries on various platforms.
Currently, the supported machines and switches (used in fft_3d.c) are
FFT_SGI, FFT_DEC, FFT_INTEL, FFT_T3E, and FFT_FFTW. The latter is a
publicly available portable FFT library, <A HREF="http://www.fftw.org">FFTW</A>,
which you can install on any machine. If none of these options is
suitable for your machine, please contact me, and we'll discuss how to
add the capability to call your machine's native FFT library.</P>
<HR>
<H3>
<A NAME="_cch3_930327155">Running LAMMPS</A></H3>
<P>
LAMMPS is run by redirecting a file of input commands into it.</P>
<P>
lmp_sgi &lt; in.lj</P>
<P>
lmp_t3e &lt; in.lj</P>
<P>
The input file contains commands that specify the parameters for the
simulation as well as read other necessary files such as a data file
that describes the initial atom positions, molecular topology, and
force-field parameters. The <A HREF="input_commands.html">input_commands</A>
page describes all the possible commands that can be used. The <A
HREF="data_format.html">data_format</A> page describes the format of
the data file. </P>
<P>
LAMMPS can be run on any number of processors, including a single
processor. In principle you should get identical answers on any number
of processors and on any machine. In practice, numerical round-off can
cause slight differences and eventual divergence of dynamical
trajectories. </P>
<P>
When LAMMPS runs, if you get an error message to the screen about
&quot;boosting&quot; something, it means one (or more) data arrays are
not allocated large enough. Some of these errors are detected at setup,
others like neighbor list overflow may not occur until the middle of a
run. When the latter happens the program will either gracefully stop
(if all processors incurred the same error) or hang (with an error
message). Unfortunately in the current version of LAMMPS which uses
static memory allocation, changing the array size(s) requires you to
edit the appropriate line(s) in the param.h file and recompile the code.</P>
<P>
I've tried to be careful about detecting memory-overflow errors in
LAMMPS. If the code ever crashes or hangs without spitting out an error
message first, it's probably a bug, so let me know about it. Of course
this applies to problems due to algorithmic or parallelism issues, not
to physics mistkaes, like specifying too big a timestep or putting 2
atoms on top of each other! One exception is that different MPI
implementations handle buffering of messages differently. If the code
hangs without an error message, it may be that you need to specify an
MPI setting or two (usually via an environment variable) to enable
buffering or boost the sizes of messages that can be buffered. </P>
<HR>
<H3>
<A NAME="_cch3_930759879">Examples</A></H3>
<P>
There are several sample problems in the examples directory. All of
them use an input file (in.*) of commands and a data file (data.*) of
initial atomic coordinates and produce one or more output files. The
*.xxx.P files are outputs on P processors on a particular machine which
you can compare your answers to.</P>
<P>
(1) lj</P>
<P>
Simple atomic simulations of Lennard-Jones atoms of 1 or 3 species with
various ensembles -- NVE, NVT, NPT.</P>
<P>
(2) charge</P>
<P>
A few timestep simulation of a box of charged atoms for testing the
Coulombic options -- cutoff, Ewald, particle-mesh Ewald (PPPM).</P>
<P>
(3) class2</P>
<P>
A simple test run of phenyalanine using DISCOVER cff95 class II force
fields.</P>
<P>
(4) min</P>
<P>
An energy minimization of a transcription protein.</P>
<P>
(5) lc</P>
<P>
Small (250 atom) and large (6750 atom) simulations of liquid crystal
molecules with various Coulombic options and periodicity settings. The
large-system date file was created by using the &quot;replicate&quot;
tool on the small-system data file.</P>
<P>
(6) flow</P>
<P>
2-d flow of Lennard-Jones atoms in a channel using various contraint
options.</P>
<P>
(7) polymer</P>
<P>
Simulations of bead-spring polymer models with one chain type and two
chain types (different size monomers). The two-chain system also has
freely diffusing monomers. This illustrates use of the setup_chain
program in the tools directory and also how to use soft potentials to
untangle the initial configurations.</P>
<HR>
<H3>
<A NAME="_cch3_931282515">Other Tools</A></H3>
<P>
The msi2lmp directory has source code for a tool that converts MSI
Discover files to LAMMPS input data files. This tool requires you to
have the Discover force-field description files in order to convert
those parameters to LAMMPS parameters. See the README file in the
msi2lmp directory for additional information.</P>
<P>
The tools directory has a C file called replicate.c which is useful for
generating new LAMMPS data files from existing ones - e.g. scaling the
atom coordinates, replicating the system to make a larger one, etc. See
the comments at the top of replicate.c for instructions on how to use
it.</P>
<P>
The tools directory has a F77 program called setup_lj (compile and link
with print.c) which can be used to generate a 3-d box of Lennard Jones
atoms (one or more atom types) like those used in examples/lj.</P>
<P>
The tools directory also has a F77 program called setup_chain.f
(compile and link with print.c) which can be used to generate random
initial polymer configurations for bead-spring models like those used
in examples/polymer. It uses an input polymer definition file (see
examples/polymer for two sample def files) that specfies how many
chains of what length, a random number seed, etc.</P>
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<H2>
Crib File</H2>
<P>
<A HREF="README.html">Return</A> to top-level of LAMMPS documentation.</P>
<P>
This file contains one-line descriptions of the key variables and
parameters used in LAMMPS. The variables are listed by their data type:</P>
<UL>
<LI>
<A HREF="#_cch3_930764945">Parameters</A>
<LI>
<A HREF="#_cch3_930764951">Arrays (real</A>)
<LI>
<A HREF="#_cch3_930764957">Arrays (integer)</A>
<LI>
<A HREF="#_cch3_930764964">Variables (real)</A>
<LI>
<A HREF="#_cch3_930764969">Variables (integer)</A>
<LI>
<A HREF="#_cch3_930764974">Variables (character)</A>
</UL>
<P>
Note: this file is somewhat out-of-date for LAMMPS 99.</P>
<HR>
<H3>
<A NAME="_cch3_930764945">Parameters: </A></H3>
<UL>
<LI>
maxown = max # of local owned atoms
<LI>
maxother = max # of local nearby atoms
<LI>
maxtotal = max # of total atoms in simulation
<LI>
maxtype = max # of atom types
<LI>
maxbond = max # of bonds to compute on one procesor
<LI>
maxangle = max # of angles to compute on one processor
<LI>
maxdihed = max # of dihedrals to compute on one processor
<LI>
maximpro = max # of impropers to compute on one processor
<LI>
maxbondper = max # of bonds of one atom
<LI>
maxangleper = max # of angles of one atom
<LI>
maxdihedper = max # of dihedrals of one atom
<LI>
maximproper = max # of impropers of one atom
<LI>
maxbondtype = max # of bond types
<LI>
maxangletype = max # of angle types
<LI>
maxdihedtype = max # of dihedral types
<LI>
maximprotype = max # of improper types
<LI>
maxexch = max # of atoms in exchange buffer
<LI>
maxsend = max # of atoms to send to all neighbors in all swaps
<LI>
maxsendone = max # of atoms to send in one swap
<LI>
maxswap = max # of swaps to do at each timestep
<LI>
maxneigh = max # of neighbors per owned atom
<LI>
maxsneigh = max # of special neighbors of one atom
<LI>
maxbin = max # of local neighbor bins
<LI>
maxfix = max # of defined constraints + 1
<LI>
maxdiag = max # of diagnostic routines
<LI>
maxgrid = max size of PPPM grid with ghosts on one processor
<LI>
maxfft = max size of PPPM FFT grid on one processor
<LI>
maxperatom = max # of data items stored/comm/output per atom
<LI>
maxatom = maxown + maxother = total # of own and nearby atoms
<LI>
maxexchtot = maxexch * (maxperatom + maxsneigh + 3*maxbondper +
4*maxangleper + 5*maxdihedper + 5*maximproper) = total data volume for
all exchanged atoms
<LI>
maxrestot = maxown * (maxperatom - 3 + 3*maxbondper + 4*maxangleper +
5*maxdihedper + 5*maximproper)+1 = total data volume for all buffered
restart atoms
<LI>
maxsendspec = 2 * maxsneigh * maxown total data volume for sending
special requests
<LI>
maxrecvspec = maxsneigh + 1 total data volume for receiving a list of
specials
</UL>
<HR>
<H3>
<A NAME="_cch3_930764951">Arrays (real): </A></H3>
<UL>
<LI>
anglecoeff(2,maxangletype) = angle coeffs for each angle type
<LI>
bondcoeff(5,maxbondtype) = bond coeffs for each bond type
<LI>
boundhi(maxswap) = hi slab boundary on atom positions for each swap
send
<LI>
boundlo(maxswap) = lo slab boundary on atom positions for each swap
send
<LI>
buf1(maxexchtot) = comm buffer for sending exchange atoms
<LI>
buf2(2*maxexchtot) = comm buffer for 2 recv of exchange atoms
<LI>
buf3(3*maxsendone) = comm buffer for sending one set of swap atom
positions
<LI>
buf4(8*maxown) = comm buffer for output
<LI>
buf5(maxrestot) = comm buffer for restart atoms
<LI>
buf6(maxsendone) = comm buffer for sending one set of swap charges
<LI>
cutforcesq(maxtype,maxtype) = force cutoff squared for atom pair
(LJ/Coul)
<LI>
cutljsq(maxtype,maxtype) = LJ cutoff squared for atom pairs
<LI>
cutljinner(maxtype,maxtype) = inner LJ cutoff for switched LJ
<LI>
cutljinnersq(maxtype,maxtype) = inner LJ cutoff squared for switched LJ
<LI>
cutneighsq(maxtype,maxtype) = neigh cutoff squared for atom pair
(LJ/Coul + skin)
<LI>
diagparams(6,maxdiag) = parameters to pass into a diagnostic routine
<LI>
dihedcoeff(3,maxdihedtype) = dihedral coeffs for each dihedral type
<LI>
f(3,maxown) = forces on own atoms
<LI>
fixcoeff(8,maxfix) = constraint coeffs for each constraint
<LI>
fixstore(5*maxfix) = accumulated quantities for each constraint
<LI>
improcoeff(2,maximprotype) = improper coeffs for each improper type
<LI>
lj12345(maxtype,maxtype) = pre-computed LJ coeffs for use in energy and
force
<LI>
ljsw01234(maxtype,maxtype) = pre-computed switched LJ coeffs for eng
and force
<LI>
mass(maxtype) = mass of each atom type
<LI>
noncoeff1234(maxtype,maxtype) = nonbond coeffs input for atom pairs
<LI>
offset(maxtype,maxtype) = LJ potential offsets at cutoff for energy
calc
<LI>
q(maxatom) = charge of own and nearby atoms (electron units)
<LI>
v(3,maxown) = velocity of owned atoms
<LI>
x(3,maxatom) = positions of own and nearby atoms
<LI>
xhold(3,maxown) = positions of own atoms at last reneighboring
</UL>
<HR>
<H3>
<A NAME="_cch3_930764957">Arrays (integer): </A></H3>
<UL>
<LI>
angleatom123(maxangleper,maxown) = angle atoms for angles of owned
atoms
<LI>
anglelist(4,maxangle) = atoms and type of each angle to compute locally
<LI>
angletype(maxangleper,maxown) = angle type for angles of owned atoms
<LI>
bin(maxatom) = linked list pointers from one atom to next in bin
<LI>
binpnt(maxbin) = pointer to 1st atom in each bin
<LI>
bondatom12(maxbondper,maxown) = bond atoms for bonds of owned atoms
<LI>
bondlist(3,maxbond) = atoms and type of each bond to compute locally
<LI>
bondtype(maxbondper,maxown) = bond type for bonds of owned atoms
<LI>
bondtypeflag(maxbondtype) = flag for whether bond coeffs are set
<LI>
diagfileflag(maxdiag) = whether a file has been specified for a diag
routine
<LI>
diagfreq(maxdiag) = call a diagnostic routine every this many steps
<LI>
diagnparams(maxdiag) = # of parameters specified for a diagnostic
routine
<LI>
diagstyle(maxdiag) = whether a diagnostic has been set 0/1
<LI>
dihedatom1234(maxdihedper,maxown) = dihed atoms for diheds of owned
atoms
<LI>
dihedlist(5,maxdihed) = atoms and type of each dihedral to compute
locally
<LI>
dihedtype(maxdihedper,maxown) = dihed type for diheds of owned atoms
<LI>
fix(maxown) = constraint assignments for each owned atom
<LI>
fixflag(3,maxfix) = 0/1 flags for various fix styles
<LI>
fixptr(maxfix) = how many values are accumulated for each constraint
<LI>
fixstyle(maxfix) = style of each constraint
<LI>
ibuf1(maxsendone) = comm buffer for sending one set of swap atom tags
<LI>
ibuf2(maxsendone) = comm buffer for sending one set of swap atom types
<LI>
ibuf3(maxspec) = comm buffer for sending special requests
<LI>
ibuf4(maxspec) = comm buffer for receiving special lists
<LI>
improatom1234(maximproper,maxown) = impro atoms for impros of owned
atoms
<LI>
improlist(5,maximpro) = atoms and type of each improper to compute
locally
<LI>
improtype(maximproper,maxown) = impro type for impros of owned atoms
<LI>
list(maxown) = linked list of local atoms (last one -&gt; maxown+1)
<LI>
localptr(0:maxtotal) = ptr from global atom to local array (0 if don't
have)
<LI>
molecule(maxown) = molecule id # each owned atom is in
<LI>
nlist(maxown*maxneigh+maxneigh) = neighbor lists of own atoms
<LI>
nliststart(maxown) = pointer to where neighbor list for this atom
starts
<LI>
nliststop(maxown) = pointer to where neighbor list for this atom stops
<LI>
nontypeflag(maxtype,maxtype) = flag for whether nonbond coeffs are set
<LI>
nrlist(maxswap+1) = prt to where received other atoms start for each
swap
<LI>
nslist(maxswap+1) = pointer to where swap list starts for each swap
<LI>
numangle(maxown) = # of angles of each owned atom
<LI>
numbond(maxown) = # of 1st neighbors bonded to each owned atom
<LI>
num2bond(maxown) = # of 2nd neighbors for each owned atom
<LI>
num3bond(maxown) = # of 3rd neighbors for each owned atom
<LI>
numdihed(maxown) = # of dihedrals of each owned atom
<LI>
numimpro(maxown) = # of impropers of each owned atom
<LI>
rpart(maxswap) = node # of who to recv from for each swap
<LI>
slist(maxsend) = send list of atoms to send out in all swaps
<LI>
spart(maxswap) = node # of who to send to for each swap
<LI>
specbond(maxsneigh,maxown) = special bond neighbors of each owned atom
<LI>
tag(maxatom) = global id # of own and nearby atoms
<LI>
true(maxown) = which periodic box atom is truly in for all 3 dims
<LI>
type(maxatom) = type # of own and nearby atoms
<LI>
typecheck(maxtype) = consistency check for all existing atom types
<LI>
typechecktmp(maxtype) = summing array for atom type consistency check
<LI>
velflag(maxown) = whether velocity for each atom has been created
</UL>
<HR>
<H3>
<A NAME="_cch3_930764964">Variables (real): </A></H3>
<UL>
<LI>
binsize[xyz] = size of global neighbor bins in each dimension
<LI>
boltz = Boltzmann factor
<LI>
border(2,3) = lo/hi boundaries of my sub-box in each dimension
<LI>
coulpre = Coulombic force prefactor
<LI>
createregion(6) = bounding box for atoms to create temperature for
<LI>
createvec(3) = initial velocity for create temp atoms
<LI>
cutcoul = input force cutoff for Coulombic interactions
<LI>
cutcoulsq = Coul cutoff squared for all atom pairs
<LI>
cutforce = max force cutoff for all atom pairs (LJ/Coul)
<LI>
cutlj = input global (default) LJ cutoff for all atom pairs
<LI>
cutljinterior = global inner LJ cutoff for switched LJ
<LI>
cutneigh = max neighbor cutoff for all atom pairs (LJ/Coul + skin)
<LI>
dielectric = dielectric constant
<LI>
dt = timestep
<LI>
dtfactor = timestep conversion factor from input to program units
<LI>
dthalf = timestep / 2
<LI>
efactor = energy conversion factor from Coulombic to Kcals
<LI>
e_angle = energy in angles
<LI>
e_bond = energy in bonds
<LI>
e_coul = energy in nonbond Coulombic
<LI>
e_dihedral = energy in dihedrals
<LI>
e_improper = energy in impropers
<LI>
e_total = total energy
<LI>
e_vdwl = energy in nonbond LJ
<LI>
fixregion(6) = bounding box for atoms to assign to a constraint
<LI>
skin = distance between force and neighbor cutoffs
<LI>
special(3) = weight factors for special neighbors
<LI>
triggersq = squared distance to trigger neighbor list rebuild
<LI>
two16 = 2 ^ (1/6) constant for use in FENE bond potentials
<LI>
t_create = requested initialization temp
<LI>
t_current = current temp returned from temp routine
<LI>
t_nph = default temp for constant NPH
<LI>
t_start = target temp at beginning of run
<LI>
t_stop = target temp at end of run
<LI>
t_window = control temp within this window
<LI>
time_angle = angle time
<LI>
time_bond = bond time
<LI>
time_comm = communication time
<LI>
time_current = current time
<LI>
time_dihedral = dihedral time
<LI>
time_exch = exchange time
<LI>
time_improper = improper time
<LI>
time_io = i/o time
<LI>
time_loop = time for integration loop
<LI>
time_neigh1 = neighboring time in nonbond
<LI>
time_neigh2 = neighboring time in bonds
<LI>
time_nonbond = nonbond force time
<LI>
time_other = other miscellaneous time
<LI>
time_total = total run time of entire simulation
<LI>
x[yz]mc = box size minus force cutoff for PBC checks
<LI>
x[yz]ms box size minus neighbor list cutoff for PBC checks
<LI>
x[yz]boundlo = lower global box boundary in each dimension
<LI>
x[yz]boundhi = upper global box boundary in each dimension
<LI>
x[yz]prd = global box size in each dimension
</UL>
<HR>
<H3>
<A NAME="_cch3_930764969">Variables (integer): </A></H3>
<UL>
<LI>
atompnt = pointer to 1st atom in my list
<LI>
bondstyle = style of bond computation
<LI>
boxflag = flag if box has been remapped (non-PBC)
<LI>
coulstyle = style of Coulomb interaction
<LI>
creategroup = kind of atom group to create temp for
<LI>
createstyle = style of temp creation
<LI>
createtypehi = upper range of atom types to create temp for
<LI>
createtypelo = lower range of atom types to create temp for
<LI>
dumpfileflag = has dump file been opened or not (1/0)
<LI>
dumpflag = dump atoms to file every this many steps (0 = never)
<LI>
dumpforcefileflag = has dump force file been opened or not (1/0)
<LI>
dumpforceflag = dump forces to file every this many steps (0 = never)
<LI>
dumpvelfileflag = has dump velocity file been opened or not (1/0)
<LI>
dumpvelflag = dump vels to file every this many steps (0 = never)
<LI>
fixatom = assign atom/molecule with this tag to a constraint
<LI>
fixgroup = kind of atom group to assign to a constraint
<LI>
fixnum = total # of accumulated values for all constraints
<LI>
fixtype = assign group of atoms of this type to a constraint
<LI>
fixwhich = which constraint a atom group is to be assigned to
<LI>
freepnt = pointer to 1st free space in list (last one -&gt; 0)
<LI>
idimension = dimension of problem (2-d or 3-d)
<LI>
iseed = RNG seed for generating initial velocities
<LI>
itime = current timestep loop counter in integrator
<LI>
iversion = version number of restart files (for backward compat)
<LI>
max_angle = most angles I ever have to compute
<LI>
max_angleper = most angles ever attached to any atom
<LI>
max_bond = most bonds I ever have to compute
<LI>
max_bondper = most bonds ever attached to any atom
<LI>
max_dihed = most diheds I ever have to compute
<LI>
max_dihedper = most diheds ever attached to any atom
<LI>
max_exch = most atoms ever leaving my box (in one dimension)
<LI>
max_impro = most impros I ever have to compute
<LI>
max_improper = most impros ever attached to any atom
<LI>
max_nlocal = most atoms I ever owned
<LI>
max_neigh = most neighbors ever stored in neighbor list
<LI>
max_nother = most nearby atoms I ever stored
<LI>
max_slist = biggest size swap list ever reached
<LI>
max_swap = most atoms ever sent in one swap
<LI>
mbin[xyz] = # of bins in my box with nearby atoms included
<LI>
mbin[xyz]lo = global bin indices (offset) at corner of extended box
<LI>
me(3) = which box I am (0 - pgrid-1) in each dimension
<LI>
mixflag = whether mixing style has been set or not
<LI>
mixstyle = style of mixing for nonbond coeffs (arith,geom,sixth)
<LI>
mpart(2,3)= node # of neighbor processor in each dimension
<LI>
nanglelocal = local # of angless to compute
<LI>
nangles = total # of angles
<LI>
nangletypes = total # of angle types
<LI>
natoms = total # of atoms
<LI>
nbin[xyz] # of global neighbor bins in each dimension
<LI>
nbondlocal = local # of bonds to compute
<LI>
nbonds = total # of bonds
<LI>
nbondtypes = total # of bond types
<LI>
ndanger = # of neighbor rebuilds triggered by 1st check
<LI>
ndiags = # of user-specified diagnostic routines
<LI>
ndihedlocal = local # of dihedrals to compute
<LI>
ndihedrals = total # of diheds
<LI>
ndihedtypes = total # of dihedral types
<LI>
need(3) how many processors I need neighbors from in each dim
<LI>
neighago = how many timesteps ago neighboring was done
<LI>
neighdelay = delay neighbor list build for this many steps
<LI>
neighfreq = build neighbor list every this many steps
<LI>
neighstyle = neighboring by (0) N^2 or (1) binning method
<LI>
neightop = last used position in neighbor list (nlist)
<LI>
neightrigger = always (0) do neighbor list or trigger (1) on atom move
<LI>
newton = flag for kind of Newton's 3rd law used (0,1,2,3)
<LI>
newton_bond = Newton's 3rd is not used (0) or (1) used for bonds
<LI>
newton_nonbond = Newton's 3rd is not used (0) or (1) used for nonbonds
<LI>
nfixes = # of constraints
<LI>
nimprolocal = local # of impropers to compute
<LI>
nimpropers = total # of impros
<LI>
nimprotypes = total # of improper types
<LI>
nlocal = # of atoms I currently own
<LI>
nother = # of nearby atoms I currently store
<LI>
node = my node #
<LI>
nonstyle = style on nonbond computation
<LI>
nprocs = total # of processors
<LI>
nsteps = # of timesteps to simulate
<LI>
nswap = # of swaps at each timestep
<LI>
ntimestep = current global timestep
<LI>
ntypes = total # of atom types
<LI>
numneigh = number of times reneighboring is done
<LI>
offsetflag = whether to include energy offset in LJ energy calc
<LI>
peratom = # of values/atom not including bond info
<LI>
perflagx[yz] = flag for periodic (0) or non-periodic (1) BC
<LI>
pgrid(3) = # of processors in each dimension
<LI>
readflag = whether atom input file has been read or not (1/0)
<LI>
restartfileflag = which restart file to open next (0/1)
<LI>
restartflag = write restart file every this many steps (0=never)
<LI>
t_every = rescale/replace temp every this many steps
<LI>
tempflag = constant temperature style flag
<LI>
thermoflag = print thermo info every this many steps (0 = never)
<LI>
thermostyle = style of thermo output (0 = full, 1 = reduced)
<LI>
trueflag = whether to dump remapped or true atom positions
<LI>
units = flag for real vs reduced LJ units
</UL>
<HR>
<H3>
<A NAME="_cch3_930764974">Variables (character): </A></H3>
<UL>
<LI>
datafile = file to read atom and connectivity info from
<LI>
diagfile(maxdiag) = files to print user-specified diagnostics to
<LI>
diagname(maxdiag) = name of a user-specified diagnostic routine
<LI>
dumpfile = file to dump atom info to
<LI>
dumpforcefile = file to dump force info to
<LI>
dumpvelfile = file to dump velocity info to
<LI>
restart_in = file to read restart info from
<LI>
restart_out[12] = files to write restart info to
</UL>
<P>
</P>
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<BODY>
<H2>
LAMMPS Data Format</H2>
<P>
<A HREF="README.html">Return</A> to top-level of LAMMPS documentation</P>
<P>
This file describes the format of the data file read into LAMMPS with
the &quot;read data&quot; command. The data file contains basic
information about the size of the problem to be run, the initial atomic
coordinates, molecular topology, and (optionally) force-field
coefficients. It will be easiest to understand this file if you read it
while looking at a sample data file from the examples.</P>
<P>
This page has 2 sections:</P>
<UL>
<LI>
<A HREF="#_cch3_930958962">Rules for formatting the Data File</A>
<LI>
<A HREF="#_cch3_930958969">Sample file with Annotations</A>
</UL>
<HR>
<H3>
<A NAME="_cch3_930958962">Rules for formatting the Data File: </A></H3>
<P>
Blank lines are important. After the header section, new entries are
separated by blank lines. </P>
<P>
Indentation and space between words/numbers on one line is not
important except that entry keywords (e.g. Masses, Bond Coeffs) must be
left-justified and capitalized as shown. </P>
<P>
The header section (thru box bounds) must appear first in the file, the
remaining entries (Masses, various Coeffs, Atoms, Bonds, etc) can come
in any order. </P>
<P>
These entries must be in the file: header section, Masses, Atoms. </P>
<P>
These entries must be in the file if there are a non-zero number of
them: Bonds, Angles, Dihedrals, Impropers, Bond Coeffs, Angle Coeffs,
Dihedral Coeffs, Improper Coeffs. Cross-term coefficients for a
particular kind of interaction (e.g. BondAngle Coeffs for bonds) must
appear if class II force fields have been turned on in the input
command file via a &quot;style&quot; command. </P>
<P>
The Nonbond Coeffs entry contains one line for each atom type. These
are the coefficients for an interaction between 2 atoms of the same
type. The cross-type coeffs are computed by the appropriate class I or
class II mixing rules, or can be specified explicitly using the
&quot;nonbond coeff&quot; command in the input command script. See the <A
HREF="force_fields.html">force_fields</A> page for more information. </P>
<P>
The Nonbond Coeffs and Bond Coeffs entries are optional since they can
be specified from the input command script. This is not true if bond
style is set to class II since those coeffs can only be specified in
this data file. </P>
<P>
In the Atoms entry, the atoms can be in any order so long as there are
N entries. The 1st number on the line is the atom-tag (number from 1 to
N) which is used to identify the atom throughout the simulation. The
molecule-tag is a second identifier which is attached to the atom; it
can be 0, or a counter for the molecule the atom is part of, or any
other number you wish. The q value is the charge of the atom in
electron units (e.g. +1 for a proton). The xyz values are the initial
position of the atom. For 2-d simulations specify z as 0.0.</P>
<P>
The final 3 nx,ny,nz values on a line of the Atoms entry are optional.
LAMMPS only reads them if the &quot;true flag&quot; command is
specified in the input command script. Otherwise they are initialized
to 0 by LAMMPS. Their meaning, for each dimension, is that
&quot;n&quot; box-lengths are added to xyz to get the atom's
&quot;true&quot; un-remapped position. This can be useful in pre- or
post-processing to enable the unwrapping of long-chained molecules
which wrap thru the periodic box one or more times. The value of
&quot;n&quot; can be positive, negative, or zero. For 2-d simulations
specify nz as 0. </P>
<P>
For simulations with periodic boundary conditions, xyz are remapped
into the periodic box (from as far away as needed), so the initial
coordinates need not be inside the box. The nx,ny,nz values (as read in
or as set to zero by LAMMPS) are appropriately adjusted by this
remapping. </P>
<P>
The number of coefficients specified on each line of coefficient
entries (Nonbond Coeffs, Bond Coeffs, etc) depends on the
&quot;style&quot; of interaction. This is specified in the input
command script, unless the default is used. See the <A
HREF="input_commands.html">input_commands</A> page for a description
of the various style options. The <A HREF="input_commands.html">input_commands</A>
and <A HREF="force_fields.html">force_fields</A> pages explain the
meaning and valid ranges for each of the coefficients. </P>
<HR>
<H3>
<A NAME="_cch3_930958969">Sample file with Annotations</A></H3>
<P>
Here is a sample file with annotations in parenthesis and lengthy
sections replaced by dots (...). Note that the blank lines are
important in this example.</P>
<PRE>
LAMMPS Description (1st line of file)
100 atoms (this must be the 3rd line, 1st 2 lines are ignored)
95 bonds (# of bonds to be simulated)
50 angles (include these lines even if number = 0)
30 dihedrals
20 impropers
5 atom types (# of nonbond atom types)
10 bond types (# of bond types = sets of bond coefficients)
18 angle types
20 dihedral types (do not include a bond,angle,dihedral,improper type
2 improper types line if number of bonds,angles,etc is 0)
-0.5 0.5 xlo xhi (for periodic systems this is box size,
-0.5 0.5 ylo yhi for non-periodic it is min/max extent of atoms)
-0.5 0.5 zlo zhi (do not include this line for 2-d simulations)
Masses
1 mass
...
N mass (N = # of atom types)
Nonbond Coeffs
1 coeff1 coeff2 ...
...
N coeff1 coeff2 ... (N = # of atom types)
Bond Coeffs
1 coeff1 coeff2 ...
...
N coeff1 coeff2 ... (N = # of bond types)
Angle Coeffs
1 coeff1 coeff2 ...
...
N coeff1 coeff2 ... (N = # of angle types)
Dihedral Coeffs
1 coeff1 coeff2 ...
...
N coeff1 coeff2 ... (N = # of dihedral types)
Improper Coeffs
1 coeff1 coeff2 ...
...
N coeff1 coeff2 ... (N = # of improper types)
BondBond Coeffs
1 coeff1 coeff2 ...
...
N coeff1 coeff2 ... (N = # of angle types)
BondAngle Coeffs
1 coeff1 coeff2 ...
...
N coeff1 coeff2 ... (N = # of angle types)
MiddleBondTorsion Coeffs
1 coeff1 coeff2 ...
...
N coeff1 coeff2 ... (N = # of dihedral types)
EndBondTorsion Coeffs
1 coeff1 coeff2 ...
...
N coeff1 coeff2 ... (N = # of dihedral types)
AngleTorsion Coeffs
1 coeff1 coeff2 ...
...
N coeff1 coeff2 ... (N = # of dihedral types)
AngleAngleTorsion Coeffs
1 coeff1 coeff2 ...
...
N coeff1 coeff2 ... (N = # of dihedral types)
BondBond13 Coeffs
1 coeff1 coeff2 ...
...
N coeff1 coeff2 ... (N = # of dihedral types)
AngleAngle Coeffs
1 coeff1 coeff2 ...
...
N coeff1 coeff2 ... (N = # of improper types)
Atoms
1 molecule-tag atom-type q x y z nx ny nz (nx,ny,nz are optional -
... see &quot;true flag&quot; input command)
...
N molecule-tag atom-type q x y z nx ny nz (N = # of atoms)
Bonds
1 bond-type atom-1 atom-2
...
N bond-type atom-1 atom-2 (N = # of bonds)
Angles
1 angle-type atom-1 atom-2 atom-3 (atom-2 is the center atom in angle)
...
N angle-type atom-1 atom-2 atom-3 (N = # of angles)
Dihedrals
1 dihedral-type atom-1 atom-2 atom-3 atom-4 (atoms 2-3 form central bond)
...
N dihedral-type atom-1 atom-2 atom-3 atom-4 (N = # of dihedrals)
Impropers
1 improper-type atom-1 atom-2 atom-3 atom-4 (atom-1 is central atom)
...
N improper-type atom-1 atom-2 atom-3 atom-4 (N = # of impropers)
</PRE>
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<H2>
LAMMPS Force Fields</H2>
<P>
<A HREF="README.html">Return</A> to top-level of LAMMPS documentation</P>
<P>
This file outlines the force-field formulas used in LAMMPS. Read this
file in conjunction with the <A HREF="data_format.html">data_format</A>
and <A HREF="units.html">units</A> file.</P>
<P>
The sections of this page are as follows:</P>
<UL>
<LI>
<A HREF="#_cch3_930957465">Nonbond Coulomb</A>
<LI>
<A HREF="#_cch3_930957471">Nonbond Lennard-Jones</A>
<LI>
<A HREF="#_cch3_930957478">Mixing Rules for Lennard-Jones</A>
<LI>
<A HREF="#_cch3_930957482">Bonds</A>
<LI>
<A HREF="#_cch3_930957488">Angles</A>
<LI>
<A HREF="#_cch3_930957509">Dihedrals</A>
<LI>
<A HREF="#_cch3_930957513">Impropers</A>
<LI>
<A HREF="#_cch3_930957527">Class II Force Field</A>
</UL>
<HR>
<H3>
<A NAME="_cch3_930957465">Nonbond Coulomb</A></H3>
<P>
Whatever Coulomb style is specified in the input command file, the
short-range Coulombic interactions are computed by this formula,
modified by an appropriate smoother for the smooth, Ewald, and PPPM
styles.</P>
<PRE>
E = C q1 q2 / (epsilon * r)
r = distance (computed by LAMMPS)
C = hardwired constant to convert to energy units
q1,q2 = charge of each atom in electron units (proton = +1),
specified in &quot;Atoms&quot; entry in data file
epsilon = dielectric constant (vacuum = 1.0),
set by user in input command file
</PRE>
<HR>
<H3>
<A NAME="_cch3_930957471">Nonbond Lennard-Jones </A></H3>
<P>
The style of nonbond potential is specified in the input command file. </P>
<H4>
(1) lj/cutoff </H4>
<PRE>
E = 4 epsilon [ (sigma/r)^12 - (sigma/r)^6 ]
standard Lennard Jones potential
r = distance (computed by LAMMPS)
coeff1 = epsilon (energy)
coeff2 = sigma (distance)
2 coeffs are listed in data file or set in input script
1 cutoff is set in input script
</PRE>
<H4>
(2) lj/switch </H4>
<PRE>
E = 4 epsilon [ (sigma/r)^12 - (sigma/r)^6 ] for r &lt; r_inner
= spline fit for r_inner &lt; r &lt; cutoff
= 0 for r &gt; cutoff
switching function (spline fit) is applied to standard LJ
within a switching region (from r_inner to cutoff) so that
energy and force go smoothly to zero
spline coefficients are computed by LAMMPS
so that at inner cutoff (r_inner) the potential, force,
and 1st-derivative of force are all continuous,
and at outer cutoff (cutoff) the potential and force
both go to zero
r = distance (computed by LAMMPS)
coeff1 = epsilon (energy)
coeff2 = sigma (distance)
2 coeffs are listed in data file or set in input script
2 cutoffs (r_inner and cutoff) are set in input script
</PRE>
<H4>
(3) lj/shift </H4>
<PRE>
E = 4 epsilon [ (sigma/(r - delta))^12 - (sigma/(r - delta))^6 ]
same as lj/cutoff except that r is shifted by delta
r = distance (computed by LAMMPS)
coeff1 = epsilon (energy)
coeff2 = sigma (distance)
coeff3 = delta (distance)
3 coeffs are listed in data file or set in input script
1 cutoff is set in input script
</PRE>
<H4>
(4) soft </H4>
<PRE>
E = A * [ 1 + cos( pi * r / cutoff ) ]
useful for pushing apart overlapping atoms by ramping A over time
r = distance (computed by LAMMPS)
coeff1 = prefactor A at start of run (energy)
coeff2 = prefactor A at end of run (energy)
2 coeffs are listed in data file or set in input script
1 cutoff is set in input script
</PRE>
<H4>
(5) class2/cutoff </H4>
<PRE>
E = epsilon [ 2 (sigma/r)^9 - 3 (sigma/r)^6 ]
used with class2 bonded force field
r = distance (computed by LAMMPS)
coeff1 = epsilon (energy)
coeff2 = sigma (distance)
2 coeffs are listed in data file or set in input script
1 cutoff is set in input script
</PRE>
<HR>
<H3>
<A NAME="_cch3_930957478">Mixing Rules for Lennard-Jones</A></H3>
<P>
The coefficients for each nonbond style are input in either the data
file by the &quot;read data&quot; command or in the input script using
the &quot;nonbond coeff&quot; command. In the former case, only one set
of coefficients is input for each atom type. The cross-type coeffs are
computed using one of three possible mixing rules: </P>
<PRE>
geometric: epsilon_ij = sqrt(epsilon_i * epsilon_j)
sigma_ij = sqrt(sigma_i * sigma_j)
arithmetic: epsilon_ij = sqrt(epsilon_i * epsilon_j)
sigma_ij = (sigma_i + sigma_j) / 2
sixthpower: epsilon_ij =
(2 * sqrt(epsilon_i*epsilon_j) * sigma_i^3 * sigma_j^3) /
(sigma_i^6 + sigma_j^6)
sigma_ij= ((sigma_i**6 + sigma_j**6) / 2) ^ (1/6)
</PRE>
<P>
The default mixing rule for nonbond styles lj/cutoff, lj/switch,
lj/shift, and soft is &quot;geometric&quot;. The default for nonbond
style class2/cutoff is &quot;sixthpower&quot;. </P>
<P>
The default can be overridden using the &quot;mixing style&quot;
command. The one exception to this is for the nonbond style soft, for
which only an epsilon prefactor is input. This is always mixed
geometrically. </P>
<P>
Also, for nonbond style lj/shift, the delta coefficient is always mixed
using the rule </P>
<UL>
<LI>
delta_ij = (delta_i + delta_j) / 2
</UL>
<HR>
<H3>
<A NAME="_cch3_930957482">Bonds</A></H3>
<P>
The style of bond potential is specified in the input command file.</P>
<H4>
(1) harmonic </H4>
<PRE>
E = K (r - r0)^2
standard harmonic spring
r = distance (computed by LAMMPS)
coeff1 = K (energy/distance^2) (the usual 1/2 is included in the K)
coeff2 = r0 (distance)
2 coeffs are listed in data file or set in input script
</PRE>
<H4>
(2) FENE/standard </H4>
<PRE>
E = -0.5 K R0^2 * ln[1 - (r/R0)^2] +
4 epsilon [(sigma/r)^12 - (sigma/r)^6] + epsilon
finite extensible nonlinear elastic (FENE) potential for
polymer bead-spring models
see Kremer, Grest, J Chem Phys, 92, p 5057 (1990)
r = distance (computed by LAMMPS)
coeff1 = K (energy/distance^2)
coeff2 = R0 (distance)
coeff3 = epsilon (energy)
coeff4 = sigma (distance)
1st term is attraction, 2nd term is repulsion (shifted LJ)
1st term extends to R0
2nd term only extends to the minimum of the LJ potential,
a cutoff distance computed by LAMMPS (2^(1/6) * sigma)
4 coeffs are listed in data file or set in input script
</PRE>
<H4>
(3) FENE/shift </H4>
<PRE>
E = -0.5 K R0^2 * ln[1 - ((r - delta)/R0)^2] +
4 epsilon [(sigma/(r - delta))^12 - (sigma/(r - delta))^6] + epsilon
same as FENE/standard expect that r is shifted by delta
r = distance (computed by LAMMPS)
coeff1 = K (energy/distance^2)
coeff2 = R0 (distance)
coeff3 = epsilon (energy)
coeff4 = sigma (distance)
coeff5 = delta (distance)
1st term is attraction, 2nd term is repulsion (shifted LJ)
1st term extends to R0
2nd term only extends to the minimum of the LJ potential,
a cutoff distance computed by LAMMPS (2^(1/6) * sigma + delta)
5 coeffs are listed in data file or set in input script
</PRE>
<H4>
(4) nonlinear </H4>
<PRE>
E = epsilon (r - r0)^2 / [ lamda^2 - (r - r0)^2 ]
non-harmonic spring of equilibrium length r0
with finite extension of lamda
see Rector, Van Swol, Henderson, Molecular Physics, 82, p 1009 (1994)
r = distance (computed by LAMMPS)
coeff1 = epsilon (energy)
coeff2 = r0 (distance)
coeff3 = lamda (distance)
3 coeffs are listed in data file or set in input script
</PRE>
<H4>
(5) class2 </H4>
<PRE>
E = K2 (r - r0)^2 + K3 (r - r0)^3 + K4 (r - r0)^4
r = distance (computed by LAMMPS)
coeff1 = r0 (distance)
coeff2 = K2 (energy/distance^2)
coeff3 = K3 (energy/distance^3)
coeff4 = K4 (energy/distance^4)
4 coeffs are listed in data file - cannot be set in input script
</PRE>
<HR>
<H3>
<A NAME="_cch3_930957488">Angles </A></H3>
<P>
The style of angle potential is specified in the input command file. </P>
<H4>
(1) harmonic </H4>
<PRE>
E = K (theta - theta0)^2
theta = radians (computed by LAMMPS)
coeff1 = K (energy/radian^2) (the usual 1/2 is included in the K)
coeff2 = theta0 (degrees) (converted to radians within LAMMPS)
2 coeffs are listed in data file
</PRE>
<H4>
(2) class2 </H4>
<PRE>
E = K2 (theta - theta0)^2 + K3 (theta - theta0)^3 +
K4 (theta - theta0)^4
theta = radians (computed by LAMMPS)
coeff1 = theta0 (degrees) (converted to radians within LAMMPS)
coeff2 = K2 (energy/radian^2)
coeff3 = K3 (energy/radian^3)
coeff4 = K4 (energy/radian^4)
4 coeffs are listed in data file
</PRE>
<HR>
<H3>
<A NAME="_cch3_930957509">Dihedrals </A></H3>
<P>
The style of dihedral potential is specified in the input command file. </P>
<H4>
(1) harmonic </H4>
<PRE>
E = K [1 + d * cos (n * phi) ]
phi = radians (computed by LAMMPS)
coeff1 = K (energy)
coeff2 = d (always +1 or -1)
coeff3 = n (1,2,3,4,6)
Cautions when comparing to other force fields:
some force fields reverse the sign convention on d so that
E = K [1 - d * cos(n*phi)]
some force fields divide/multiply K by the number of multiple
torsions that contain the j-k bond in an i-j-k-l torsion
some force fields let n be positive or negative which
corresponds to d = 1,-1
in the LAMMPS force field, the trans position = 180 degrees, while
in some force fields trans = 0 degrees
3 coeffs are listed in data file
</PRE>
<H4>
(2) class2 </H4>
<PRE>
E = SUM(n=1,3) { K_n [ 1 - cos( n*Phi - Phi0_n ) ] }
phi = radians (computed by LAMMPS)
coeff1 = K_1 (energy)
coeff2 = Phi0_1 (degrees) (converted to radians within LAMMPS)
coeff3 = K_2 (energy)
coeff4 = Phi0_2 (degrees) (converted to radians within LAMMPS)
coeff5 = K_3 (energy)
coeff6 = Phi0_3 (degrees) (converted to radians within LAMMPS)
6 coeffs are listed in data file
</PRE>
<HR>
<H3>
<A NAME="_cch3_930957513">Impropers</A></H3>
<P>
The style of improper potential is specified in the input command file. </P>
<H4>
(1) harmonic </H4>
<PRE>
E = K (chi - chi0)^2
chi = radians (computed by LAMMPS)
coeff1 = K (energy/radian^2) (the usual 1/2 is included in the K)
coeff2 = chi0 (degrees) (converted to radians within LAMMPS)
in data file, listing of 4 atoms requires atom-1 as central atom
some force fields (AMBER,Discover) have atom-2 as central atom - it is really
an out-of-plane torsion, may need to treat as dihedral in LAMMPS
2 coeffs are listed in data file
</PRE>
<H4>
(2) class2 </H4>
<PRE>
same formula, coeffs, and meaning as &quot;harmonic&quot; except that LAMMPS
averages all 3 angle-contributions to chi
in class II this is called a Wilson out-of-plane interaction
2 coeffs are listed in data file
</PRE>
<HR>
<H3>
<A NAME="_cch3_930957527">Class II Force Field</A></H3>
<P>
If class II force fields are selected in the input command file,
additional cross terms are computed as part of the force field.</P>
<H4>
Bond-Bond (computed within class II angles) </H4>
<PRE>
E = K (r - r0) * (r' - r0')
r,r' = distance (computed by LAMMPS)
coeff1 = K (energy/distance^2)
coeff2 = r0 (distance)
coeff3 = r0' (distance)
3 coeffs are input in data file
</PRE>
<H4>
Bond-Angle (computed within class II angles for each of 2 bonds) </H4>
<PRE>
E = K_n (r - r0_n) * (theta - theta0)
r = distance (computed by LAMMPS)
theta = radians (computed by LAMMPS)
coeff1 = K_1 (energy/distance-radians)
coeff2 = K_2 (energy/distance-radians)
coeff3 = r0_1 (distance)
coeff4 = r0_2 (distance)
Note: theta0 is known from angle coeffs so don't need it specified here
4 coeffs are listed in data file
</PRE>
<H4>
Middle-Bond-Torsion (computed within class II dihedral) </H4>
<PRE>
E = (r - r0) * [ F1*cos(phi) + F2*cos(2*phi) + F3*cos(3*phi) ]
r = distance (computed by LAMMPS)
phi = radians (computed by LAMMPS)
coeff1 = F1 (energy/distance)
coeff2 = F2 (energy/distance)
coeff3 = F3 (energy/distance)
coeff4 = r0 (distance)
4 coeffs are listed in data file
</PRE>
<H4>
End-Bond-Torsion (computed within class II dihedral for each of 2
bonds) </H4>
<PRE>
E = (r - r0_n) * [ F1_n*cos(phi) + F2_n*cos(2*phi) + F3_n*cos(3*phi) ]
r = distance (computed by LAMMPS)
phi = radians (computed by LAMMPS)
coeff1 = F1_1 (energy/distance)
coeff2 = F2_1 (energy/distance)
coeff3 = F3_1 (energy/distance)
coeff4 = F1_2 (energy/distance)
coeff5 = F2_3 (energy/distance)
coeff6 = F3_3 (energy/distance)
coeff7 = r0_1 (distance)
coeff8 = r0_2 (distance)
8 coeffs are listed in data file
</PRE>
<H4>
Angle-Torsion (computed within class II dihedral for each of 2 angles) </H4>
<PRE>
E = (theta - theta0) * [ F1_n*cos(phi) + F2_n*cos(2*phi) + F3_n*cos(3*phi) ]
theta = radians (computed by LAMMPS)
phi = radians (computed by LAMMPS)
coeff1 = F1_1 (energy/radians)
coeff2 = F2_1 (energy/radians)
coeff3 = F3_1 (energy/radians)
coeff4 = F1_2 (energy/radians)
coeff5 = F2_3 (energy/radians)
coeff6 = F3_3 (energy/radians)
coeff7 = theta0_1 (degrees) (converted to radians within LAMMPS)
coeff8 = theta0_2 (degrees) (converted to radians within LAMMPS)
8 coeffs are listed in data file
</PRE>
<H4>
Angle-Angle-Torsion (computed within class II dihedral) </H4>
<PRE>
E = K (theta - theta0) * (theta' - theta0') * (phi - phi0)
theta,theta' = radians (computed by LAMMPS)
phi = radians (computed by LAMMPS)
coeff1 = K (energy/radians^3)
coeff2 = theta0 (degrees) (converted to radians within LAMMPS)
coeff3 = theta0' (degrees) (converted to radians within LAMMPS)
Note: phi0 is known from dihedral coeffs so don't need it specified here
3 coeffs are listed in data file
</PRE>
<H4>
Bond-Bond-13-Torsion (computed within class II dihedral) </H4>
<PRE>
(undocumented)
</PRE>
<H4>
Angle-Angle (computed within class II improper for each of 3 pairs of
angles) </H4>
<PRE>
E = K_n (theta - theta0_n) * (theta' - theta0_n')
theta,theta' = radians (computed by LAMMPS)
coeff1 = K_1 (energy/radians^2)
coeff2 = K_2 (energy/radians^2)
coeff3 = K_3 (energy/radians^2)
coeff4 = theta0_1 (degrees) (converted to radians within LAMMPS)
coeff5 = theta0_2 (degrees) (converted to radians within LAMMPS)
coeff6 = theta0_3 (degrees) (converted to radians within LAMMPS)
6 coeffs are listed in data file
</PRE>
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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2//EN">
<HTML>
<HEAD>
<META NAME="Generator" CONTENT="Cosmo Create 1.0.3">
</HEAD>
<BODY>
<H2>
History of LAMMPS</H2>
<P>
<A HREF="README.html">Return</A> to top-level of LAMMPS documentation.</P>
<P>
This is a brief history of features added to each version of LAMMPS.</P>
<HR>
<H3>
LAMMPS 99 - June 99 </H3>
<UL>
<LI>
all-MPI version of code (F77 + C + MPI) for maximum portablility
<LI>
only one PPPM choice now, the better of the two earlier ones
<LI>
PPPM uses portable FFTs and data remapping routines, written in C w/
MPI, can now use non-power-of-2 processors and grid sizes
<LI>
auto-mapping of simulation box to processors
<LI>
removed a few unused/unneeded commands (bdump, log file, id string,
limit)
<LI>
changed syntax of some commands for simplicity &amp; consistency (see <A
HREF="input_commands.html">input commands</A>)
<LI>
changed method of calling/writing user diagnostic routines to be simpler
<LI>
documentation in HTML format
</UL>
<HR>
<H3>
Version 5.0 - Oct 1997 </H3>
<UL>
<LI>
final version of class II force fields
<LI>
new formulation of NVE, NVT, NPT and rRESPA integrators
<LI>
new version of msi2lmp pre-processing tool, does not require DISCOVER
to run, only DISCOVER force field files
<LI>
energy minimizer, Hessian-free truncated Newton method
<LI>
new pressure controllers and constraints
<LI>
replicate tool for generating new data files from old ones
</UL>
<HR ALIGN="LEFT">
<H3>
Version 4.0 - March 1997 </H3>
<UL>
<LI>
1st version of class II force fields
<LI>
new, faster PPPM solver (newpppm)
<LI>
rRESPA
<LI>
new data file format
<LI>
new constraints, diagnostics
<LI>
msi2lmp pre-processing tool
</UL>
<HR>
<H3>
Version 3.0 - March 1996 </H3>
<UL>
<LI>
more general force-field formulation
<LI>
atom/group constraints
<LI>
LJ units and bond potentials
<LI>
smoothed LJ potential option
<LI>
Langevin thermostat
<LI>
Newton's 3rd law option
<LI>
hook for user-supplied diagnostic routines
</UL>
<HR>
<H3>
Version 2.0 - October 1995 </H3>
<UL>
<LI>
bug fix of velocity initialization which caused drift
<LI>
PPPM for long-range Coulombic
<LI>
constant NPT
</UL>
<HR>
<H3>
Version 1.1 - February 1995 </H3>
<UL>
<LI>
Ewald for long-range Coulombic
<LI>
full Newton's 3rd law (doubled communication)
<LI>
dumping of atom positions and velocities
<LI>
restart files
</UL>
<HR>
<H3>
Version 1.0 - January 1995 </H3>
<UL>
<LI>
short-range bonded and non-bonded forces
<LI>
partial Newton's 3rd law
<LI>
velocity-Verlet integrator
</UL>
</BODY>
</HTML>

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<!DOCTYPE HTML PUBLIC "-//W3C//DTD HTML 3.2//EN">
<HTML>
<HEAD>
<META NAME="Generator" CONTENT="Cosmo Create 1.0.3">
</HEAD>
<BODY>
<H2>
LAMMPS Units</H2>
<P>
<A HREF="README.html">Return</A> to top-level LAMMPS documentation.</P>
<P>
This file describes the units associated with many of the key variables
and equations used inside the LAMMPS code. Units used for input command
parameters are described in the input_commands file. The input command
&quot;units&quot; selects between conventional and Lennard-Jones units.
See the force_fields file for more information on units for the force
field parameters that are input from data files. </P>
<P>
Conventional units: </P>
<UL>
<LI>
distance = Angstroms
<LI>
time = femtoseconds
<LI>
mass = grams/mole
<LI>
temperature = degrees K
<LI>
pressure = atmospheres
<LI>
energy = Kcal/mole
<LI>
velocity = Angstroms/femtosecond
<LI>
force = grams/mole * Angstroms/femtosecond^2
<LI>
charge = +/- 1.0 is proton/electron
</UL>
<P>
LJ reduced units: </P>
<UL>
<LI>
distance = sigmas
<LI>
time = reduced LJ tau
<LI>
mass = ratio to unitless 1.0
<LI>
temperature = reduced LJ temp
<LI>
pressure = reduced LJ pressure
<LI>
energy = epsilons
<LI>
velocity = sigmas/tau
<LI>
force = reduced LJ force (sigmas/tau^2)
<LI>
charge = ratio to unitless 1.0
</UL>
<HR>
<P>
This listing of variables assumes conventional units; to convert to LJ
reduced units, simply substitute the appropriate term from the list
above. E.g. x is in sigmas in LJ units. Per-mole in any of the units
simply means for 6.023 x 10^23 atoms.</P>
<P>
</P>
<PRE>
Meaning Variable Units
positions x Angstroms
velocities v Angstroms / click (see below)
forces f Kcal / (mole - Angstrom)
masses mass gram / mole
charges q electron units (-1 for an electron)
(1 e.u. = 1.602 x 10^-19 coul)
time --- clicks (1 click = 48.88821 fmsec)
timestep dt clicks
input timestep dt_in fmsec
time convert dtfactor 48.88821 fmsec / click
temperature t_current degrees K
t_start
t_stop
input damping t_freq_in inverse fmsec
internal temp t_freq inverse clicks
damping
dielec const dielectric 1.0 (unitless)
Boltmann const boltz 0.001987191 Kcal / (mole - degree K)
virial virial[xyz] Kcal/mole = r dot F
pressure factor pfactor 68589.796 (convert internal to atmospheres)
internal p_current Kcal / (mole - Angs^3)
pressure p_start
p_stop
input press p_start_in atmospheres
p_stop_in
output press log file atmospheres
input damping p_freq_in inverse time
internal press p_freq inverse clicks
damping
pot eng e_potential Kcal/mole
kin eng e_kinetic Kcal/mole
eng convert efactor 332.0636 (Kcal - Ang) / (q^2 - mole)
(convert Coulomb eng to Kcal/mole)
LJ coeffs lja,ljb Kcal-Angs^(6,12)/mole
bond various see force_fields file
parameters 2,3,4-body
terms
</PRE>
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# create dvi files for every LaTex eq
latex angle_charmm.tex
latex angle_class2.tex
latex angle_cosine.tex
latex angle_cosine_squared.tex
latex angle_harmonic.tex
latex bond_class2.tex
latex bond_fene.tex
latex bond_fene_expand.tex
latex bond_harmonic.tex
latex bond_morse.tex
latex bond_nonlinear.tex
latex bond_quartic.tex
latex centro_symmetry.tex
latex dihedral_charmm.tex
latex dihedral_class2.tex
latex dihedral_harmonic.tex
latex dihedral_helix.tex
latex dihedral_multiharmonic.tex
latex dihedral_opls.tex
latex fix_gyration.tex
latex fix_orient_fcc.tex
latex fix_spring_rg.tex
latex fix_wall_lj93.tex
latex improper_class2.tex
latex improper_cvff.tex
latex improper_harmonic.tex
latex pair_buck.tex
latex pair_charmm.tex
latex pair_class2.tex
latex pair_coulomb.tex
latex pair_debye.tex
latex pair_dpd.tex
latex pair_eam.tex
latex pair_eam_fs.tex
latex pair_granular.tex
latex pair_lj.tex
latex pair_lj_expand.tex
latex pair_lj_smooth.tex
latex pair_morse.tex
latex pair_soft.tex
latex pair_yukawa.tex
latex stress_tensor.tex

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This is TeX, Version 3.14159 (Web2C 7.3.1) (format=latex 2003.2.18) 9 NOV 2005 10:54
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LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 3.
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[1
]
(angle_charmm.aux) )
Here is how much of TeX's memory you used:
214 strings out of 20880
2131 string characters out of 196184
45503 words of memory out of 350001
3229 multiletter control sequences out of 10000+15000
6376 words of font info for 23 fonts, out of 400000 for 1000
14 hyphenation exceptions out of 10000
22i,4n,19p,118b,162s stack positions out of 3000i,100n,1500p,50000b,4000s
Output written on angle_charmm.dvi (1 page, 508 bytes).

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\documentclass[12pt]{article}
\begin{document}
$$
E = K (\theta - \theta_0)^2 + K_{UB} (r - r_{UB})^2
$$
\end{document}

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This is TeX, Version 3.14159 (Web2C 7.3.1) (format=latex 2003.2.18) 9 NOV 2005 10:54
**angle_class2.tex
(angle_class2.tex
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LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 3.
LaTeX Font Info: ... okay on input line 3.
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LaTeX Font Info: ... okay on input line 3.
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LaTeX Font Info: ... okay on input line 3.
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LaTeX Font Info: Checking defaults for OMX/cmex/m/n on input line 3.
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LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 3.
LaTeX Font Info: ... okay on input line 3.
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LaTeX Font Info: External font `cmex10' loaded for size
(Font) <8> on input line 5.
LaTeX Font Info: External font `cmex10' loaded for size
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[1
]
(angle_class2.aux) )
Here is how much of TeX's memory you used:
214 strings out of 20880
2131 string characters out of 196184
46503 words of memory out of 350001
3229 multiletter control sequences out of 10000+15000
6376 words of font info for 23 fonts, out of 400000 for 1000
14 hyphenation exceptions out of 10000
22i,6n,19p,118b,162s stack positions out of 3000i,100n,1500p,50000b,4000s
Output written on angle_class2.dvi (1 page, 964 bytes).

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\documentclass[12pt]{article}
\begin{document}
\begin{eqnarray*}
E & = & E_a + E_{bb} + E_{ba} \\
E_a & = & K_2 (\theta - \theta_0)^2 + K_3 (\theta - \theta_0)^3 + K_4 (\theta - \theta_0)^4 \\
E_{bb} & = & M (r_{ij} - r_1) (r_{jk} - r_2) \\
E_{ba} & = & N_1 (r_{ij} - r_1) (\theta - \theta_0) + N_2 (r_{jk} - r_2) (\theta - \theta_0)
\end{eqnarray*}
\end{document}

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This is TeX, Version 3.14159 (Web2C 7.3.1) (format=latex 2003.2.18) 9 NOV 2005 10:54
**angle_cosine.tex
(angle_cosine.tex
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LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 3.
LaTeX Font Info: ... okay on input line 3.
LaTeX Font Info: Checking defaults for T1/cmr/m/n on input line 3.
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LaTeX Font Info: Checking defaults for OMS/cmsy/m/n on input line 3.
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LaTeX Font Info: Checking defaults for OMX/cmex/m/n on input line 3.
LaTeX Font Info: ... okay on input line 3.
LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 3.
LaTeX Font Info: ... okay on input line 3.
LaTeX Font Info: External font `cmex10' loaded for size
(Font) <12> on input line 5.
LaTeX Font Info: External font `cmex10' loaded for size
(Font) <8> on input line 5.
LaTeX Font Info: External font `cmex10' loaded for size
(Font) <6> on input line 5.
[1
]
(angle_cosine.aux) )
Here is how much of TeX's memory you used:
214 strings out of 20880
2131 string characters out of 196184
45503 words of memory out of 350001
3229 multiletter control sequences out of 10000+15000
6376 words of font info for 23 fonts, out of 400000 for 1000
14 hyphenation exceptions out of 10000
22i,4n,19p,118b,162s stack positions out of 3000i,100n,1500p,50000b,4000s
Output written on angle_cosine.dvi (1 page, 308 bytes).

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\documentclass[12pt]{article}
\begin{document}
$$
E = K [1 + \cos(\theta)]
$$
\end{document}

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This is TeX, Version 3.14159 (Web2C 7.3.1) (format=latex 2003.2.18) 5 JUN 2006 11:21
**angle_cosine_squared
(angle_cosine_squared.tex
LaTeX2e <2001/06/01>
Babel <v3.7h> and hyphenation patterns for american, french, german, ngerman, i
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Document Class: article 2001/04/21 v1.4e Standard LaTeX document class
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) (angle_cosine_squared.aux)
\openout1 = `angle_cosine_squared.aux'.
LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 3.
LaTeX Font Info: ... okay on input line 3.
LaTeX Font Info: Checking defaults for T1/cmr/m/n on input line 3.
LaTeX Font Info: ... okay on input line 3.
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LaTeX Font Info: ... okay on input line 3.
LaTeX Font Info: Checking defaults for OMX/cmex/m/n on input line 3.
LaTeX Font Info: ... okay on input line 3.
LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 3.
LaTeX Font Info: ... okay on input line 3.
LaTeX Font Info: External font `cmex10' loaded for size
(Font) <12> on input line 5.
LaTeX Font Info: External font `cmex10' loaded for size
(Font) <8> on input line 5.
LaTeX Font Info: External font `cmex10' loaded for size
(Font) <6> on input line 5.
[1
] (angle_cosine_squared.aux) )
Here is how much of TeX's memory you used:
214 strings out of 20880
2171 string characters out of 196184
45503 words of memory out of 350001
3229 multiletter control sequences out of 10000+15000
6376 words of font info for 23 fonts, out of 400000 for 1000
14 hyphenation exceptions out of 10000
22i,4n,19p,122b,162s stack positions out of 3000i,100n,1500p,50000b,4000s
Output written on angle_cosine_squared.dvi (1 page, 428 bytes).

9
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\documentclass[12pt]{article}
\begin{document}
$$
E = K [\cos(\theta) - \cos(\theta_0)]^2
$$
\end{document}

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This is TeX, Version 3.14159 (Web2C 7.3.1) (format=latex 2003.2.18) 9 NOV 2005 10:54
**angle_harmonic.tex
(angle_harmonic.tex
LaTeX2e <2001/06/01>
Babel <v3.7h> and hyphenation patterns for american, french, german, ngerman, i
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(/usr/share/texmf/tex/latex/base/article.cls
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) (angle_harmonic.aux)
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LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 3.
LaTeX Font Info: ... okay on input line 3.
LaTeX Font Info: Checking defaults for T1/cmr/m/n on input line 3.
LaTeX Font Info: ... okay on input line 3.
LaTeX Font Info: Checking defaults for OT1/cmr/m/n on input line 3.
LaTeX Font Info: ... okay on input line 3.
LaTeX Font Info: Checking defaults for OMS/cmsy/m/n on input line 3.
LaTeX Font Info: ... okay on input line 3.
LaTeX Font Info: Checking defaults for OMX/cmex/m/n on input line 3.
LaTeX Font Info: ... okay on input line 3.
LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 3.
LaTeX Font Info: ... okay on input line 3.
LaTeX Font Info: External font `cmex10' loaded for size
(Font) <12> on input line 5.
LaTeX Font Info: External font `cmex10' loaded for size
(Font) <8> on input line 5.
LaTeX Font Info: External font `cmex10' loaded for size
(Font) <6> on input line 5.
[1
]
(angle_harmonic.aux) )
Here is how much of TeX's memory you used:
214 strings out of 20880
2141 string characters out of 196184
45503 words of memory out of 350001
3229 multiletter control sequences out of 10000+15000
6376 words of font info for 23 fonts, out of 400000 for 1000
14 hyphenation exceptions out of 10000
22i,4n,19p,120b,162s stack positions out of 3000i,100n,1500p,50000b,4000s
Output written on angle_harmonic.dvi (1 page, 404 bytes).

9
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\documentclass[12pt]{article}
\begin{document}
$$
E = K (\theta - \theta_0)^2
$$
\end{document}

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This is TeX, Version 3.14159 (Web2C 7.3.1) (format=latex 2003.2.18) 9 NOV 2005 10:54
**bond_class2.tex
(bond_class2.tex
LaTeX2e <2001/06/01>
Babel <v3.7h> and hyphenation patterns for american, french, german, ngerman, i
talian, nohyphenation, loaded.
(/usr/share/texmf/tex/latex/base/article.cls
Document Class: article 2001/04/21 v1.4e Standard LaTeX document class
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\abovecaptionskip=\skip41
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) (bond_class2.aux)
\openout1 = `bond_class2.aux'.
LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 3.
LaTeX Font Info: ... okay on input line 3.
LaTeX Font Info: Checking defaults for T1/cmr/m/n on input line 3.
LaTeX Font Info: ... okay on input line 3.
LaTeX Font Info: Checking defaults for OT1/cmr/m/n on input line 3.
LaTeX Font Info: ... okay on input line 3.
LaTeX Font Info: Checking defaults for OMS/cmsy/m/n on input line 3.
LaTeX Font Info: ... okay on input line 3.
LaTeX Font Info: Checking defaults for OMX/cmex/m/n on input line 3.
LaTeX Font Info: ... okay on input line 3.
LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 3.
LaTeX Font Info: ... okay on input line 3.
LaTeX Font Info: External font `cmex10' loaded for size
(Font) <12> on input line 5.
LaTeX Font Info: External font `cmex10' loaded for size
(Font) <8> on input line 5.
LaTeX Font Info: External font `cmex10' loaded for size
(Font) <6> on input line 5.
[1
]
(bond_class2.aux) )
Here is how much of TeX's memory you used:
214 strings out of 20880
2126 string characters out of 196184
45503 words of memory out of 350001
3229 multiletter control sequences out of 10000+15000
6376 words of font info for 23 fonts, out of 400000 for 1000
14 hyphenation exceptions out of 10000
22i,4n,19p,117b,162s stack positions out of 3000i,100n,1500p,50000b,4000s
Output written on bond_class2.dvi (1 page, 508 bytes).

9
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\documentclass[12pt]{article}
\begin{document}
$$
E = K_2 (r - r_0)^2 + K_3 (r - r_0)^3 + K_4 (r - r_0)^4
$$
\end{document}

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This is TeX, Version 3.14159 (Web2C 7.3.1) (format=latex 2003.2.18) 9 NOV 2005 10:54
**bond_fene.tex
(bond_fene.tex
LaTeX2e <2001/06/01>
Babel <v3.7h> and hyphenation patterns for american, french, german, ngerman, i
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) (bond_fene.aux)
\openout1 = `bond_fene.aux'.
LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 3.
LaTeX Font Info: ... okay on input line 3.
LaTeX Font Info: Checking defaults for T1/cmr/m/n on input line 3.
LaTeX Font Info: ... okay on input line 3.
LaTeX Font Info: Checking defaults for OT1/cmr/m/n on input line 3.
LaTeX Font Info: ... okay on input line 3.
LaTeX Font Info: Checking defaults for OMS/cmsy/m/n on input line 3.
LaTeX Font Info: ... okay on input line 3.
LaTeX Font Info: Checking defaults for OMX/cmex/m/n on input line 3.
LaTeX Font Info: ... okay on input line 3.
LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 3.
LaTeX Font Info: ... okay on input line 3.
LaTeX Font Info: External font `cmex10' loaded for size
(Font) <12> on input line 5.
LaTeX Font Info: External font `cmex10' loaded for size
(Font) <8> on input line 5.
LaTeX Font Info: External font `cmex10' loaded for size
(Font) <6> on input line 5.
[1
]
(bond_fene.aux) )
Here is how much of TeX's memory you used:
214 strings out of 20880
2116 string characters out of 196184
45503 words of memory out of 350001
3229 multiletter control sequences out of 10000+15000
6376 words of font info for 23 fonts, out of 400000 for 1000
14 hyphenation exceptions out of 10000
22i,4n,19p,115b,162s stack positions out of 3000i,100n,1500p,50000b,4000s
Output written on bond_fene.dvi (1 page, 788 bytes).

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\documentclass[12pt]{article}
\begin{document}
$$
E = -0.5 K R_0^2 \ln \left[ 1 - \left(\frac{r}{R_0}\right)^2\right] +
4 \epsilon \left[ \left(\frac{\sigma}{r}\right)^{12} -
\left(\frac{\sigma}{r}\right)^6 \right] + \epsilon
$$
\end{document}

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This is TeX, Version 3.14159 (Web2C 7.3.1) (format=latex 2003.2.18) 9 NOV 2005 10:54
**bond_fene_expand.tex
(bond_fene_expand.tex
LaTeX2e <2001/06/01>
Babel <v3.7h> and hyphenation patterns for american, french, german, ngerman, i
talian, nohyphenation, loaded.
(/usr/share/texmf/tex/latex/base/article.cls
Document Class: article 2001/04/21 v1.4e Standard LaTeX document class
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File: size12.clo 2001/04/21 v1.4e Standard LaTeX file (size option)
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\abovecaptionskip=\skip41
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\bibindent=\dimen102
) (bond_fene_expand.aux)
\openout1 = `bond_fene_expand.aux'.
LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 3.
LaTeX Font Info: ... okay on input line 3.
LaTeX Font Info: Checking defaults for T1/cmr/m/n on input line 3.
LaTeX Font Info: ... okay on input line 3.
LaTeX Font Info: Checking defaults for OT1/cmr/m/n on input line 3.
LaTeX Font Info: ... okay on input line 3.
LaTeX Font Info: Checking defaults for OMS/cmsy/m/n on input line 3.
LaTeX Font Info: ... okay on input line 3.
LaTeX Font Info: Checking defaults for OMX/cmex/m/n on input line 3.
LaTeX Font Info: ... okay on input line 3.
LaTeX Font Info: Checking defaults for U/cmr/m/n on input line 3.
LaTeX Font Info: ... okay on input line 3.
LaTeX Font Info: External font `cmex10' loaded for size
(Font) <12> on input line 5.
LaTeX Font Info: External font `cmex10' loaded for size
(Font) <8> on input line 5.
LaTeX Font Info: External font `cmex10' loaded for size
(Font) <6> on input line 5.
[1
]
(bond_fene_expand.aux) )
Here is how much of TeX's memory you used:
214 strings out of 20880
2151 string characters out of 196184
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\documentclass[12pt]{article}
\begin{document}
$$
E = -0.5 K R_0
\ln \left[1 -\left( \frac{\left(r - \Delta\right)}{R_0}\right)^2 \right] +
4 \epsilon \left[ \left(\frac{\sigma}{\left(r -
\Delta\right)}\right)^{12} - \left(\frac{\sigma}{\left(r -
\Delta\right)}\right)^6 \right] + \epsilon
$$
\end{document}

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This is TeX, Version 3.14159 (Web2C 7.3.1) (format=latex 2003.2.18) 9 NOV 2005 10:54
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[1
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(bond_harmonic.aux) )
Here is how much of TeX's memory you used:
214 strings out of 20880
2136 string characters out of 196184
45503 words of memory out of 350001
3229 multiletter control sequences out of 10000+15000
6376 words of font info for 23 fonts, out of 400000 for 1000
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\documentclass[12pt]{article}
\begin{document}
$$
E = K (r - r_0)^2
$$
\end{document}

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This is TeX, Version 3.14159 (Web2C 7.3.1) (format=latex 2003.2.18) 9 NOV 2005 10:54
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[1
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(bond_morse.aux) )
Here is how much of TeX's memory you used:
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2121 string characters out of 196184
45503 words of memory out of 350001
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6376 words of font info for 23 fonts, out of 400000 for 1000
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Output written on bond_morse.dvi (1 page, 616 bytes).

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\documentclass[12pt]{article}
\begin{document}
$$
% E = D \left[ 1 - \exp \left( -\alpha (r - r_0) \right) \right]^2
E = D \left[ 1 - e^{-\alpha (r - r_0)} \right]^2
$$
\end{document}

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This is TeX, Version 3.14159 (Web2C 7.3.1) (format=latex 2003.2.18) 9 NOV 2005 10:54
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[1
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(bond_nonlinear.aux) )
Here is how much of TeX's memory you used:
214 strings out of 20880
2141 string characters out of 196184
45503 words of memory out of 350001
3229 multiletter control sequences out of 10000+15000
6376 words of font info for 23 fonts, out of 400000 for 1000
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Output written on bond_nonlinear.dvi (1 page, 492 bytes).

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\documentclass[12pt]{article}
\begin{document}
$$
E = \frac{\epsilon (r - r_0)^2}{ [ \lambda^2 - (r - r_0)^2 ]}
$$
\end{document}

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This is TeX, Version 3.14159 (Web2C 7.3.1) (format=latex 2003.2.18) 25 APR 2006 17:17
**bond_quartic
(bond_quartic.tex
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[1
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(bond_quartic.aux) )
Here is how much of TeX's memory you used:
214 strings out of 20880
2131 string characters out of 196184
45503 words of memory out of 350001
3229 multiletter control sequences out of 10000+15000
6376 words of font info for 23 fonts, out of 400000 for 1000
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Output written on bond_quartic.dvi (1 page, 800 bytes).

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\documentclass[12pt]{article}
\begin{document}
$$
E = K (r - R_c)^ 2 (r - R_c - B_1) (r - R_c - B_2) + U_0 +
4 \epsilon \left[ \left(\frac{\sigma}{r}\right)^{12} -
\left(\frac{\sigma}{r}\right)^6 \right] + \epsilon
$$
\end{document}

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This is TeX, Version 3.14159 (Web2C 7.3.1) (format=latex 2003.2.18) 9 NOV 2005 10:54
**centro_symmetry.tex
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[1
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(centro_symmetry.aux) )
Here is how much of TeX's memory you used:
214 strings out of 20880
2146 string characters out of 196184
45503 words of memory out of 350001
3229 multiletter control sequences out of 10000+15000
6376 words of font info for 23 fonts, out of 400000 for 1000
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Output written on centro_symmetry.dvi (1 page, 580 bytes).

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\documentclass[12pt]{article}
\begin{document}
$$
P = \sum_{i = 1}^{6} | \vec{R}_i + \vec{R}_{i+6} |^2
$$
\end{document}

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This is TeX, Version 3.14159 (Web2C 7.3.1) (format=latex 2003.2.18) 9 NOV 2005 10:54
**dihedral_charmm.tex
(dihedral_charmm.tex
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Babel <v3.7h> and hyphenation patterns for american, french, german, ngerman, i
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LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 3.
LaTeX Font Info: ... okay on input line 3.
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LaTeX Font Info: ... okay on input line 3.
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[1
]
(dihedral_charmm.aux) )
Here is how much of TeX's memory you used:
214 strings out of 20880
2146 string characters out of 196184
45503 words of memory out of 350001
3229 multiletter control sequences out of 10000+15000
6376 words of font info for 23 fonts, out of 400000 for 1000
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\documentclass[12pt]{article}
\begin{document}
$$
E = K [ 1 + \cos (n \phi + d) ]
$$
\end{document}

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This is TeX, Version 3.14159 (Web2C 7.3.1) (format=latex 2003.2.18) 9 NOV 2005 10:54
**dihedral_class2.tex
(dihedral_class2.tex
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Babel <v3.7h> and hyphenation patterns for american, french, german, ngerman, i
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LaTeX Font Info: Checking defaults for OML/cmm/m/it on input line 3.
LaTeX Font Info: ... okay on input line 3.
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LaTeX Font Info: ... okay on input line 3.
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LaTeX Font Info: Checking defaults for OMS/cmsy/m/n on input line 3.
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LaTeX Font Info: ... okay on input line 3.
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LaTeX Font Info: External font `cmex10' loaded for size
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[1
]
(dihedral_class2.aux) )
Here is how much of TeX's memory you used:
214 strings out of 20880
2146 string characters out of 196184
47503 words of memory out of 350001
3229 multiletter control sequences out of 10000+15000
6376 words of font info for 23 fonts, out of 400000 for 1000
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Output written on dihedral_class2.dvi (1 page, 1804 bytes).

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\documentclass[12pt]{article}
\begin{document}
\begin{eqnarray*}
E & = & E_d + E_{mbt} + E_{ebt} + E_{at} + E_{aat} + E_{bb13} \\
E_d & = & \sum_{n=1}^{3} K_n [ 1 - \cos (n \phi - \phi_n) ] \\
E_{mbt} & = & (r_{jk} - r_2) [ A_1 \cos (\phi) + A_2 \cos (2\phi) + A_3 \cos (3\phi) ] \\
E_{ebt} & = & (r_{ij} - r_1) [ B_1 \cos (\phi) + B_2 \cos (2\phi) + B_3 \cos (3\phi) ] + \\
& & (r_{kl} - r_3) [ C_1 \cos (\phi) + C_2 \cos (2\phi) + C_3 \cos (3\phi) ] \\
E_{at} & = & (\theta_{ijk} - \theta_1) [ D_1 \cos (\phi) + D_2 \cos (2\phi) + D_3 \cos (3\phi) ] + \\
& & (\theta_{jkl} - \theta_2) [ E_1 \cos (\phi) + E_2 \cos (2\phi) + E_3 \cos (3\phi) ] \\
E_{aat} & = & M (\theta_{ijk} - \theta_1) (\theta_{jkl} - \theta_2) \cos (\phi) \\
E_{bb13} & = & N (r_{ij} - r_1) (r_{kl} - r_3)
\end{eqnarray*}
\end{document}

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\documentclass[12pt]{article}
\begin{document}
$$
E = K [ 1 + d \cos (n \phi) ]
$$
\end{document}

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