"Previous Section"_Section_accelerate.html - "LAMMPS WWW Site"_lws - "LAMMPS Documentation"_ld - "LAMMPS Commands"_lc - "Next Section"_Section_example.html :c

:link(lws,http://lammps.sandia.gov)
:link(ld,Manual.html)
:link(lc,Section_commands.html#comm)

:line

6. How-to discussions :h3

This section describes how to perform common tasks using LAMMPS.

6.1 "Restarting a simulation"_#howto_1
6.2 "2d simulations"_#howto_2
6.3 "CHARMM, AMBER, and DREIDING force fields"_#howto_3
6.4 "Running multiple simulations from one input script"_#howto_4
6.5 "Multi-replica simulations"_#howto_5
6.6 "Granular models"_#howto_6
6.7 "TIP3P water model"_#howto_7
6.8 "TIP4P water model"_#howto_8
6.9 "SPC water model"_#howto_9
6.10 "Coupling LAMMPS to other codes"_#howto_10
6.11 "Visualizing LAMMPS snapshots"_#howto_11
6.12 "Triclinic (non-orthogonal) simulation boxes"_#howto_12
6.13 "NEMD simulations"_#howto_13
6.14 "Finite-size spherical and aspherical particles"_#howto_14
6.15 "Output from LAMMPS (thermo, dumps, computes, fixes, variables)"_#howto_15
6.16 "Thermostatting, barostatting and computing temperature"_#howto_16
6.17 "Walls"_#howto_17
6.18 "Elastic constants"_#howto_18
6.19 "Library interface to LAMMPS"_#howto_19
6.20 "Calculating thermal conductivity"_#howto_20
6.21 "Calculating viscosity"_#howto_21
6.22 "Calculating a diffusion coefficient"_#howto_22
6.23 "Using chunks to calculate system properties"_#howto_23
6.24 "Setting parameters for the kspace_style pppm/disp command"_#howto_24
6.25 "Polarizable models"_#howto_25
6.26 "Adiabatic core/shell model"_#howto_26
6.27 "Drude induced dipoles"_#howto_27 :all(b)

The example input scripts included in the LAMMPS distribution and
highlighted in "Section 7"_Section_example.html also show how to
setup and run various kinds of simulations.

:line
:line

6.1 Restarting a simulation :link(howto_1),h4

There are 3 ways to continue a long LAMMPS simulation.  Multiple
"run"_run.html commands can be used in the same input script.  Each
run will continue from where the previous run left off.  Or binary
restart files can be saved to disk using the "restart"_restart.html
command.  At a later time, these binary files can be read via a
"read_restart"_read_restart.html command in a new script.  Or they can
be converted to text data files using the "-r command-line
switch"_Section_start.html#start_6 and read by a
"read_data"_read_data.html command in a new script.

Here we give examples of 2 scripts that read either a binary restart
file or a converted data file and then issue a new run command to
continue where the previous run left off.  They illustrate what
settings must be made in the new script.  Details are discussed in the
documentation for the "read_restart"_read_restart.html and
"read_data"_read_data.html commands.

Look at the {in.chain} input script provided in the {bench} directory
of the LAMMPS distribution to see the original script that these 2
scripts are based on.  If that script had the line

restart         50 tmp.restart :pre

added to it, it would produce 2 binary restart files (tmp.restart.50
and tmp.restart.100) as it ran.

This script could be used to read the 1st restart file and re-run the
last 50 timesteps:

read_restart    tmp.restart.50 :pre

neighbor        0.4 bin
neigh_modify    every 1 delay 1 :pre

fix             1 all nve
fix             2 all langevin 1.0 1.0 10.0 904297 :pre

timestep        0.012 :pre

run             50 :pre

Note that the following commands do not need to be repeated because
their settings are included in the restart file: {units, atom_style,
special_bonds, pair_style, bond_style}.  However these commands do
need to be used, since their settings are not in the restart file:
{neighbor, fix, timestep}.

If you actually use this script to perform a restarted run, you will
notice that the thermodynamic data match at step 50 (if you also put a
"thermo 50" command in the original script), but do not match at step
100.  This is because the "fix langevin"_fix_langevin.html command
uses random numbers in a way that does not allow for perfect restarts.

As an alternate approach, the restart file could be converted to a data
file as follows:

lmp_g++ -r tmp.restart.50 tmp.restart.data :pre

Then, this script could be used to re-run the last 50 steps:

units           lj
atom_style      bond
pair_style      lj/cut 1.12
pair_modify     shift yes
bond_style      fene
special_bonds   0.0 1.0 1.0 :pre

read_data       tmp.restart.data :pre

neighbor        0.4 bin
neigh_modify    every 1 delay 1 :pre

fix             1 all nve
fix             2 all langevin 1.0 1.0 10.0 904297 :pre

timestep        0.012 :pre

reset_timestep  50
run             50 :pre

Note that nearly all the settings specified in the original {in.chain}
script must be repeated, except the {pair_coeff} and {bond_coeff}
commands since the new data file lists the force field coefficients.
Also, the "reset_timestep"_reset_timestep.html command is used to tell
LAMMPS the current timestep.  This value is stored in restart files,
but not in data files.

:line

6.2 2d simulations :link(howto_2),h4

Use the "dimension"_dimension.html command to specify a 2d simulation.

Make the simulation box periodic in z via the "boundary"_boundary.html
command.  This is the default.

If using the "create box"_create_box.html command to define a
simulation box, set the z dimensions narrow, but finite, so that the
create_atoms command will tile the 3d simulation box with a single z
plane of atoms - e.g.

"create box"_create_box.html 1 -10 10 -10 10 -0.25 0.25 :pre

If using the "read data"_read_data.html command to read in a file of
atom coordinates, set the "zlo zhi" values to be finite but narrow,
similar to the create_box command settings just described.  For each
atom in the file, assign a z coordinate so it falls inside the
z-boundaries of the box - e.g. 0.0.

Use the "fix enforce2d"_fix_enforce2d.html command as the last
defined fix to insure that the z-components of velocities and forces
are zeroed out every timestep.  The reason to make it the last fix is
so that any forces induced by other fixes will be zeroed out.

Many of the example input scripts included in the LAMMPS distribution
are for 2d models.

NOTE: Some models in LAMMPS treat particles as finite-size spheres, as
opposed to point particles.  See the "atom_style
sphere"_atom_style.html and "fix nve/sphere"_fix_nve_sphere.html
commands for details.  By default, for 2d simulations, such particles
will still be modeled as 3d spheres, not 2d discs (circles), meaning
their moment of inertia will be that of a sphere.  If you wish to
model them as 2d discs, see the "set density/disc"_set.html command
and the {disc} option for the "fix nve/sphere"_fix_nve_sphere.html,
"fix nvt/sphere"_fix_nvt_sphere.html, "fix
nph/sphere"_fix_nph_sphere.html, "fix npt/sphere"_fix_npt_sphere.html
commands.

:line

6.3 CHARMM, AMBER, and DREIDING force fields :link(howto_3),h4

A force field has 2 parts: the formulas that define it and the
coefficients used for a particular system.  Here we only discuss
formulas implemented in LAMMPS that correspond to formulas commonly
used in the CHARMM, AMBER, and DREIDING force fields.  Setting
coefficients is done in the input data file via the
"read_data"_read_data.html command or in the input script with
commands like "pair_coeff"_pair_coeff.html or
"bond_coeff"_bond_coeff.html.  See "Section 9"_Section_tools.html
for additional tools that can use CHARMM or AMBER to assign force
field coefficients and convert their output into LAMMPS input.

See "(MacKerell)"_#howto-MacKerell for a description of the CHARMM force
field.  See "(Cornell)"_#howto-Cornell for a description of the AMBER force
field.

:link(charmm,http://www.scripps.edu/brooks)
:link(amber,http://amber.scripps.edu)

These style choices compute force field formulas that are consistent
with common options in CHARMM or AMBER.  See each command's
documentation for the formula it computes.

"bond_style"_bond_harmonic.html harmonic
"angle_style"_angle_charmm.html charmm
"dihedral_style"_dihedral_charmm.html charmmfsh
"dihedral_style"_dihedral_charmm.html charmm
"pair_style"_pair_charmm.html lj/charmmfsw/coul/charmmfsh
"pair_style"_pair_charmm.html lj/charmmfsw/coul/long
"pair_style"_pair_charmm.html lj/charmm/coul/charmm
"pair_style"_pair_charmm.html lj/charmm/coul/charmm/implicit
"pair_style"_pair_charmm.html lj/charmm/coul/long :ul

"special_bonds"_special_bonds.html charmm
"special_bonds"_special_bonds.html amber :ul

NOTE: For CHARMM, newer {charmmfsw} or {charmmfsh} styles were
released in March 2017.  We recommend they be used instead of the
older {charmm} styles.  See discussion of the differences on the "pair
charmm"_pair_charmm.html and "dihedral charmm"_dihedral_charmm.html
doc pages.

DREIDING is a generic force field developed by the "Goddard
group"_http://www.wag.caltech.edu at Caltech and is useful for
predicting structures and dynamics of organic, biological and
main-group inorganic molecules. The philosophy in DREIDING is to use
general force constants and geometry parameters based on simple
hybridization considerations, rather than individual force constants
and geometric parameters that depend on the particular combinations of
atoms involved in the bond, angle, or torsion terms. DREIDING has an
"explicit hydrogen bond term"_pair_hbond_dreiding.html to describe
interactions involving a hydrogen atom on very electronegative atoms
(N, O, F).

See "(Mayo)"_#howto-Mayo for a description of the DREIDING force field

These style choices compute force field formulas that are consistent
with the DREIDING force field.  See each command's
documentation for the formula it computes.

"bond_style"_bond_harmonic.html harmonic
"bond_style"_bond_morse.html morse :ul

"angle_style"_angle_harmonic.html harmonic
"angle_style"_angle_cosine.html cosine
"angle_style"_angle_cosine_periodic.html cosine/periodic :ul

"dihedral_style"_dihedral_charmm.html charmm
"improper_style"_improper_umbrella.html umbrella :ul

"pair_style"_pair_buck.html buck
"pair_style"_pair_buck.html buck/coul/cut
"pair_style"_pair_buck.html buck/coul/long
"pair_style"_pair_lj.html lj/cut
"pair_style"_pair_lj.html lj/cut/coul/cut
"pair_style"_pair_lj.html lj/cut/coul/long :ul

"pair_style"_pair_hbond_dreiding.html hbond/dreiding/lj
"pair_style"_pair_hbond_dreiding.html hbond/dreiding/morse :ul

"special_bonds"_special_bonds.html dreiding :ul

:line

6.4 Running multiple simulations from one input script :link(howto_4),h4

This can be done in several ways.  See the documentation for
individual commands for more details on how these examples work.

If "multiple simulations" means continue a previous simulation for
more timesteps, then you simply use the "run"_run.html command
multiple times.  For example, this script

units lj
atom_style atomic
read_data data.lj
run 10000
run 10000
run 10000
run 10000
run 10000 :pre

would run 5 successive simulations of the same system for a total of
50,000 timesteps.

If you wish to run totally different simulations, one after the other,
the "clear"_clear.html command can be used in between them to
re-initialize LAMMPS.  For example, this script

units lj
atom_style atomic
read_data data.lj
run 10000
clear
units lj
atom_style atomic
read_data data.lj.new
run 10000 :pre

would run 2 independent simulations, one after the other.

For large numbers of independent simulations, you can use
"variables"_variable.html and the "next"_next.html and
"jump"_jump.html commands to loop over the same input script
multiple times with different settings.  For example, this
script, named in.polymer

variable d index run1 run2 run3 run4 run5 run6 run7 run8
shell cd $d
read_data data.polymer
run 10000
shell cd ..
clear
next d
jump in.polymer :pre

would run 8 simulations in different directories, using a data.polymer
file in each directory.  The same concept could be used to run the
same system at 8 different temperatures, using a temperature variable
and storing the output in different log and dump files, for example

variable a loop 8
variable t index 0.8 0.85 0.9 0.95 1.0 1.05 1.1 1.15
log log.$a
read data.polymer
velocity all create $t 352839
fix 1 all nvt $t $t 100.0
dump 1 all atom 1000 dump.$a
run 100000
clear
next t
next a
jump in.polymer :pre

All of the above examples work whether you are running on 1 or
multiple processors, but assumed you are running LAMMPS on a single
partition of processors.  LAMMPS can be run on multiple partitions via
the "-partition" command-line switch as described in "this
section"_Section_start.html#start_6 of the manual.

In the last 2 examples, if LAMMPS were run on 3 partitions, the same
scripts could be used if the "index" and "loop" variables were
replaced with {universe}-style variables, as described in the
"variable"_variable.html command.  Also, the "next t" and "next a"
commands would need to be replaced with a single "next a t" command.
With these modifications, the 8 simulations of each script would run
on the 3 partitions one after the other until all were finished.
Initially, 3 simulations would be started simultaneously, one on each
partition.  When one finished, that partition would then start
the 4th simulation, and so forth, until all 8 were completed.

:line

6.5 Multi-replica simulations :link(howto_5),h4

Several commands in LAMMPS run mutli-replica simulations, meaning
that multiple instances (replicas) of your simulation are run
simultaneously, with small amounts of data exchanged between replicas
periodically.

These are the relevant commands:

"neb"_neb.html for nudged elastic band calculations
"prd"_prd.html for parallel replica dynamics
"tad"_tad.html for temperature accelerated dynamics
"temper"_temper.html for parallel tempering
"fix pimd"_fix_pimd.html for path-integral molecular dynamics (PIMD) :ul

NEB is a method for finding transition states and barrier energies.
PRD and TAD are methods for performing accelerated dynamics to find
and perform infrequent events.  Parallel tempering or replica exchange
runs different replicas at a series of temperature to facilitate
rare-event sampling.

These commands can only be used if LAMMPS was built with the REPLICA
package.  See the "Making LAMMPS"_Section_start.html#start_3 section
for more info on packages.

PIMD runs different replicas whose individual particles are coupled
together by springs to model a system or ring-polymers.

This commands can only be used if LAMMPS was built with the USER-MISC
package.  See the "Making LAMMPS"_Section_start.html#start_3 section
for more info on packages.

In all these cases, you must run with one or more processors per
replica.  The processors assigned to each replica are determined at
run-time by using the "-partition command-line
switch"_Section_start.html#start_6 to launch LAMMPS on multiple
partitions, which in this context are the same as replicas.  E.g.
these commands:

mpirun -np 16 lmp_linux -partition 8x2 -in in.temper
mpirun -np 8 lmp_linux -partition 8x1 -in in.neb :pre

would each run 8 replicas, on either 16 or 8 processors.  Note the use
of the "-in command-line switch"_Section_start.html#start_6 to specify
the input script which is required when running in multi-replica mode.

Also note that with MPI installed on a machine (e.g. your desktop),
you can run on more (virtual) processors than you have physical
processors.  Thus the above commands could be run on a
single-processor (or few-processor) desktop so that you can run
a multi-replica simulation on more replicas than you have
physical processors.

:line

6.6 Granular models :link(howto_6),h4

Granular system are composed of spherical particles with a diameter,
as opposed to point particles.  This means they have an angular
velocity and torque can be imparted to them to cause them to rotate.

To run a simulation of a granular model, you will want to use
the following commands:

"atom_style sphere"_atom_style.html
"fix nve/sphere"_fix_nve_sphere.html
"fix gravity"_fix_gravity.html :ul

This compute

"compute erotate/sphere"_compute_erotate_sphere.html :ul

calculates rotational kinetic energy which can be "output with
thermodynamic info"_Section_howto.html#howto_15.

Use one of these 3 pair potentials, which compute forces and torques
between interacting pairs of particles:

"pair_style"_pair_style.html gran/history
"pair_style"_pair_style.html gran/no_history
"pair_style"_pair_style.html gran/hertzian :ul

These commands implement fix options specific to granular systems:

"fix freeze"_fix_freeze.html
"fix pour"_fix_pour.html
"fix viscous"_fix_viscous.html
"fix wall/gran"_fix_wall_gran.html :ul

The fix style {freeze} zeroes both the force and torque of frozen
atoms, and should be used for granular system instead of the fix style
{setforce}.

For computational efficiency, you can eliminate needless pairwise
computations between frozen atoms by using this command:

"neigh_modify"_neigh_modify.html exclude :ul

NOTE: By default, for 2d systems, granular particles are still modeled
as 3d spheres, not 2d discs (circles), meaning their moment of inertia
will be the same as in 3d.  If you wish to model granular particles in
2d as 2d discs, see the note on this topic in "Section
6.2"_Section_howto.html#howto_2, where 2d simulations are disussed.

:line

6.7 TIP3P water model :link(howto_7),h4

The TIP3P water model as implemented in CHARMM
"(MacKerell)"_#howto-MacKerell specifies a 3-site rigid water molecule with
charges and Lennard-Jones parameters assigned to each of the 3 atoms.
In LAMMPS the "fix shake"_fix_shake.html command can be used to hold
the two O-H bonds and the H-O-H angle rigid.  A bond style of
{harmonic} and an angle style of {harmonic} or {charmm} should also be
used.

These are the additional parameters (in real units) to set for O and H
atoms and the water molecule to run a rigid TIP3P-CHARMM model with a
cutoff.  The K values can be used if a flexible TIP3P model (without
fix shake) is desired.  If the LJ epsilon and sigma for HH and OH are
set to 0.0, it corresponds to the original 1983 TIP3P model
"(Jorgensen)"_#Jorgensen1.

O mass = 15.9994
H mass = 1.008
O charge = -0.834
H charge = 0.417
LJ epsilon of OO = 0.1521
LJ sigma of OO = 3.1507
LJ epsilon of HH = 0.0460
LJ sigma of HH = 0.4000
LJ epsilon of OH = 0.0836
LJ sigma of OH = 1.7753
K of OH bond = 450
r0 of OH bond = 0.9572
K of HOH angle = 55
theta of HOH angle = 104.52 :all(b),p

These are the parameters to use for TIP3P with a long-range Coulombic
solver (e.g. Ewald or PPPM in LAMMPS), see "(Price)"_#Price1 for
details:

O mass = 15.9994
H mass = 1.008
O charge = -0.830
H charge = 0.415
LJ epsilon of OO = 0.102
LJ sigma of OO = 3.188
LJ epsilon, sigma of OH, HH = 0.0
K of OH bond = 450
r0 of OH bond = 0.9572
K of HOH angle = 55
theta of HOH angle = 104.52 :all(b),p

Wikipedia also has a nice article on "water
models"_http://en.wikipedia.org/wiki/Water_model.

:line

6.8 TIP4P water model :link(howto_8),h4

The four-point TIP4P rigid water model extends the traditional
three-point TIP3P model by adding an additional site, usually
massless, where the charge associated with the oxygen atom is placed.
This site M is located at a fixed distance away from the oxygen along
the bisector of the HOH bond angle.  A bond style of {harmonic} and an
angle style of {harmonic} or {charmm} should also be used.

A TIP4P model is run with LAMMPS using either this command
for a cutoff model:

"pair_style lj/cut/tip4p/cut"_pair_lj.html

or these two commands for a long-range model:

"pair_style lj/cut/tip4p/long"_pair_lj.html
"kspace_style pppm/tip4p"_kspace_style.html :ul

For both models, the bond lengths and bond angles should be held fixed
using the "fix shake"_fix_shake.html command.

These are the additional parameters (in real units) to set for O and H
atoms and the water molecule to run a rigid TIP4P model with a cutoff
"(Jorgensen)"_#Jorgensen1.  Note that the OM distance is specified in
the "pair_style"_pair_style.html command, not as part of the pair
coefficients.

O mass = 15.9994
H mass = 1.008
O charge = -1.040
H charge = 0.520
r0 of OH bond = 0.9572
theta of HOH angle = 104.52
OM distance = 0.15
LJ epsilon of O-O = 0.1550
LJ sigma of O-O = 3.1536
LJ epsilon, sigma of OH, HH = 0.0
Coulombic cutoff = 8.5 :all(b),p

For the TIP4/Ice model (J Chem Phys, 122, 234511 (2005);
http://dx.doi.org/10.1063/1.1931662) these values can be used:

O mass = 15.9994
H mass =  1.008
O charge = -1.1794
H charge =  0.5897
r0 of OH bond = 0.9572
theta of HOH angle = 104.52
OM distance = 0.1577
LJ epsilon of O-O = 0.21084
LJ sigma of O-O = 3.1668
LJ epsilon, sigma of OH, HH = 0.0
Coulombic cutoff = 8.5 :all(b),p

For the TIP4P/2005 model (J Chem Phys, 123, 234505 (2005);
http://dx.doi.org/10.1063/1.2121687), these values can be used:

O mass = 15.9994
H mass =  1.008
O charge = -1.1128
H charge = 0.5564
r0 of OH bond = 0.9572
theta of HOH angle = 104.52
OM distance = 0.1546
LJ epsilon of O-O = 0.1852
LJ sigma of O-O = 3.1589
LJ epsilon, sigma of OH, HH = 0.0
Coulombic cutoff = 8.5 :all(b),p

These are the parameters to use for TIP4P with a long-range Coulombic
solver (e.g. Ewald or PPPM in LAMMPS):

O mass = 15.9994
H mass = 1.008
O charge = -1.0484
H charge = 0.5242
r0 of OH bond = 0.9572
theta of HOH angle = 104.52
OM distance = 0.1250
LJ epsilon of O-O = 0.16275
LJ sigma of O-O = 3.16435
LJ epsilon, sigma of OH, HH = 0.0 :all(b),p

Note that the when using the TIP4P pair style, the neighbor list
cutoff for Coulomb interactions is effectively extended by a distance
2 * (OM distance), to account for the offset distance of the
fictitious charges on O atoms in water molecules.  Thus it is
typically best in an efficiency sense to use a LJ cutoff >= Coulomb
cutoff + 2*(OM distance), to shrink the size of the neighbor list.
This leads to slightly larger cost for the long-range calculation, so
you can test the trade-off for your model.  The OM distance and the LJ
and Coulombic cutoffs are set in the "pair_style
lj/cut/tip4p/long"_pair_lj.html command.

Wikipedia also has a nice article on "water
models"_http://en.wikipedia.org/wiki/Water_model.

:line

6.9 SPC water model :link(howto_9),h4

The SPC water model specifies a 3-site rigid water molecule with
charges and Lennard-Jones parameters assigned to each of the 3 atoms.
In LAMMPS the "fix shake"_fix_shake.html command can be used to hold
the two O-H bonds and the H-O-H angle rigid.  A bond style of
{harmonic} and an angle style of {harmonic} or {charmm} should also be
used.

These are the additional parameters (in real units) to set for O and H
atoms and the water molecule to run a rigid SPC model.

O mass = 15.9994
H mass = 1.008
O charge = -0.820
H charge = 0.410
LJ epsilon of OO = 0.1553
LJ sigma of OO = 3.166
LJ epsilon, sigma of OH, HH = 0.0
r0 of OH bond = 1.0
theta of HOH angle = 109.47 :all(b),p

Note that as originally proposed, the SPC model was run with a 9
Angstrom cutoff for both LJ and Coulommbic terms.  It can also be used
with long-range Coulombics (Ewald or PPPM in LAMMPS), without changing
any of the parameters above, though it becomes a different model in
that mode of usage.

The SPC/E (extended) water model is the same, except
the partial charge assignments change:

O charge = -0.8476
H charge = 0.4238 :all(b),p

See the "(Berendsen)"_#howto-Berendsen reference for more details on both
the SPC and SPC/E models.

Wikipedia also has a nice article on "water
models"_http://en.wikipedia.org/wiki/Water_model.

:line

6.10 Coupling LAMMPS to other codes :link(howto_10),h4

LAMMPS is designed to allow it to be coupled to other codes.  For
example, a quantum mechanics code might compute forces on a subset of
atoms and pass those forces to LAMMPS.  Or a continuum finite element
(FE) simulation might use atom positions as boundary conditions on FE
nodal points, compute a FE solution, and return interpolated forces on
MD atoms.

LAMMPS can be coupled to other codes in at least 3 ways.  Each has
advantages and disadvantages, which you'll have to think about in the
context of your application.

(1) Define a new "fix"_fix.html command that calls the other code.  In
this scenario, LAMMPS is the driver code.  During its timestepping,
the fix is invoked, and can make library calls to the other code,
which has been linked to LAMMPS as a library.  This is the way the
"POEMS"_poems package that performs constrained rigid-body motion on
groups of atoms is hooked to LAMMPS.  See the
"fix poems"_fix_poems.html command for more details.  See "this
section"_Section_modify.html of the documentation for info on how to add
a new fix to LAMMPS.

:link(poems,http://www.rpi.edu/~anderk5/lab)

(2) Define a new LAMMPS command that calls the other code.  This is
conceptually similar to method (1), but in this case LAMMPS and the
other code are on a more equal footing.  Note that now the other code
is not called during the timestepping of a LAMMPS run, but between
runs.  The LAMMPS input script can be used to alternate LAMMPS runs
with calls to the other code, invoked via the new command.  The
"run"_run.html command facilitates this with its {every} option, which
makes it easy to run a few steps, invoke the command, run a few steps,
invoke the command, etc.

In this scenario, the other code can be called as a library, as in
(1), or it could be a stand-alone code, invoked by a system() call
made by the command (assuming your parallel machine allows one or more
processors to start up another program).  In the latter case the
stand-alone code could communicate with LAMMPS thru files that the
command writes and reads.

See "Section 10"_Section_modify.html of the documentation for how
to add a new command to LAMMPS.

(3) Use LAMMPS as a library called by another code.  In this case the
other code is the driver and calls LAMMPS as needed.  Or a wrapper
code could link and call both LAMMPS and another code as libraries.
Again, the "run"_run.html command has options that allow it to be
invoked with minimal overhead (no setup or clean-up) if you wish to do
multiple short runs, driven by another program.

Examples of driver codes that call LAMMPS as a library are included in
the examples/COUPLE directory of the LAMMPS distribution; see
examples/COUPLE/README for more details:

simple: simple driver programs in C++ and C which invoke LAMMPS as a
library :ulb,l

lammps_quest: coupling of LAMMPS and "Quest"_quest, to run classical
MD with quantum forces calculated by a density functional code :l

lammps_spparks: coupling of LAMMPS and "SPPARKS"_spparks, to couple
a kinetic Monte Carlo model for grain growth using MD to calculate
strain induced across grain boundaries :l
:ule

:link(quest,http://dft.sandia.gov/Quest)
:link(spparks,http://www.sandia.gov/~sjplimp/spparks.html)

"This section"_Section_start.html#start_5 of the documentation
describes how to build LAMMPS as a library.  Once this is done, you
can interface with LAMMPS either via C++, C, Fortran, or Python (or
any other language that supports a vanilla C-like interface).  For
example, from C++ you could create one (or more) "instances" of
LAMMPS, pass it an input script to process, or execute individual
commands, all by invoking the correct class methods in LAMMPS.  From C
or Fortran you can make function calls to do the same things.  See
"Section 11"_Section_python.html of the manual for a description
of the Python wrapper provided with LAMMPS that operates through the
LAMMPS library interface.

The files src/library.cpp and library.h contain the C-style interface
to LAMMPS.  See "Section 6.19"_Section_howto.html#howto_19 of the
manual for a description of the interface and how to extend it for
your needs.

Note that the lammps_open() function that creates an instance of
LAMMPS takes an MPI communicator as an argument.  This means that
instance of LAMMPS will run on the set of processors in the
communicator.  Thus the calling code can run LAMMPS on all or a subset
of processors.  For example, a wrapper script might decide to
alternate between LAMMPS and another code, allowing them both to run
on all the processors.  Or it might allocate half the processors to
LAMMPS and half to the other code and run both codes simultaneously
before syncing them up periodically.  Or it might instantiate multiple
instances of LAMMPS to perform different calculations.

:line

6.11 Visualizing LAMMPS snapshots :link(howto_11),h4

LAMMPS itself does not do visualization, but snapshots from LAMMPS
simulations can be visualized (and analyzed) in a variety of ways.

LAMMPS snapshots are created by the "dump"_dump.html command which can
create files in several formats. The native LAMMPS dump format is a
text file (see "dump atom" or "dump custom") which can be visualized
by several popular visualization tools. The "dump image"_dump_image.html
and "dump movie"_dump_image.html styles can output internally rendered
images and convert a sequence of them to a movie during the MD run.
Several programs included with LAMMPS as auxiliary tools can convert
between LAMMPS format files and other formats.
See the "Section 9"_Section_tools.html doc page for details.

A Python-based toolkit distributed by our group can read native LAMMPS
dump files, including custom dump files with additional columns of
user-specified atom information, and convert them to various formats
or pipe them into visualization software directly.  See the "Pizza.py
WWW site"_pizza for details.  Specifically, Pizza.py can convert
LAMMPS dump files into PDB, XYZ, "Ensight"_ensight, and VTK formats.
Pizza.py can pipe LAMMPS dump files directly into the Raster3d and
RasMol visualization programs.  Pizza.py has tools that do interactive
3d OpenGL visualization and one that creates SVG images of dump file
snapshots.

:link(pizza,http://www.sandia.gov/~sjplimp/pizza.html)
:link(ensight,http://www.ensight.com)
:link(atomeye,http://mt.seas.upenn.edu/Archive/Graphics/A)

:line

6.12 Triclinic (non-orthogonal) simulation boxes :link(howto_12),h4

By default, LAMMPS uses an orthogonal simulation box to encompass the
particles.  The "boundary"_boundary.html command sets the boundary
conditions of the box (periodic, non-periodic, etc).  The orthogonal
box has its "origin" at (xlo,ylo,zlo) and is defined by 3 edge vectors
starting from the origin given by [a] = (xhi-xlo,0,0); [b] =
(0,yhi-ylo,0); [c] = (0,0,zhi-zlo).  The 6 parameters
(xlo,xhi,ylo,yhi,zlo,zhi) are defined at the time the simulation box
is created, e.g. by the "create_box"_create_box.html or
"read_data"_read_data.html or "read_restart"_read_restart.html
commands.  Additionally, LAMMPS defines box size parameters lx,ly,lz
where lx = xhi-xlo, and similarly in the y and z dimensions.  The 6
parameters, as well as lx,ly,lz, can be output via the "thermo_style
custom"_thermo_style.html command.

LAMMPS also allows simulations to be performed in triclinic
(non-orthogonal) simulation boxes shaped as a parallelepiped with
triclinic symmetry.  The parallelepiped has its "origin" at
(xlo,ylo,zlo) and is defined by 3 edge vectors starting from the
origin given by [a] = (xhi-xlo,0,0); [b] = (xy,yhi-ylo,0); [c] =
(xz,yz,zhi-zlo).  {xy,xz,yz} can be 0.0 or positive or negative values
and are called "tilt factors" because they are the amount of
displacement applied to faces of an originally orthogonal box to
transform it into the parallelepiped.  In LAMMPS the triclinic
simulation box edge vectors [a], [b], and [c] cannot be arbitrary
vectors.  As indicated, [a] must lie on the positive x axis.  [b] must
lie in the xy plane, with strictly positive y component. [c] may have
any orientation with strictly positive z component.  The requirement
that [a], [b], and [c] have strictly positive x, y, and z components,
respectively, ensures that [a], [b], and [c] form a complete
right-handed basis.  These restrictions impose no loss of generality,
since it is possible to rotate/invert any set of 3 crystal basis
vectors so that they conform to the restrictions.

For example, assume that the 3 vectors [A],[B],[C] are the edge
vectors of a general parallelepiped, where there is no restriction on
[A],[B],[C] other than they form a complete right-handed basis i.e.
[A] x [B] . [C] > 0.  The equivalent LAMMPS [a],[b],[c] are a linear
rotation of [A], [B], and [C] and can be computed as follows:

:c,image(Eqs/transform.jpg)

where A = | [A] | indicates the scalar length of [A]. The hat symbol (^)
indicates the corresponding unit vector. {beta} and {gamma} are angles
between the vectors described below. Note that by construction,
[a], [b], and [c] have strictly positive x, y, and z components, respectively.
If it should happen that
[A], [B], and [C] form a left-handed basis, then the above equations
are not valid for [c]. In this case, it is necessary
to first apply an inversion. This can be achieved
by interchanging two basis vectors or by changing the sign of one of them.

For consistency, the same rotation/inversion applied to the basis vectors
must also be applied to atom positions, velocities,
and any other vector quantities.
This can be conveniently achieved by first converting to
fractional coordinates in the
old basis and then converting to distance coordinates in the new basis.
The transformation is given by the following equation:

:c,image(Eqs/rotate.jpg)

where {V} is the volume of the box, [X] is the original vector quantity and
[x] is the vector in the LAMMPS basis.

There is no requirement that a triclinic box be periodic in any
dimension, though it typically should be in at least the 2nd dimension
of the tilt (y in xy) if you want to enforce a shift in periodic
boundary conditions across that boundary.  Some commands that work
with triclinic boxes, e.g. the "fix deform"_fix_deform.html and "fix
npt"_fix_nh.html commands, require periodicity or non-shrink-wrap
boundary conditions in specific dimensions.  See the command doc pages
for details.

The 9 parameters (xlo,xhi,ylo,yhi,zlo,zhi,xy,xz,yz) are defined at the
time the simulation box is created.  This happens in one of 3 ways.
If the "create_box"_create_box.html command is used with a region of
style {prism}, then a triclinic box is setup.  See the
"region"_region.html command for details.  If the
"read_data"_read_data.html command is used to define the simulation
box, and the header of the data file contains a line with the "xy xz
yz" keyword, then a triclinic box is setup.  See the
"read_data"_read_data.html command for details.  Finally, if the
"read_restart"_read_restart.html command reads a restart file which
was written from a simulation using a triclinic box, then a triclinic
box will be setup for the restarted simulation.

Note that you can define a triclinic box with all 3 tilt factors =
0.0, so that it is initially orthogonal.  This is necessary if the box
will become non-orthogonal, e.g. due to the "fix npt"_fix_nh.html or
"fix deform"_fix_deform.html commands.  Alternatively, you can use the
"change_box"_change_box.html command to convert a simulation box from
orthogonal to triclinic and vice versa.

As with orthogonal boxes, LAMMPS defines triclinic box size parameters
lx,ly,lz where lx = xhi-xlo, and similarly in the y and z dimensions.
The 9 parameters, as well as lx,ly,lz, can be output via the
"thermo_style custom"_thermo_style.html command.

To avoid extremely tilted boxes (which would be computationally
inefficient), LAMMPS normally requires that no tilt factor can skew
the box more than half the distance of the parallel box length, which
is the 1st dimension in the tilt factor (x for xz).  This is required
both when the simulation box is created, e.g. via the
"create_box"_create_box.html or "read_data"_read_data.html commands,
as well as when the box shape changes dynamically during a simulation,
e.g. via the "fix deform"_fix_deform.html or "fix npt"_fix_nh.html
commands.

For example, if xlo = 2 and xhi = 12, then the x box length is 10 and
the xy tilt factor must be between -5 and 5.  Similarly, both xz and
yz must be between -(xhi-xlo)/2 and +(yhi-ylo)/2.  Note that this is
not a limitation, since if the maximum tilt factor is 5 (as in this
example), then configurations with tilt = ..., -15, -5, 5, 15, 25,
... are geometrically all equivalent.  If the box tilt exceeds this
limit during a dynamics run (e.g. via the "fix deform"_fix_deform.html
command), then the box is "flipped" to an equivalent shape with a tilt
factor within the bounds, so the run can continue.  See the "fix
deform"_fix_deform.html doc page for further details.

One exception to this rule is if the 1st dimension in the tilt
factor (x for xy) is non-periodic.  In that case, the limits on the
tilt factor are not enforced, since flipping the box in that dimension
does not change the atom positions due to non-periodicity.  In this
mode, if you tilt the system to extreme angles, the simulation will
simply become inefficient, due to the highly skewed simulation box.

The limitation on not creating a simulation box with a tilt factor
skewing the box more than half the distance of the parallel box length
can be overridden via the "box"_box.html command.  Setting the {tilt}
keyword to {large} allows any tilt factors to be specified.

Box flips that may occur using the "fix deform"_fix_deform.html or
"fix npt"_fix_nh.html commands can be turned off using the {flip no}
option with either of the commands.

Note that if a simulation box has a large tilt factor, LAMMPS will run
less efficiently, due to the large volume of communication needed to
acquire ghost atoms around a processor's irregular-shaped sub-domain.
For extreme values of tilt, LAMMPS may also lose atoms and generate an
error.

Triclinic crystal structures are often defined using three lattice
constants {a}, {b}, and {c}, and three angles {alpha}, {beta} and
{gamma}. Note that in this nomenclature, the a, b, and c lattice
constants are the scalar lengths of the edge vectors [a], [b], and [c]
defined above.  The relationship between these 6 quantities
(a,b,c,alpha,beta,gamma) and the LAMMPS box sizes (lx,ly,lz) =
(xhi-xlo,yhi-ylo,zhi-zlo) and tilt factors (xy,xz,yz) is as follows:

:c,image(Eqs/box.jpg)

The inverse relationship can be written as follows:

:c,image(Eqs/box_inverse.jpg)

The values of {a}, {b}, {c} , {alpha}, {beta} , and {gamma} can be printed
out or accessed by computes using the
"thermo_style custom"_thermo_style.html keywords
{cella}, {cellb}, {cellc}, {cellalpha}, {cellbeta}, {cellgamma},
respectively.

As discussed on the "dump"_dump.html command doc page, when the BOX
BOUNDS for a snapshot is written to a dump file for a triclinic box,
an orthogonal bounding box which encloses the triclinic simulation box
is output, along with the 3 tilt factors (xy, xz, yz) of the triclinic
box, formatted as follows:

ITEM: BOX BOUNDS xy xz yz
xlo_bound xhi_bound xy
ylo_bound yhi_bound xz
zlo_bound zhi_bound yz :pre

This bounding box is convenient for many visualization programs and is
calculated from the 9 triclinic box parameters
(xlo,xhi,ylo,yhi,zlo,zhi,xy,xz,yz) as follows:

xlo_bound = xlo + MIN(0.0,xy,xz,xy+xz)
xhi_bound = xhi + MAX(0.0,xy,xz,xy+xz)
ylo_bound = ylo + MIN(0.0,yz)
yhi_bound = yhi + MAX(0.0,yz)
zlo_bound = zlo
zhi_bound = zhi :pre

These formulas can be inverted if you need to convert the bounding box
back into the triclinic box parameters, e.g. xlo = xlo_bound -
MIN(0.0,xy,xz,xy+xz).

One use of triclinic simulation boxes is to model solid-state crystals
with triclinic symmetry.  The "lattice"_lattice.html command can be
used with non-orthogonal basis vectors to define a lattice that will
tile a triclinic simulation box via the
"create_atoms"_create_atoms.html command.

A second use is to run Parinello-Rahman dynamics via the "fix
npt"_fix_nh.html command, which will adjust the xy, xz, yz tilt
factors to compensate for off-diagonal components of the pressure
tensor.  The analog for an "energy minimization"_minimize.html is
the "fix box/relax"_fix_box_relax.html command.

A third use is to shear a bulk solid to study the response of the
material.  The "fix deform"_fix_deform.html command can be used for
this purpose.  It allows dynamic control of the xy, xz, yz tilt
factors as a simulation runs.  This is discussed in the next section
on non-equilibrium MD (NEMD) simulations.

:line

6.13 NEMD simulations :link(howto_13),h4

Non-equilibrium molecular dynamics or NEMD simulations are typically
used to measure a fluid's rheological properties such as viscosity.
In LAMMPS, such simulations can be performed by first setting up a
non-orthogonal simulation box (see the preceding Howto section).

A shear strain can be applied to the simulation box at a desired
strain rate by using the "fix deform"_fix_deform.html command.  The
"fix nvt/sllod"_fix_nvt_sllod.html command can be used to thermostat
the sheared fluid and integrate the SLLOD equations of motion for the
system.  Fix nvt/sllod uses "compute
temp/deform"_compute_temp_deform.html to compute a thermal temperature
by subtracting out the streaming velocity of the shearing atoms.  The
velocity profile or other properties of the fluid can be monitored via
the "fix ave/chunk"_fix_ave_chunk.html command.

As discussed in the previous section on non-orthogonal simulation
boxes, the amount of tilt or skew that can be applied is limited by
LAMMPS for computational efficiency to be 1/2 of the parallel box
length.  However, "fix deform"_fix_deform.html can continuously strain
a box by an arbitrary amount.  As discussed in the "fix
deform"_fix_deform.html command, when the tilt value reaches a limit,
the box is flipped to the opposite limit which is an equivalent tiling
of periodic space.  The strain rate can then continue to change as
before.  In a long NEMD simulation these box re-shaping events may
occur many times.

In a NEMD simulation, the "remap" option of "fix
deform"_fix_deform.html should be set to "remap v", since that is what
"fix nvt/sllod"_fix_nvt_sllod.html assumes to generate a velocity
profile consistent with the applied shear strain rate.

An alternative method for calculating viscosities is provided via the
"fix viscosity"_fix_viscosity.html command.

NEMD simulations can also be used to measure transport properties of a fluid
through a pore or channel. Simulations of steady-state flow can be performed
using the "fix flow/gauss"_fix_flow_gauss.html command.

:line

6.14 Finite-size spherical and aspherical particles :link(howto_14),h4

Typical MD models treat atoms or particles as point masses.  Sometimes
it is desirable to have a model with finite-size particles such as
spheroids or ellipsoids or generalized aspherical bodies.  The
difference is that such particles have a moment of inertia, rotational
energy, and angular momentum.  Rotation is induced by torque coming
from interactions with other particles.

LAMMPS has several options for running simulations with these kinds of
particles.  The following aspects are discussed in turn:

atom styles
pair potentials
time integration
computes, thermodynamics, and dump output
rigid bodies composed of finite-size particles :ul

Example input scripts for these kinds of models are in the body,
colloid, dipole, ellipse, line, peri, pour, and tri directories of the
"examples directory"_Section_example.html in the LAMMPS distribution.

Atom styles :h5

There are several "atom styles"_atom_style.html that allow for
definition of finite-size particles: sphere, dipole, ellipsoid, line,
tri, peri, and body.

The sphere style defines particles that are spheriods and each
particle can have a unique diameter and mass (or density).  These
particles store an angular velocity (omega) and can be acted upon by
torque.  The "set" command can be used to modify the diameter and mass
of individual particles, after then are created.

The dipole style does not actually define finite-size particles, but
is often used in conjunction with spherical particles, via a command
like

atom_style hybrid sphere dipole :pre

This is because when dipoles interact with each other, they induce
torques, and a particle must be finite-size (i.e. have a moment of
inertia) in order to respond and rotate.  See the "atom_style
dipole"_atom_style.html command for details.  The "set" command can be
used to modify the orientation and length of the dipole moment of
individual particles, after then are created.

The ellipsoid style defines particles that are ellipsoids and thus can
be aspherical.  Each particle has a shape, specified by 3 diameters,
and mass (or density).  These particles store an angular momentum and
their orientation (quaternion), and can be acted upon by torque.  They
do not store an angular velocity (omega), which can be in a different
direction than angular momentum, rather they compute it as needed.
The "set" command can be used to modify the diameter, orientation, and
mass of individual particles, after then are created.  It also has a
brief explanation of what quaternions are.

The line style defines line segment particles with two end points and
a mass (or density).  They can be used in 2d simulations, and they can
be joined together to form rigid bodies which represent arbitrary
polygons.

The tri style defines triangular particles with three corner points
and a mass (or density).  They can be used in 3d simulations, and they
can be joined together to form rigid bodies which represent arbitrary
particles with a triangulated surface.

The peri style is used with "Peridynamic models"_pair_peri.html and
defines particles as having a volume, that is used internally in the
"pair_style peri"_pair_peri.html potentials.

The body style allows for definition of particles which can represent
complex entities, such as surface meshes of discrete points,
collections of sub-particles, deformable objects, etc.  The body style
is discussed in more detail on the "body"_body.html doc page.

Note that if one of these atom styles is used (or multiple styles via
the "atom_style hybrid"_atom_style.html command), not all particles in
the system are required to be finite-size or aspherical.

For example, in the ellipsoid style, if the 3 shape parameters are set
to the same value, the particle will be a sphere rather than an
ellipsoid.  If the 3 shape parameters are all set to 0.0 or if the
diameter is set to 0.0, it will be a point particle.  In the line or
tri style, if the lineflag or triflag is specified as 0, then it
will be a point particle.

Some of the pair styles used to compute pairwise interactions between
finite-size particles also compute the correct interaction with point
particles as well, e.g. the interaction between a point particle and a
finite-size particle or between two point particles.  If necessary,
"pair_style hybrid"_pair_hybrid.html can be used to insure the correct
interactions are computed for the appropriate style of interactions.
Likewise, using groups to partition particles (ellipsoids versus
spheres versus point particles) will allow you to use the appropriate
time integrators and temperature computations for each class of
particles.  See the doc pages for various commands for details.

Also note that for "2d simulations"_dimension.html, atom styles sphere
and ellipsoid still use 3d particles, rather than as circular disks or
ellipses.  This means they have the same moment of inertia as the 3d
object.  When temperature is computed, the correct degrees of freedom
are used for rotation in a 2d versus 3d system.

Pair potentials :h5

When a system with finite-size particles is defined, the particles
will only rotate and experience torque if the force field computes
such interactions.  These are the various "pair
styles"_pair_style.html that generate torque:

"pair_style gran/history"_pair_gran.html
"pair_style gran/hertzian"_pair_gran.html
"pair_style gran/no_history"_pair_gran.html
"pair_style dipole/cut"_pair_dipole.html
"pair_style gayberne"_pair_gayberne.html
"pair_style resquared"_pair_resquared.html
"pair_style brownian"_pair_brownian.html
"pair_style lubricate"_pair_lubricate.html
"pair_style line/lj"_pair_line_lj.html
"pair_style tri/lj"_pair_tri_lj.html
"pair_style body"_pair_body.html :ul

The granular pair styles are used with spherical particles.  The
dipole pair style is used with the dipole atom style, which could be
applied to spherical or ellipsoidal particles.  The GayBerne and
REsquared potentials require ellipsoidal particles, though they will
also work if the 3 shape parameters are the same (a sphere).  The
Brownian and lubrication potentials are used with spherical particles.
The line, tri, and body potentials are used with line segment,
triangular, and body particles respectively.

Time integration :h5

There are several fixes that perform time integration on finite-size
spherical particles, meaning the integrators update the rotational
orientation and angular velocity or angular momentum of the particles:

"fix nve/sphere"_fix_nve_sphere.html
"fix nvt/sphere"_fix_nvt_sphere.html
"fix npt/sphere"_fix_npt_sphere.html :ul

Likewise, there are 3 fixes that perform time integration on
ellipsoidal particles:

"fix nve/asphere"_fix_nve_asphere.html
"fix nvt/asphere"_fix_nvt_asphere.html
"fix npt/asphere"_fix_npt_asphere.html :ul

The advantage of these fixes is that those which thermostat the
particles include the rotational degrees of freedom in the temperature
calculation and thermostatting.  The "fix langevin"_fix_langevin
command can also be used with its {omgea} or {angmom} options to
thermostat the rotational degrees of freedom for spherical or
ellipsoidal particles.  Other thermostatting fixes only operate on the
translational kinetic energy of finite-size particles.

These fixes perform constant NVE time integration on line segment,
triangular, and body particles:

"fix nve/line"_fix_nve_line.html
"fix nve/tri"_fix_nve_tri.html
"fix nve/body"_fix_nve_body.html :ul

Note that for mixtures of point and finite-size particles, these
integration fixes can only be used with "groups"_group.html which
contain finite-size particles.

Computes, thermodynamics, and dump output :h5

There are several computes that calculate the temperature or
rotational energy of spherical or ellipsoidal particles:

"compute temp/sphere"_compute_temp_sphere.html
"compute temp/asphere"_compute_temp_asphere.html
"compute erotate/sphere"_compute_erotate_sphere.html
"compute erotate/asphere"_compute_erotate_asphere.html :ul

These include rotational degrees of freedom in their computation.  If
you wish the thermodynamic output of temperature or pressure to use
one of these computes (e.g. for a system entirely composed of
finite-size particles), then the compute can be defined and the
"thermo_modify"_thermo_modify.html command used.  Note that by default
thermodynamic quantities will be calculated with a temperature that
only includes translational degrees of freedom.  See the
"thermo_style"_thermo_style.html command for details.

These commands can be used to output various attributes of finite-size
particles:

"dump custom"_dump.html
"compute property/atom"_compute_property_atom.html
"dump local"_dump.html
"compute body/local"_compute_body_local.html :ul

Attributes include the dipole moment, the angular velocity, the
angular momentum, the quaternion, the torque, the end-point and
corner-point coordinates (for line and tri particles), and
sub-particle attributes of body particles.

Rigid bodies composed of finite-size particles :h5

The "fix rigid"_fix_rigid.html command treats a collection of
particles as a rigid body, computes its inertia tensor, sums the total
force and torque on the rigid body each timestep due to forces on its
constituent particles, and integrates the motion of the rigid body.

If any of the constituent particles of a rigid body are finite-size
particles (spheres or ellipsoids or line segments or triangles), then
their contribution to the inertia tensor of the body is different than
if they were point particles.  This means the rotational dynamics of
the rigid body will be different.  Thus a model of a dimer is
different if the dimer consists of two point masses versus two
spheroids, even if the two particles have the same mass.  Finite-size
particles that experience torque due to their interaction with other
particles will also impart that torque to a rigid body they are part
of.

See the "fix rigid" command for example of complex rigid-body models
it is possible to define in LAMMPS.

Note that the "fix shake"_fix_shake.html command can also be used to
treat 2, 3, or 4 particles as a rigid body, but it always assumes the
particles are point masses.

Also note that body particles cannot be modeled with the "fix
rigid"_fix_rigid.html command.  Body particles are treated by LAMMPS
as single particles, though they can store internal state, such as a
list of sub-particles.  Individual body partices are typically treated
as rigid bodies, and their motion integrated with a command like "fix
nve/body"_fix_nve_body.html.  Interactions between pairs of body
particles are computed via a command like "pair_style
body"_pair_body.html.

:line

6.15 Output from LAMMPS (thermo, dumps, computes, fixes, variables) :link(howto_15),h4

There are four basic kinds of LAMMPS output:

"Thermodynamic output"_thermo_style.html, which is a list
of quantities printed every few timesteps to the screen and logfile. :ulb,l

"Dump files"_dump.html, which contain snapshots of atoms and various
per-atom values and are written at a specified frequency. :l

Certain fixes can output user-specified quantities to files: "fix
ave/time"_fix_ave_time.html for time averaging, "fix
ave/chunk"_fix_ave_chunk.html for spatial or other averaging, and "fix
print"_fix_print.html for single-line output of
"variables"_variable.html.  Fix print can also output to the
screen. :l

"Restart files"_restart.html. :l
:ule

A simulation prints one set of thermodynamic output and (optionally)
restart files.  It can generate any number of dump files and fix
output files, depending on what "dump"_dump.html and "fix"_fix.html
commands you specify.

As discussed below, LAMMPS gives you a variety of ways to determine
what quantities are computed and printed when the thermodynamics,
dump, or fix commands listed above perform output.  Throughout this
discussion, note that users can also "add their own computes and fixes
to LAMMPS"_Section_modify.html which can then generate values that can
then be output with these commands.

The following sub-sections discuss different LAMMPS command related
to output and the kind of data they operate on and produce:

"Global/per-atom/local data"_#global
"Scalar/vector/array data"_#scalar
"Thermodynamic output"_#thermo
"Dump file output"_#dump
"Fixes that write output files"_#fixoutput
"Computes that process output quantities"_#computeoutput
"Fixes that process output quantities"_#fixprocoutput
"Computes that generate values to output"_#compute
"Fixes that generate values to output"_#fix
"Variables that generate values to output"_#variable
"Summary table of output options and data flow between commands"_#table :ul

Global/per-atom/local data :h5,link(global)

Various output-related commands work with three different styles of
data: global, per-atom, or local.  A global datum is one or more
system-wide values, e.g. the temperature of the system.  A per-atom
datum is one or more values per atom, e.g. the kinetic energy of each
atom.  Local datums are calculated by each processor based on the
atoms it owns, but there may be zero or more per atom, e.g. a list of
bond distances.

Scalar/vector/array data :h5,link(scalar)

Global, per-atom, and local datums can each come in three kinds: a
single scalar value, a vector of values, or a 2d array of values.  The
doc page for a "compute" or "fix" or "variable" that generates data
will specify both the style and kind of data it produces, e.g. a
per-atom vector.

When a quantity is accessed, as in many of the output commands
discussed below, it can be referenced via the following bracket
notation, where ID in this case is the ID of a compute.  The leading
"c_" would be replaced by "f_" for a fix, or "v_" for a variable:

c_ID | entire scalar, vector, or array
c_ID\[I\] | one element of vector, one column of array
c_ID\[I\]\[J\] | one element of array :tb(s=|)

In other words, using one bracket reduces the dimension of the data
once (vector -> scalar, array -> vector).  Using two brackets reduces
the dimension twice (array -> scalar).  Thus a command that uses
scalar values as input can typically also process elements of a vector
or array.

Thermodynamic output :h5,link(thermo)

The frequency and format of thermodynamic output is set by the
"thermo"_thermo.html, "thermo_style"_thermo_style.html, and
"thermo_modify"_thermo_modify.html commands.  The
"thermo_style"_thermo_style.html command also specifies what values
are calculated and written out.  Pre-defined keywords can be specified
(e.g. press, etotal, etc).  Three additional kinds of keywords can
also be specified (c_ID, f_ID, v_name), where a "compute"_compute.html
or "fix"_fix.html or "variable"_variable.html provides the value to be
output.  In each case, the compute, fix, or variable must generate
global values for input to the "thermo_style custom"_dump.html
command.

Note that thermodynamic output values can be "extensive" or
"intensive".  The former scale with the number of atoms in the system
(e.g. total energy), the latter do not (e.g. temperature).  The
setting for "thermo_modify norm"_thermo_modify.html determines whether
extensive quantities are normalized or not.  Computes and fixes
produce either extensive or intensive values; see their individual doc
pages for details.  "Equal-style variables"_variable.html produce only
intensive values; you can include a division by "natoms" in the
formula if desired, to make an extensive calculation produce an
intensive result.

Dump file output :h5,link(dump)

Dump file output is specified by the "dump"_dump.html and
"dump_modify"_dump_modify.html commands.  There are several
pre-defined formats (dump atom, dump xtc, etc).

There is also a "dump custom"_dump.html format where the user
specifies what values are output with each atom.  Pre-defined atom
attributes can be specified (id, x, fx, etc).  Three additional kinds
of keywords can also be specified (c_ID, f_ID, v_name), where a
"compute"_compute.html or "fix"_fix.html or "variable"_variable.html
provides the values to be output.  In each case, the compute, fix, or
variable must generate per-atom values for input to the "dump
custom"_dump.html command.

There is also a "dump local"_dump.html format where the user specifies
what local values to output.  A pre-defined index keyword can be
specified to enumerate the local values.  Two additional kinds of
keywords can also be specified (c_ID, f_ID), where a
"compute"_compute.html or "fix"_fix.html or "variable"_variable.html
provides the values to be output.  In each case, the compute or fix
must generate local values for input to the "dump local"_dump.html
command.

Fixes that write output files :h5,link(fixoutput)

Several fixes take various quantities as input and can write output
files: "fix ave/time"_fix_ave_time.html, "fix
ave/chunk"_fix_ave_chunk.html, "fix ave/histo"_fix_ave_histo.html,
"fix ave/correlate"_fix_ave_correlate.html, and "fix
print"_fix_print.html.

The "fix ave/time"_fix_ave_time.html command enables direct output to
a file and/or time-averaging of global scalars or vectors.  The user
specifies one or more quantities as input.  These can be global
"compute"_compute.html values, global "fix"_fix.html values, or
"variables"_variable.html of any style except the atom style which
produces per-atom values.  Since a variable can refer to keywords used
by the "thermo_style custom"_thermo_style.html command (like temp or
press) and individual per-atom values, a wide variety of quantities
can be time averaged and/or output in this way.  If the inputs are one
or more scalar values, then the fix generate a global scalar or vector
of output.  If the inputs are one or more vector values, then the fix
generates a global vector or array of output.  The time-averaged
output of this fix can also be used as input to other output commands.

The "fix ave/chunk"_fix_ave_chunk.html command enables direct output
to a file of chunk-averaged per-atom quantities like those output in
dump files.  Chunks can represent spatial bins or other collections of
atoms, e.g. individual molecules.  The per-atom quantities can be atom
density (mass or number) or atom attributes such as position,
velocity, force.  They can also be per-atom quantities calculated by a
"compute"_compute.html, by a "fix"_fix.html, or by an atom-style
"variable"_variable.html.  The chunk-averaged output of this fix can
also be used as input to other output commands.

The "fix ave/histo"_fix_ave_histo.html command enables direct output
to a file of histogrammed quantities, which can be global or per-atom
or local quantities.  The histogram output of this fix can also be
used as input to other output commands.

The "fix ave/correlate"_fix_ave_correlate.html command enables direct
output to a file of time-correlated quantities, which can be global
values.  The correlation matrix output of this fix can also be used as
input to other output commands.

The "fix print"_fix_print.html command can generate a line of output
written to the screen and log file or to a separate file, periodically
during a running simulation.  The line can contain one or more
"variable"_variable.html values for any style variable except the
vector or atom styles).  As explained above, variables themselves can
contain references to global values generated by "thermodynamic
keywords"_thermo_style.html, "computes"_compute.html,
"fixes"_fix.html, or other "variables"_variable.html, or to per-atom
values for a specific atom.  Thus the "fix print"_fix_print.html
command is a means to output a wide variety of quantities separate
from normal thermodynamic or dump file output.

Computes that process output quantities :h5,link(computeoutput)

The "compute reduce"_compute_reduce.html and "compute
reduce/region"_compute_reduce.html commands take one or more per-atom
or local vector quantities as inputs and "reduce" them (sum, min, max,
ave) to scalar quantities.  These are produced as output values which
can be used as input to other output commands.

The "compute slice"_compute_slice.html command take one or more global
vector or array quantities as inputs and extracts a subset of their
values to create a new vector or array.  These are produced as output
values which can be used as input to other output commands.

The "compute property/atom"_compute_property_atom.html command takes a
list of one or more pre-defined atom attributes (id, x, fx, etc) and
stores the values in a per-atom vector or array.  These are produced
as output values which can be used as input to other output commands.
The list of atom attributes is the same as for the "dump
custom"_dump.html command.

The "compute property/local"_compute_property_local.html command takes
a list of one or more pre-defined local attributes (bond info, angle
info, etc) and stores the values in a local vector or array.  These
are produced as output values which can be used as input to other
output commands.

Fixes that process output quantities :h5,link(fixprocoutput)

The "fix vector"_fix_vector.html command can create global vectors as
output from global scalars as input, accumulating them one element at
a time.

The "fix ave/atom"_fix_ave_atom.html command performs time-averaging
of per-atom vectors.  The per-atom quantities can be atom attributes
such as position, velocity, force.  They can also be per-atom
quantities calculated by a "compute"_compute.html, by a
"fix"_fix.html, or by an atom-style "variable"_variable.html.  The
time-averaged per-atom output of this fix can be used as input to
other output commands.

The "fix store/state"_fix_store_state.html command can archive one or
more per-atom attributes at a particular time, so that the old values
can be used in a future calculation or output.  The list of atom
attributes is the same as for the "dump custom"_dump.html command,
including per-atom quantities calculated by a "compute"_compute.html,
by a "fix"_fix.html, or by an atom-style "variable"_variable.html.
The output of this fix can be used as input to other output commands.

Computes that generate values to output :h5,link(compute)

Every "compute"_compute.html in LAMMPS produces either global or
per-atom or local values.  The values can be scalars or vectors or
arrays of data.  These values can be output using the other commands
described in this section.  The doc page for each compute command
describes what it produces.  Computes that produce per-atom or local
values have the word "atom" or "local" in their style name.  Computes
without the word "atom" or "local" produce global values.

Fixes that generate values to output :h5,link(fix)

Some "fixes"_fix.html in LAMMPS produces either global or per-atom or
local values which can be accessed by other commands.  The values can
be scalars or vectors or arrays of data.  These values can be output
using the other commands described in this section.  The doc page for
each fix command tells whether it produces any output quantities and
describes them.

Variables that generate values to output :h5,link(variable)

"Variables"_variable.html defined in an input script can store one or
more strings.  But equal-style, vector-style, and atom-style or
atomfile-style variables generate a global scalar value, global vector
or values, or a per-atom vector, respectively, when accessed.  The
formulas used to define these variables can contain references to the
thermodynamic keywords and to global and per-atom data generated by
computes, fixes, and other variables.  The values generated by
variables can be used as input to and thus output by the other
commands described in this section.

Summary table of output options and data flow between commands :h5,link(table)

This table summarizes the various commands that can be used for
generating output from LAMMPS.  Each command produces output data of
some kind and/or writes data to a file.  Most of the commands can take
data from other commands as input.  Thus you can link many of these
commands together in pipeline form, where data produced by one command
is used as input to another command and eventually written to the
screen or to a file.  Note that to hook two commands together the
output and input data types must match, e.g. global/per-atom/local
data and scalar/vector/array data.

Also note that, as described above, when a command takes a scalar as
input, that could be an element of a vector or array.  Likewise a
vector input could be a column of an array.

Command: Input: Output:
"thermo_style custom"_thermo_style.html: global scalars: screen, log file:
"dump custom"_dump.html: per-atom vectors: dump file:
"dump local"_dump.html: local vectors: dump file:
"fix print"_fix_print.html: global scalar from variable: screen, file:
"print"_print.html: global scalar from variable: screen:
"computes"_compute.html: N/A: global/per-atom/local scalar/vector/array:
"fixes"_fix.html: N/A: global/per-atom/local scalar/vector/array:
"variables"_variable.html: global scalars and vectors, per-atom vectors: global scalar and vector, per-atom vector:
"compute reduce"_compute_reduce.html: per-atom/local vectors: global scalar/vector:
"compute slice"_compute_slice.html: global vectors/arrays: global vector/array:
"compute property/atom"_compute_property_atom.html: per-atom vectors: per-atom vector/array:
"compute property/local"_compute_property_local.html: local vectors: local vector/array:
"fix vector"_fix_vector.html: global scalars: global vector:
"fix ave/atom"_fix_ave_atom.html: per-atom vectors: per-atom vector/array:
"fix ave/time"_fix_ave_time.html: global scalars/vectors: global scalar/vector/array, file:
"fix ave/chunk"_fix_ave_chunk.html: per-atom vectors: global array, file:
"fix ave/histo"_fix_ave_histo.html: global/per-atom/local scalars and vectors: global array, file:
"fix ave/correlate"_fix_ave_correlate.html: global scalars: global array, file:
"fix store/state"_fix_store_state.html: per-atom vectors: per-atom vector/array :tb(c=3,s=:)

:line

6.16 Thermostatting, barostatting, and computing temperature :link(howto_16),h4

Thermostatting means controlling the temperature of particles in an MD
simulation.  Barostatting means controlling the pressure.  Since the
pressure includes a kinetic component due to particle velocities, both
these operations require calculation of the temperature.  Typically a
target temperature (T) and/or pressure (P) is specified by the user,
and the thermostat or barostat attempts to equilibrate the system to
the requested T and/or P.

Temperature is computed as kinetic energy divided by some number of
degrees of freedom (and the Boltzmann constant).  Since kinetic energy
is a function of particle velocity, there is often a need to
distinguish between a particle's advection velocity (due to some
aggregate motion of particles) and its thermal velocity.  The sum of
the two is the particle's total velocity, but the latter is often what
is wanted to compute a temperature.

LAMMPS has several options for computing temperatures, any of which
can be used in thermostatting and barostatting.  These "compute
commands"_compute.html calculate temperature, and the "compute
pressure"_compute_pressure.html command calculates pressure.

"compute temp"_compute_temp.html
"compute temp/sphere"_compute_temp_sphere.html
"compute temp/asphere"_compute_temp_asphere.html
"compute temp/com"_compute_temp_com.html
"compute temp/deform"_compute_temp_deform.html
"compute temp/partial"_compute_temp_partial.html
"compute temp/profile"_compute_temp_profile.html
"compute temp/ramp"_compute_temp_ramp.html
"compute temp/region"_compute_temp_region.html :ul

All but the first 3 calculate velocity biases directly (e.g. advection
velocities) that are removed when computing the thermal temperature.
"Compute temp/sphere"_compute_temp_sphere.html and "compute
temp/asphere"_compute_temp_asphere.html compute kinetic energy for
finite-size particles that includes rotational degrees of freedom.
They both allow for velocity biases indirectly, via an optional extra
argument, another temperature compute that subtracts a velocity bias.
This allows the translational velocity of spherical or aspherical
particles to be adjusted in prescribed ways.

Thermostatting in LAMMPS is performed by "fixes"_fix.html, or in one
case by a pair style.  Several thermostatting fixes are available:
Nose-Hoover (nvt), Berendsen, CSVR, Langevin, and direct rescaling
(temp/rescale).  Dissipative particle dynamics (DPD) thermostatting
can be invoked via the {dpd/tstat} pair style:

"fix nvt"_fix_nh.html
"fix nvt/sphere"_fix_nvt_sphere.html
"fix nvt/asphere"_fix_nvt_asphere.html
"fix nvt/sllod"_fix_nvt_sllod.html
"fix temp/berendsen"_fix_temp_berendsen.html
"fix temp/csvr"_fix_temp_csvr.html
"fix langevin"_fix_langevin.html
"fix temp/rescale"_fix_temp_rescale.html
"pair_style dpd/tstat"_pair_dpd.html :ul

"Fix nvt"_fix_nh.html only thermostats the translational velocity of
particles.  "Fix nvt/sllod"_fix_nvt_sllod.html also does this, except
that it subtracts out a velocity bias due to a deforming box and
integrates the SLLOD equations of motion.  See the "NEMD
simulations"_#howto_13 section of this page for further details.  "Fix
nvt/sphere"_fix_nvt_sphere.html and "fix
nvt/asphere"_fix_nvt_asphere.html thermostat not only translation
velocities but also rotational velocities for spherical and aspherical
particles.

DPD thermostatting alters pairwise interactions in a manner analogous
to the per-particle thermostatting of "fix
langevin"_fix_langevin.html.

Any of the thermostatting fixes can use temperature computes that
remove bias which has two effects.  First, the current calculated
temperature, which is compared to the requested target temperature, is
calculated with the velocity bias removed.  Second, the thermostat
adjusts only the thermal temperature component of the particle's
velocities, which are the velocities with the bias removed.  The
removed bias is then added back to the adjusted velocities.  See the
doc pages for the individual fixes and for the
"fix_modify"_fix_modify.html command for instructions on how to assign
a temperature compute to a thermostatting fix.  For example, you can
apply a thermostat to only the x and z components of velocity by using
it in conjunction with "compute
temp/partial"_compute_temp_partial.html.  Of you could thermostat only
the thermal temperature of a streaming flow of particles without
affecting the streaming velocity, by using "compute
temp/profile"_compute_temp_profile.html.

NOTE: Only the nvt fixes perform time integration, meaning they update
the velocities and positions of particles due to forces and velocities
respectively.  The other thermostat fixes only adjust velocities; they
do NOT perform time integration updates.  Thus they should be used in
conjunction with a constant NVE integration fix such as these:

"fix nve"_fix_nve.html
"fix nve/sphere"_fix_nve_sphere.html
"fix nve/asphere"_fix_nve_asphere.html :ul

Barostatting in LAMMPS is also performed by "fixes"_fix.html.  Two
barosttating methods are currently available: Nose-Hoover (npt and
nph) and Berendsen:

"fix npt"_fix_nh.html
"fix npt/sphere"_fix_npt_sphere.html
"fix npt/asphere"_fix_npt_asphere.html
"fix nph"_fix_nh.html
"fix press/berendsen"_fix_press_berendsen.html :ul

The "fix npt"_fix_nh.html commands include a Nose-Hoover thermostat
and barostat.  "Fix nph"_fix_nh.html is just a Nose/Hoover barostat;
it does no thermostatting.  Both "fix nph"_fix_nh.html and "fix
press/berendsen"_fix_press_berendsen.html can be used in conjunction
with any of the thermostatting fixes.

As with the thermostats, "fix npt"_fix_nh.html and "fix
nph"_fix_nh.html only use translational motion of the particles in
computing T and P and performing thermo/barostatting.  "Fix
npt/sphere"_fix_npt_sphere.html and "fix
npt/asphere"_fix_npt_asphere.html thermo/barostat using not only
translation velocities but also rotational velocities for spherical
and aspherical particles.

All of the barostatting fixes use the "compute
pressure"_compute_pressure.html compute to calculate a current
pressure.  By default, this compute is created with a simple "compute
temp"_compute_temp.html (see the last argument of the "compute
pressure"_compute_pressure.html command), which is used to calculated
the kinetic component of the pressure.  The barostatting fixes can
also use temperature computes that remove bias for the purpose of
computing the kinetic component which contributes to the current
pressure.  See the doc pages for the individual fixes and for the
"fix_modify"_fix_modify.html command for instructions on how to assign
a temperature or pressure compute to a barostatting fix.

NOTE: As with the thermostats, the Nose/Hoover methods ("fix
npt"_fix_nh.html and "fix nph"_fix_nh.html) perform time integration.
"Fix press/berendsen"_fix_press_berendsen.html does NOT, so it should
be used with one of the constant NVE fixes or with one of the NVT
fixes.

Finally, thermodynamic output, which can be setup via the
"thermo_style"_thermo_style.html command, often includes temperature
and pressure values.  As explained on the doc page for the
"thermo_style"_thermo_style.html command, the default T and P are
setup by the thermo command itself.  They are NOT the ones associated
with any thermostatting or barostatting fix you have defined or with
any compute that calculates a temperature or pressure.  Thus if you
want to view these values of T and P, you need to specify them
explicitly via a "thermo_style custom"_thermo_style.html command.  Or
you can use the "thermo_modify"_thermo_modify.html command to
re-define what temperature or pressure compute is used for default
thermodynamic output.

:line

6.17 Walls :link(howto_17),h4

Walls in an MD simulation are typically used to bound particle motion,
i.e. to serve as a boundary condition.

Walls in LAMMPS can be of rough (made of particles) or idealized
surfaces.  Ideal walls can be smooth, generating forces only in the
normal direction, or frictional, generating forces also in the
tangential direction.

Rough walls, built of particles, can be created in various ways.  The
particles themselves can be generated like any other particle, via the
"lattice"_lattice.html and "create_atoms"_create_atoms.html commands,
or read in via the "read_data"_read_data.html command.

Their motion can be constrained by many different commands, so that
they do not move at all, move together as a group at constant velocity
or in response to a net force acting on them, move in a prescribed
fashion (e.g. rotate around a point), etc.  Note that if a time
integration fix like "fix nve"_fix_nve.html or "fix nvt"_fix_nh.html
is not used with the group that contains wall particles, their
positions and velocities will not be updated.

"fix aveforce"_fix_aveforce.html - set force on particles to average value, so they move together
"fix setforce"_fix_setforce.html - set force on particles to a value, e.g. 0.0
"fix freeze"_fix_freeze.html - freeze particles for use as granular walls
"fix nve/noforce"_fix_nve_noforce.html - advect particles by their velocity, but without force
"fix move"_fix_move.html - prescribe motion of particles by a linear velocity, oscillation, rotation, variable :ul

The "fix move"_fix_move.html command offers the most generality, since
the motion of individual particles can be specified with
"variable"_variable.html formula which depends on time and/or the
particle position.

For rough walls, it may be useful to turn off pairwise interactions
between wall particles via the "neigh_modify
exclude"_neigh_modify.html command.

Rough walls can also be created by specifying frozen particles that do
not move and do not interact with mobile particles, and then tethering
other particles to the fixed particles, via a "bond"_bond_style.html.
The bonded particles do interact with other mobile particles.

Idealized walls can be specified via several fix commands.  "Fix
wall/gran"_fix_wall_gran.html creates frictional walls for use with
granular particles; all the other commands create smooth walls.

"fix wall/reflect"_fix_wall_reflect.html - reflective flat walls
"fix wall/lj93"_fix_wall.html - flat walls, with Lennard-Jones 9/3 potential
"fix wall/lj126"_fix_wall.html - flat walls, with Lennard-Jones 12/6 potential
"fix wall/colloid"_fix_wall.html - flat walls, with "pair_style colloid"_pair_colloid.html potential
"fix wall/harmonic"_fix_wall.html - flat walls, with repulsive harmonic spring potential
"fix wall/region"_fix_wall_region.html - use region surface as wall
"fix wall/gran"_fix_wall_gran.html - flat or curved walls with "pair_style granular"_pair_gran.html potential :ul

The {lj93}, {lj126}, {colloid}, and {harmonic} styles all allow the
flat walls to move with a constant velocity, or oscillate in time.
The "fix wall/region"_fix_wall_region.html command offers the most
generality, since the region surface is treated as a wall, and the
geometry of the region can be a simple primitive volume (e.g. a
sphere, or cube, or plane), or a complex volume made from the union
and intersection of primitive volumes.  "Regions"_region.html can also
specify a volume "interior" or "exterior" to the specified primitive
shape or {union} or {intersection}.  "Regions"_region.html can also be
"dynamic" meaning they move with constant velocity, oscillate, or
rotate.

The only frictional idealized walls currently in LAMMPS are flat or
curved surfaces specified by the "fix wall/gran"_fix_wall_gran.html
command.  At some point we plan to allow regoin surfaces to be used as
frictional walls, as well as triangulated surfaces.

:line

6.18 Elastic constants :link(howto_18),h4

Elastic constants characterize the stiffness of a material. The formal
definition is provided by the linear relation that holds between the
stress and strain tensors in the limit of infinitesimal deformation.
In tensor notation, this is expressed as s_ij = C_ijkl * e_kl, where
the repeated indices imply summation. s_ij are the elements of the
symmetric stress tensor. e_kl are the elements of the symmetric strain
tensor. C_ijkl are the elements of the fourth rank tensor of elastic
constants. In three dimensions, this tensor has 3^4=81 elements. Using
Voigt notation, the tensor can be written as a 6x6 matrix, where C_ij
is now the derivative of s_i w.r.t. e_j. Because s_i is itself a
derivative w.r.t. e_i, it follows that C_ij is also symmetric, with at
most 7*6/2 = 21 distinct elements.

At zero temperature, it is easy to estimate these derivatives by
deforming the simulation box in one of the six directions using the
"change_box"_change_box.html command and measuring the change in the
stress tensor. A general-purpose script that does this is given in the
examples/elastic directory described in "this
section"_Section_example.html.

Calculating elastic constants at finite temperature is more
challenging, because it is necessary to run a simulation that perfoms
time averages of differential properties. One way to do this is to
measure the change in average stress tensor in an NVT simulations when
the cell volume undergoes a finite deformation. In order to balance
the systematic and statistical errors in this method, the magnitude of
the deformation must be chosen judiciously, and care must be taken to
fully equilibrate the deformed cell before sampling the stress
tensor. Another approach is to sample the triclinic cell fluctuations
that occur in an NPT simulation. This method can also be slow to
converge and requires careful post-processing "(Shinoda)"_#Shinoda1

:line

6.19 Library interface to LAMMPS :link(howto_19),h4

As described in "Section 2.5"_Section_start.html#start_5, LAMMPS
can be built as a library, so that it can be called by another code,
used in a "coupled manner"_Section_howto.html#howto_10 with other
codes, or driven through a "Python interface"_Section_python.html.

All of these methodologies use a C-style interface to LAMMPS that is
provided in the files src/library.cpp and src/library.h.  The
functions therein have a C-style argument list, but contain C++ code
you could write yourself in a C++ application that was invoking LAMMPS
directly.  The C++ code in the functions illustrates how to invoke
internal LAMMPS operations.  Note that LAMMPS classes are defined
within a LAMMPS namespace (LAMMPS_NS) if you use them from another C++
application.

Library.cpp contains these functions for creating and destroying an
instance of LAMMPS and sending it commands to execute.  See the
documentation in the src/library.cpp file for details:

void lammps_open(int, char **, MPI_Comm, void **)
void lammps_open_no_mpi(int, char **, void **)
void lammps_close(void *)
int lammps_version(void *)
void lammps_file(void *, char *)
char *lammps_command(void *, char *)
void lammps_commands_list(void *, int, char **)
void lammps_commands_string(void *, char *)
void lammps_free(void *) :pre

The lammps_open() function is used to initialize LAMMPS, passing in a
list of strings as if they were "command-line
arguments"_Section_start.html#start_6 when LAMMPS is run in
stand-alone mode from the command line, and a MPI communicator for
LAMMPS to run under.  It returns a ptr to the LAMMPS object that is
created, and which is used in subsequent library calls.  The
lammps_open() function can be called multiple times, to create
multiple instances of LAMMPS.

LAMMPS will run on the set of processors in the communicator.  This
means the calling code can run LAMMPS on all or a subset of
processors.  For example, a wrapper script might decide to alternate
between LAMMPS and another code, allowing them both to run on all the
processors.  Or it might allocate half the processors to LAMMPS and
half to the other code and run both codes simultaneously before
syncing them up periodically.  Or it might instantiate multiple
instances of LAMMPS to perform different calculations.

The lammps_open_no_mpi() function is similar except that no MPI
communicator is passed from the caller.  Instead, MPI_COMM_WORLD is
used to instantiate LAMMPS, and MPI is initialized if necessary.

The lammps_close() function is used to shut down an instance of LAMMPS
and free all its memory.

The lammps_version() function can be used to determined the specific
version of the underlying LAMMPS code. This is particularly useful
when loading LAMMPS as a shared library via dlopen(). The code using
the library interface can than use this information to adapt to
changes to the LAMMPS command syntax between versions. The returned
LAMMPS version code is an integer (e.g. 2 Sep 2015 results in
20150902) that grows with every new LAMMPS version.

The lammps_file(), lammps_command(), lammps_commands_list(), and
lammps_commands_string() functions are used to pass one or more
commands to LAMMPS to execute, the same as if they were coming from an
input script.

Via these functions, the calling code can read or generate a series of
LAMMPS commands one or multiple at a time and pass it thru the library
interface to setup a problem and then run it in stages.  The caller
can interleave the command function calls with operations it performs,
calls to extract information from or set information within LAMMPS, or
calls to another code's library.

The lammps_file() function passes the filename of an input script.
The lammps_command() function passes a single command as a string.
The lammps_commands_list() function passes multiple commands in a
char** list.  In both lammps_command() and lammps_commands_list(),
individual commands may or may not have a trailing newline.  The
lammps_commands_string() function passes multiple commands
concatenated into one long string, separated by newline characters.
In both lammps_commands_list() and lammps_commands_string(), a single
command can be spread across multiple lines, if the last printable
character of all but the last line is "&", the same as if the lines
appeared in an input script.

The lammps_free() function is a clean-up function to free memory that
the library allocated previously via other function calls.  See
comments in src/library.cpp file for which other functions need this
clean-up.

Library.cpp also contains these functions for extracting information
from LAMMPS and setting value within LAMMPS.  Again, see the
documentation in the src/library.cpp file for details, including
which quantities can be queried by name:

void *lammps_extract_global(void *, char *)
void lammps_extract_box(void *, double *, double *,
                        double *, double *, double *, int *, int *)
void *lammps_extract_atom(void *, char *)
void *lammps_extract_compute(void *, char *, int, int)
void *lammps_extract_fix(void *, char *, int, int, int, int)
void *lammps_extract_variable(void *, char *, char *) :pre

void lammps_reset_box(void *, double *, double *, double, double, double)
int lammps_set_variable(void *, char *, char *) :pre

double lammps_get_thermo(void *, char *)
int lammps_get_natoms(void *)
void lammps_gather_atoms(void *, double *)
void lammps_scatter_atoms(void *, double *) :pre
void lammps_create_atoms(void *, int, tagint *, int *, double *, double *,
                         imageint *, int) :pre

The extract functions return a pointer to various global or per-atom
quantities stored in LAMMPS or to values calculated by a compute, fix,
or variable.  The pointer returned by the extract_global() function
can be used as a permanent reference to a value which may change.  For
the extract_atom() method, see the extract() method in the
src/atom.cpp file for a list of valid per-atom properties.  New names
could easily be added if the property you want is not listed.  For the
other extract functions, the underlying storage may be reallocated as
LAMMPS runs, so you need to re-call the function to assure a current
pointer or returned value(s).

The lammps_reset_box() function resets the size and shape of the
simulation box, e.g. as part of restoring a previously extracted and
saved state of a simulation.

The lammps_set_variable() function can set an existing string-style
variable to a new string value, so that subsequent LAMMPS commands can
access the variable.

The lammps_get_thermo() function returns the current value of a thermo
keyword as a double precision value.

The lammps_get_natoms() function returns the total number of atoms in
the system and can be used by the caller to allocate space for the
lammps_gather_atoms() and lammps_scatter_atoms() functions.  The
gather function collects peratom info of the requested type (atom
coords, types, forces, etc) from all processors, orders them by atom
ID, and returns a full list to each calling processor.  The scatter
function does the inverse.  It distributes the same peratom values,
passed by the caller, to each atom owned by individual processors.
Both methods are thus a means to extract or assign (overwrite) any
peratom quantities within LAMMPS.  See the extract() method in the
src/atom.cpp file for a list of valid per-atom properties.  New names
could easily be added if the property you want is not listed.
A special treatment is applied for accessing image flags via the
"image" property. Image flags are stored in a packed format with all
three image flags stored in a single integer. When signaling to access
the image flags as 3 individual values per atom instead of 1, the data
is transparently packed or unpacked by the library interface.

The lammps_create_atoms() function takes a list of N atoms as input
with atom types and coords (required), an optionally atom IDs and
velocities and image flags.  It uses the coords of each atom to assign
it as a new atom to the processor that owns it.  This function is
useful to add atoms to a simulation or (in tandem with
lammps_reset_box()) to restore a previously extracted and saved state
of a simulation.  Additional properties for the new atoms can then be
assigned via the lammps_scatter_atoms() or lammps_extract_atom()
functions.

The examples/COUPLE and python directories have example C++ and C and
Python codes which show how a driver code can link to LAMMPS as a
library, run LAMMPS on a subset of processors, grab data from LAMMPS,
change it, and put it back into LAMMPS.

NOTE: You can write code for additional functions as needed to define
how your code talks to LAMMPS and add them to src/library.cpp and
src/library.h, as well as to the "Python
interface"_Section_python.html.  The added functions can access or
change any LAMMPS data you wish.

:line

6.20 Calculating thermal conductivity :link(howto_20),h4

The thermal conductivity kappa of a material can be measured in at
least 4 ways using various options in LAMMPS.  See the examples/KAPPA
directory for scripts that implement the 4 methods discussed here for
a simple Lennard-Jones fluid model.  Also, see "this
section"_Section_howto.html#howto_21 of the manual for an analogous
discussion for viscosity.

The thermal conductivity tensor kappa is a measure of the propensity
of a material to transmit heat energy in a diffusive manner as given
by Fourier's law

J = -kappa grad(T)

where J is the heat flux in units of energy per area per time and
grad(T) is the spatial gradient of temperature.  The thermal
conductivity thus has units of energy per distance per time per degree
K and is often approximated as an isotropic quantity, i.e. as a
scalar.

The first method is to setup two thermostatted regions at opposite
ends of a simulation box, or one in the middle and one at the end of a
periodic box.  By holding the two regions at different temperatures
with a "thermostatting fix"_Section_howto.html#howto_13, the energy
added to the hot region should equal the energy subtracted from the
cold region and be proportional to the heat flux moving between the
regions.  See the papers by "Ikeshoji and Hafskjold"_#howto-Ikeshoji
and "Wirnsberger et al"_#howto-Wirnsberger for details of this idea.
Note that thermostatting fixes such as "fix nvt"_fix_nh.html, "fix
langevin"_fix_langevin.html, and "fix
temp/rescale"_fix_temp_rescale.html store the cumulative energy they
add/subtract.

Alternatively, as a second method, the "fix heat"_fix_heat.html or
"fix ehex"_fix_ehex.html commands can be used in place of thermostats
on each of two regions to add/subtract specified amounts of energy to
both regions.  In both cases, the resulting temperatures of the two
regions can be monitored with the "compute temp/region" command and
the temperature profile of the intermediate region can be monitored
with the "fix ave/chunk"_fix_ave_chunk.html and "compute
ke/atom"_compute_ke_atom.html commands.

The third method is to perform a reverse non-equilibrium MD simulation
using the "fix thermal/conductivity"_fix_thermal_conductivity.html
command which implements the rNEMD algorithm of Muller-Plathe.
Kinetic energy is swapped between atoms in two different layers of the
simulation box.  This induces a temperature gradient between the two
layers which can be monitored with the "fix
ave/chunk"_fix_ave_chunk.html and "compute
ke/atom"_compute_ke_atom.html commands.  The fix tallies the
cumulative energy transfer that it performs.  See the "fix
thermal/conductivity"_fix_thermal_conductivity.html command for
details.

The fourth method is based on the Green-Kubo (GK) formula which
relates the ensemble average of the auto-correlation of the heat flux
to kappa.  The heat flux can be calculated from the fluctuations of
per-atom potential and kinetic energies and per-atom stress tensor in
a steady-state equilibrated simulation.  This is in contrast to the
two preceding non-equilibrium methods, where energy flows continuously
between hot and cold regions of the simulation box.

The "compute heat/flux"_compute_heat_flux.html command can calculate
the needed heat flux and describes how to implement the Green_Kubo
formalism using additional LAMMPS commands, such as the "fix
ave/correlate"_fix_ave_correlate.html command to calculate the needed
auto-correlation.  See the doc page for the "compute
heat/flux"_compute_heat_flux.html command for an example input script
that calculates the thermal conductivity of solid Ar via the GK
formalism.

:line

6.21 Calculating viscosity :link(howto_21),h4

The shear viscosity eta of a fluid can be measured in at least 5 ways
using various options in LAMMPS.  See the examples/VISCOSITY directory
for scripts that implement the 5 methods discussed here for a simple
Lennard-Jones fluid model.  Also, see "this
section"_Section_howto.html#howto_20 of the manual for an analogous
discussion for thermal conductivity.

Eta is a measure of the propensity of a fluid to transmit momentum in
a direction perpendicular to the direction of velocity or momentum
flow.  Alternatively it is the resistance the fluid has to being
sheared.  It is given by

J = -eta grad(Vstream)

where J is the momentum flux in units of momentum per area per time.
and grad(Vstream) is the spatial gradient of the velocity of the fluid
moving in another direction, normal to the area through which the
momentum flows.  Viscosity thus has units of pressure-time.

The first method is to perform a non-equilibrium MD (NEMD) simulation
by shearing the simulation box via the "fix deform"_fix_deform.html
command, and using the "fix nvt/sllod"_fix_nvt_sllod.html command to
thermostat the fluid via the SLLOD equations of motion.
Alternatively, as a second method, one or more moving walls can be
used to shear the fluid in between them, again with some kind of
thermostat that modifies only the thermal (non-shearing) components of
velocity to prevent the fluid from heating up.

In both cases, the velocity profile setup in the fluid by this
procedure can be monitored by the "fix
ave/chunk"_fix_ave_chunk.html command, which determines
grad(Vstream) in the equation above.  E.g. the derivative in the
y-direction of the Vx component of fluid motion or grad(Vstream) =
dVx/dy.  The Pxy off-diagonal component of the pressure or stress
tensor, as calculated by the "compute pressure"_compute_pressure.html
command, can also be monitored, which is the J term in the equation
above.  See "this section"_Section_howto.html#howto_13 of the manual
for details on NEMD simulations.

The third method is to perform a reverse non-equilibrium MD simulation
using the "fix viscosity"_fix_viscosity.html command which implements
the rNEMD algorithm of Muller-Plathe.  Momentum in one dimension is
swapped between atoms in two different layers of the simulation box in
a different dimension.  This induces a velocity gradient which can be
monitored with the "fix ave/chunk"_fix_ave_chunk.html command.
The fix tallies the cumulative momentum transfer that it performs.
See the "fix viscosity"_fix_viscosity.html command for details.

The fourth method is based on the Green-Kubo (GK) formula which
relates the ensemble average of the auto-correlation of the
stress/pressure tensor to eta.  This can be done in a fully
equilibrated simulation which is in contrast to the two preceding
non-equilibrium methods, where momentum flows continuously through the
simulation box.

Here is an example input script that calculates the viscosity of
liquid Ar via the GK formalism:

# Sample LAMMPS input script for viscosity of liquid Ar :pre

units       real
variable    T equal 86.4956
variable    V equal vol
variable    dt equal 4.0
variable    p equal 400     # correlation length
variable    s equal 5       # sample interval
variable    d equal $p*$s   # dump interval :pre

# convert from LAMMPS real units to SI :pre

variable    kB equal 1.3806504e-23    # \[J/K/] Boltzmann
variable    atm2Pa equal 101325.0
variable    A2m equal 1.0e-10
variable    fs2s equal 1.0e-15
variable    convert equal $\{atm2Pa\}*$\{atm2Pa\}*$\{fs2s\}*$\{A2m\}*$\{A2m\}*$\{A2m\} :pre

# setup problem :pre

dimension    3
boundary     p p p
lattice      fcc 5.376 orient x 1 0 0 orient y 0 1 0 orient z 0 0 1
region       box block 0 4 0 4 0 4
create_box   1 box
create_atoms 1 box
mass         1 39.948
pair_style   lj/cut 13.0
pair_coeff   * * 0.2381 3.405
timestep     $\{dt\}
thermo       $d :pre

# equilibration and thermalization :pre

velocity     all create $T 102486 mom yes rot yes dist gaussian
fix          NVT all nvt temp $T $T 10 drag 0.2
run          8000 :pre

# viscosity calculation, switch to NVE if desired :pre

#unfix       NVT
#fix         NVE all nve :pre

reset_timestep 0
variable     pxy equal pxy
variable     pxz equal pxz
variable     pyz equal pyz
fix          SS all ave/correlate $s $p $d &
             v_pxy v_pxz v_pyz type auto file S0St.dat ave running
variable     scale equal $\{convert\}/($\{kB\}*$T)*$V*$s*$\{dt\}
variable     v11 equal trap(f_SS\[3\])*$\{scale\}
variable     v22 equal trap(f_SS\[4\])*$\{scale\}
variable     v33 equal trap(f_SS\[5\])*$\{scale\}
thermo_style custom step temp press v_pxy v_pxz v_pyz v_v11 v_v22 v_v33
run          100000
variable     v equal (v_v11+v_v22+v_v33)/3.0
variable     ndens equal count(all)/vol
print        "average viscosity: $v \[Pa.s\] @ $T K, $\{ndens\} /A^3" :pre

The fifth method is related to the above Green-Kubo method,
but uses the Einstein formulation, analogous to the Einstein
mean-square-displacement formulation for self-diffusivity. The
time-integrated momentum fluxes play the role of Cartesian
coordinates, whose mean-square displacement increases linearly
with time at sufficiently long times.

:line

6.22 Calculating a diffusion coefficient :link(howto_22),h4

The diffusion coefficient D of a material can be measured in at least
2 ways using various options in LAMMPS.  See the examples/DIFFUSE
directory for scripts that implement the 2 methods discussed here for
a simple Lennard-Jones fluid model.

The first method is to measure the mean-squared displacement (MSD) of
the system, via the "compute msd"_compute_msd.html command.  The slope
of the MSD versus time is proportional to the diffusion coefficient.
The instantaneous MSD values can be accumulated in a vector via the
"fix vector"_fix_vector.html command, and a line fit to the vector to
compute its slope via the "variable slope"_variable.html function, and
thus extract D.

The second method is to measure the velocity auto-correlation function
(VACF) of the system, via the "compute vacf"_compute_vacf.html
command.  The time-integral of the VACF is proportional to the
diffusion coefficient.  The instantaneous VACF values can be
accumulated in a vector via the "fix vector"_fix_vector.html command,
and time integrated via the "variable trap"_variable.html function,
and thus extract D.

:line

6.23 Using chunks to calculate system properties :link(howto_23),h4

In LAMMS, "chunks" are collections of atoms, as defined by the
"compute chunk/atom"_compute_chunk_atom.html command, which assigns
each atom to a chunk ID (or to no chunk at all).  The number of chunks
and the assignment of chunk IDs to atoms can be static or change over
time.  Examples of "chunks" are molecules or spatial bins or atoms
with similar values (e.g. coordination number or potential energy).

The per-atom chunk IDs can be used as input to two other kinds of
commands, to calculate various properties of a system:

"fix ave/chunk"_fix_ave_chunk.html
any of the "compute */chunk"_compute.html commands :ul

Here, each of the 3 kinds of chunk-related commands is briefly
overviewed.  Then some examples are given of how to compute different
properties with chunk commands.

Compute chunk/atom command: :h5

This compute can assign atoms to chunks of various styles.  Only atoms
in the specified group and optional specified region are assigned to a
chunk.  Here are some possible chunk definitions:

atoms in same molecule | chunk ID = molecule ID |
atoms of same atom type | chunk ID = atom type |
all atoms with same atom property (charge, radius, etc) | chunk ID = output of compute property/atom |
atoms in same cluster | chunk ID = output of "compute cluster/atom"_compute_cluster_atom.html command |
atoms in same spatial bin | chunk ID = bin ID |
atoms in same rigid body | chunk ID = molecule ID used to define rigid bodies |
atoms with similar potential energy | chunk ID = output of "compute pe/atom"_compute_pe_atom.html |
atoms with same local defect structure | chunk ID = output of "compute centro/atom"_compute_centro_atom.html or "compute coord/atom"_compute_coord_atom.html command :tb(s=|,c=2)

Note that chunk IDs are integer values, so for atom properties or
computes that produce a floating point value, they will be truncated
to an integer.  You could also use the compute in a variable that
scales the floating point value to spread it across multiple integers.

Spatial bins can be of various kinds, e.g. 1d bins = slabs, 2d bins =
pencils, 3d bins = boxes, spherical bins, cylindrical bins.

This compute also calculates the number of chunks {Nchunk}, which is
used by other commands to tally per-chunk data.  {Nchunk} can be a
static value or change over time (e.g. the number of clusters).  The
chunk ID for an individual atom can also be static (e.g. a molecule
ID), or dynamic (e.g. what spatial bin an atom is in as it moves).

Note that this compute allows the per-atom output of other
"computes"_compute.html, "fixes"_fix.html, and
"variables"_variable.html to be used to define chunk IDs for each
atom.  This means you can write your own compute or fix to output a
per-atom quantity to use as chunk ID.  See
"Section 10"_Section_modify.html of the documentation for how to
do this.  You can also define a "per-atom variable"_variable.html in
the input script that uses a formula to generate a chunk ID for each
atom.

Fix ave/chunk command: :h5

This fix takes the ID of a "compute
chunk/atom"_compute_chunk_atom.html command as input.  For each chunk,
it then sums one or more specified per-atom values over the atoms in
each chunk.  The per-atom values can be any atom property, such as
velocity, force, charge, potential energy, kinetic energy, stress,
etc.  Additional keywords are defined for per-chunk properties like
density and temperature.  More generally any per-atom value generated
by other "computes"_compute.html, "fixes"_fix.html, and "per-atom
variables"_variable.html, can be summed over atoms in each chunk.

Similar to other averaging fixes, this fix allows the summed per-chunk
values to be time-averaged in various ways, and output to a file.  The
fix produces a global array as output with one row of values per
chunk.

Compute */chunk commands: :h5

Currently the following computes operate on chunks of atoms to produce
per-chunk values.

"compute com/chunk"_compute_com_chunk.html
"compute gyration/chunk"_compute_gyration_chunk.html
"compute inertia/chunk"_compute_inertia_chunk.html
"compute msd/chunk"_compute_msd_chunk.html
"compute property/chunk"_compute_property_chunk.html
"compute temp/chunk"_compute_temp_chunk.html
"compute torque/chunk"_compute_vcm_chunk.html
"compute vcm/chunk"_compute_vcm_chunk.html :ul

They each take the ID of a "compute
chunk/atom"_compute_chunk_atom.html command as input.  As their names
indicate, they calculate the center-of-mass, radius of gyration,
moments of inertia, mean-squared displacement, temperature, torque,
and velocity of center-of-mass for each chunk of atoms.  The "compute
property/chunk"_compute_property_chunk.html command can tally the
count of atoms in each chunk and extract other per-chunk properties.

The reason these various calculations are not part of the "fix
ave/chunk command"_fix_ave_chunk.html, is that each requires a more
complicated operation than simply summing and averaging over per-atom
values in each chunk.  For example, many of them require calculation
of a center of mass, which requires summing mass*position over the
atoms and then dividing by summed mass.

All of these computes produce a global vector or global array as
output, wih one or more values per chunk.  They can be used
in various ways:

As input to the "fix ave/time"_fix_ave_time.html command, which can
write the values to a file and optionally time average them. :ulb,l

As input to the "fix ave/histo"_fix_ave_histo.html command to
histogram values across chunks.  E.g. a histogram of cluster sizes or
molecule diffusion rates. :l

As input to special functions of "equal-style
variables"_variable.html, like sum() and max().  E.g. to find the
largest cluster or fastest diffusing molecule. :l
:ule

Example calculations with chunks :h5

Here are examples using chunk commands to calculate various
properties:

(1) Average velocity in each of 1000 2d spatial bins:

compute cc1 all chunk/atom bin/2d x 0.0 0.1 y lower 0.01 units reduced
fix 1 all ave/chunk 100 10 1000 cc1 vx vy file tmp.out :pre

(2) Temperature in each spatial bin, after subtracting a flow
velocity:

compute cc1 all chunk/atom bin/2d x 0.0 0.1 y lower 0.1 units reduced
compute vbias all temp/profile 1 0 0 y 10
fix 1 all ave/chunk 100 10 1000 cc1 temp bias vbias file tmp.out :pre

(3) Center of mass of each molecule:

compute cc1 all chunk/atom molecule
compute myChunk all com/chunk cc1
fix 1 all ave/time 100 1 100 c_myChunk\[*\] file tmp.out mode vector :pre

(4) Total force on each molecule and ave/max across all molecules:

compute cc1 all chunk/atom molecule
fix 1 all ave/chunk 1000 1 1000 cc1 fx fy fz file tmp.out
variable xave equal ave(f_1\[2\])
variable xmax equal max(f_1\[2\])
thermo 1000
thermo_style custom step temp v_xave v_xmax :pre

(5) Histogram of cluster sizes:

compute cluster all cluster/atom 1.0
compute cc1 all chunk/atom c_cluster compress yes
compute size all property/chunk cc1 count
fix 1 all ave/histo 100 1 100 0 20 20 c_size mode vector ave running beyond ignore file tmp.histo :pre

:line

6.24 Setting parameters for the "kspace_style pppm/disp"_kspace_style.html command :link(howto_24),h4

The PPPM method computes interactions by splitting the pair potential
into two parts, one of which is computed in a normal pairwise fashion,
the so-called real-space part, and one of which is computed using the
Fourier transform, the so called reciprocal-space or kspace part.  For
both parts, the potential is not computed exactly but is approximated.
Thus, there is an error in both parts of the computation, the
real-space and the kspace error. The just mentioned facts are true
both for the PPPM for Coulomb as well as dispersion interactions. The
deciding difference - and also the reason why the parameters for
pppm/disp have to be selected with more care - is the impact of the
errors on the results: The kspace error of the PPPM for Coulomb and
dispersion interaction and the real-space error of the PPPM for
Coulomb interaction have the character of noise. In contrast, the
real-space error of the PPPM for dispersion has a clear physical
interpretation: the underprediction of cohesion. As a consequence, the
real-space error has a much stronger effect than the kspace error on
simulation results for pppm/disp.  Parameters must thus be chosen in a
way that this error is much smaller than the kspace error.

When using pppm/disp and not making any specifications on the PPPM
parameters via the kspace modify command, parameters will be tuned
such that the real-space error and the kspace error are equal.  This
will result in simulations that are either inaccurate or slow, both of
which is not desirable. For selecting parameters for the pppm/disp
that provide fast and accurate simulations, there are two approaches,
which both have their up- and downsides.

The first approach is to set desired real-space an kspace accuracies
via the {kspace_modify force/disp/real} and {kspace_modify
force/disp/kspace} commands. Note that the accuracies have to be
specified in force units and are thus dependent on the chosen unit
settings. For real units, 0.0001 and 0.002 seem to provide reasonable
accurate and efficient computations for the real-space and kspace
accuracies.  0.002 and 0.05 work well for most systems using lj
units. PPPM parameters will be generated based on the desired
accuracies. The upside of this approach is that it usually provides a
good set of parameters and will work for both the {kspace_modify diff
ad} and {kspace_modify diff ik} options.  The downside of the method
is that setting the PPPM parameters will take some time during the
initialization of the simulation.

The second approach is to set the parameters for the pppm/disp
explicitly using the {kspace_modify mesh/disp}, {kspace_modify
order/disp}, and {kspace_modify gewald/disp} commands. This approach
requires a more experienced user who understands well the impact of
the choice of parameters on the simulation accuracy and
performance. This approach provides a fast initialization of the
simulation. However, it is sensitive to errors: A combination of
parameters that will perform well for one system might result in
far-from-optimal conditions for other simulations. For example,
parameters that provide accurate and fast computations for
all-atomistic force fields can provide insufficient accuracy or
united-atomistic force fields (which is related to that the latter
typically have larger dispersion coefficients).

To avoid inaccurate or inefficient simulations, the pppm/disp stops
simulations with an error message if no action is taken to control the
PPPM parameters. If the automatic parameter generation is desired and
real-space and kspace accuracies are desired to be equal, this error
message can be suppressed using the {kspace_modify disp/auto yes}
command.

A reasonable approach that combines the upsides of both methods is to
make the first run using the {kspace_modify force/disp/real} and
{kspace_modify force/disp/kspace} commands, write down the PPPM
parameters from the outut, and specify these parameters using the
second approach in subsequent runs (which have the same composition,
force field, and approximately the same volume).

Concerning the performance of the pppm/disp there are two more things
to consider. The first is that when using the pppm/disp, the cutoff
parameter does no longer affect the accuracy of the simulation
(subject to that gewald/disp is adjusted when changing the cutoff).
The performance can thus be increased by examining different values
for the cutoff parameter. A lower bound for the cutoff is only set by
the truncation error of the repulsive term of pair potentials.

The second is that the mixing rule of the pair style has an impact on
the computation time when using the pppm/disp. Fastest computations
are achieved when using the geometric mixing rule. Using the
arithmetic mixing rule substantially increases the computational cost.
The computational overhead can be reduced using the {kspace_modify
mix/disp geom} and {kspace_modify splittol} commands. The first
command simply enforces geometric mixing of the dispersion
coefficients in kspace computations.  This introduces some error in
the computations but will also significantly speed-up the
simulations. The second keyword sets the accuracy with which the
dispersion coefficients are approximated using a matrix factorization
approach.  This may result in better accuracy then using the first
command, but will usually also not provide an equally good increase of
efficiency.

Finally, pppm/disp can also be used when no mixing rules apply.
This can be achieved using the {kspace_modify mix/disp none} command.
Note that the code does not check automatically whether any mixing
rule is fulfilled. If mixing rules do not apply, the user will have
to specify this command explicitly.

:line

6.25 Polarizable models :link(howto_25),h4

In polarizable force fields the charge distributions in molecules and
materials respond to their electrostatic environments. Polarizable
systems can be simulated in LAMMPS using three methods:

the fluctuating charge method, implemented in the "QEQ"_fix_qeq.html
package, :ulb,l
the adiabatic core-shell method, implemented in the
"CORESHELL"_#howto_26 package, :l
the thermalized Drude dipole method, implemented in the
"USER-DRUDE"_#howto_27 package. :l
:ule

The fluctuating charge method calculates instantaneous charges on
interacting atoms based on the electronegativity equalization
principle. It is implemented in the "fix qeq"_fix_qeq.html which is
available in several variants. It is a relatively efficient technique
since no additional particles are introduced. This method allows for
charge transfer between molecules or atom groups. However, because the
charges are located at the interaction sites, off-plane components of
polarization cannot be represented in planar molecules or atom groups.

The two other methods share the same basic idea: polarizable atoms are
split into one core atom and one satellite particle (called shell or
Drude particle) attached to it by a harmonic spring.  Both atoms bear
a charge and they represent collectively an induced electric dipole.
These techniques are computationally more expensive than the QEq
method because of additional particles and bonds. These two
charge-on-spring methods differ in certain features, with the
core-shell model being normally used for ionic/crystalline materials,
whereas the so-called Drude model is normally used for molecular
systems and fluid states.

The core-shell model is applicable to crystalline materials where the
high symmetry around each site leads to stable trajectories of the
core-shell pairs. However, bonded atoms in molecules can be so close
that a core would interact too strongly or even capture the Drude
particle of a neighbor. The Drude dipole model is relatively more
complex in order to remediate this and other issues. Specifically, the
Drude model includes specific thermostating of the core-Drude pairs
and short-range damping of the induced dipoles.

The three polarization methods can be implemented through a
self-consistent calculation of charges or induced dipoles at each
timestep. In the fluctuating charge scheme this is done by the matrix
inversion method in "fix qeq/point"_fix_qeq.html, but for core-shell
or Drude-dipoles the relaxed-dipoles technique would require an slow
iterative procedure. These self-consistent solutions yield accurate
trajectories since the additional degrees of freedom representing
polarization are massless.  An alternative is to attribute a mass to
the additional degrees of freedom and perform time integration using
an extended Lagrangian technique. For the fluctuating charge scheme
this is done by "fix qeq/dynamic"_fix_qeq.html, and for the
charge-on-spring models by the methods outlined in the next two
sections. The assignment of masses to the additional degrees of
freedom can lead to unphysical trajectories if care is not exerted in
choosing the parameters of the polarizable models and the simulation
conditions.

In the core-shell model the vibration of the shells is kept faster
than the ionic vibrations to mimic the fast response of the
polarizable electrons.  But in molecular systems thermalizing the
core-Drude pairs at temperatures comparable to the rest of the
simulation leads to several problems (kinetic energy transfer, too
short a timestep, etc.) In order to avoid these problems the relative
motion of the Drude particles with respect to their cores is kept
"cold" so the vibration of the core-Drude pairs is very slow,
approaching the self-consistent regime.  In both models the
temperature is regulated using the velocities of the center of mass of
core+shell (or Drude) pairs, but in the Drude model the actual
relative core-Drude particle motion is thermostated separately as
well.

:line

6.26 Adiabatic core/shell model :link(howto_26),h4

The adiabatic core-shell model by "Mitchell and
Fincham"_#MitchellFincham is a simple method for adding
polarizability to a system.  In order to mimic the electron shell of
an ion, a satellite particle is attached to it. This way the ions are
split into a core and a shell where the latter is meant to react to
the electrostatic environment inducing polarizability.

Technically, shells are attached to the cores by a spring force f =
k*r where k is a parametrized spring constant and r is the distance
between the core and the shell. The charges of the core and the shell
add up to the ion charge, thus q(ion) = q(core) + q(shell). This
setup introduces the ion polarizability (alpha) given by
alpha = q(shell)^2 / k. In a
similar fashion the mass of the ion is distributed on the core and the
shell with the core having the larger mass.

To run this model in LAMMPS, "atom_style"_atom_style.html {full} can
be used since atom charge and bonds are needed.  Each kind of
core/shell pair requires two atom types and a bond type.  The core and
shell of a core/shell pair should be bonded to each other with a
harmonic bond that provides the spring force. For example, a data file
for NaCl, as found in examples/coreshell, has this format:

432   atoms  # core and shell atoms
216   bonds  # number of core/shell springs :pre

4     atom types  # 2 cores and 2 shells for Na and Cl
2     bond types :pre

0.0 24.09597 xlo xhi
0.0 24.09597 ylo yhi
0.0 24.09597 zlo zhi :pre

Masses       # core/shell mass ratio = 0.1 :pre

1 20.690784  # Na core
2 31.90500   # Cl core
3 2.298976   # Na shell
4 3.54500    # Cl shell :pre

Atoms :pre

1    1    2   1.5005    0.00000000   0.00000000   0.00000000 # core of core/shell pair 1
2    1    4  -2.5005    0.00000000   0.00000000   0.00000000 # shell of core/shell pair 1
3    2    1   1.5056    4.01599500   4.01599500   4.01599500 # core of core/shell pair 2
4    2    3  -0.5056    4.01599500   4.01599500   4.01599500 # shell of core/shell pair 2
(...) :pre

Bonds   # Bond topology for spring forces :pre

1     2     1     2   # spring for core/shell pair 1
2     2     3     4   # spring for core/shell pair 2
(...) :pre

Non-Coulombic (e.g. Lennard-Jones) pairwise interactions are only
defined between the shells.  Coulombic interactions are defined
between all cores and shells.  If desired, additional bonds can be
specified between cores.

The "special_bonds"_special_bonds.html command should be used to
turn-off the Coulombic interaction within core/shell pairs, since that
interaction is set by the bond spring.  This is done using the
"special_bonds"_special_bonds.html command with a 1-2 weight = 0.0,
which is the default value.  It needs to be considered whether one has
to adjust the "special_bonds"_special_bonds.html weighting according
to the molecular topology since the interactions of the shells are
bypassed over an extra bond.

Note that this core/shell implementation does not require all ions to
be polarized.  One can mix core/shell pairs and ions without a
satellite particle if desired.

Since the core/shell model permits distances of r = 0.0 between the
core and shell, a pair style with a "cs" suffix needs to be used to
implement a valid long-range Coulombic correction.  Several such pair
styles are provided in the CORESHELL package.  See "this doc
page"_pair_cs.html for details.  All of the core/shell enabled pair
styles require the use of a long-range Coulombic solver, as specified
by the "kspace_style"_kspace_style.html command.  Either the PPPM or
Ewald solvers can be used.

For the NaCL example problem, these pair style and bond style settings
are used:

pair_style      born/coul/long/cs 20.0 20.0
pair_coeff      * *      0.0 1.000   0.00  0.00   0.00
pair_coeff      3 3    487.0 0.23768 0.00  1.05   0.50 #Na-Na
pair_coeff      3 4 145134.0 0.23768 0.00  6.99   8.70 #Na-Cl
pair_coeff      4 4 405774.0 0.23768 0.00 72.40 145.40 #Cl-Cl :pre

bond_style      harmonic
bond_coeff      1 63.014 0.0
bond_coeff      2 25.724 0.0 :pre

When running dynamics with the adiabatic core/shell model, the
following issues should be considered.  The relative motion of
the core and shell particles corresponds to the polarization,
hereby an instantaneous relaxation of the shells is approximated
and a fast core/shell spring frequency ensures a nearly constant
internal kinetic energy during the simulation.
Thermostats can alter this polarization behaviour, by scaling the
internal kinetic energy, meaning the shell will not react freely to
its electrostatic environment.
Therefore it is typically desirable to decouple the relative motion of
the core/shell pair, which is an imaginary degree of freedom, from the
real physical system.  To do that, the "compute
temp/cs"_compute_temp_cs.html command can be used, in conjunction with
any of the thermostat fixes, such as "fix nvt"_fix_nh.html or "fix
langevin"_fix_langevin.  This compute uses the center-of-mass velocity
of the core/shell pairs to calculate a temperature, and insures that
velocity is what is rescaled for thermostatting purposes.  This
compute also works for a system with both core/shell pairs and
non-polarized ions (ions without an attached satellite particle).  The
"compute temp/cs"_compute_temp_cs.html command requires input of two
groups, one for the core atoms, another for the shell atoms.
Non-polarized ions which might also be included in the treated system
should not be included into either of these groups, they are taken
into account by the {group-ID} (2nd argument) of the compute.  The
groups can be defined using the "group {type}"_group.html command.
Note that to perform thermostatting using this definition of
temperature, the "fix modify temp"_fix_modify.html command should be
used to assign the compute to the thermostat fix.  Likewise the
"thermo_modify temp"_thermo_modify.html command can be used to make
this temperature be output for the overall system.

For the NaCl example, this can be done as follows:

group cores type 1 2
group shells type 3 4
compute CSequ all temp/cs cores shells
fix thermoberendsen all temp/berendsen 1427 1427 0.4    # thermostat for the true physical system
fix thermostatequ all nve                               # integrator as needed for the berendsen thermostat
fix_modify thermoberendsen temp CSequ
thermo_modify temp CSequ                                # output of center-of-mass derived temperature :pre

The pressure for the core/shell system is computed via the regular
LAMMPS convention by "treating the cores and shells as individual
particles"_#MitchellFincham2. For the thermo output of the pressure
as well as for the application of a barostat, it is necessary to
use an additional "pressure"_compute_pressure compute based on the
default "temperature"_compute_temp and specifying it as a second
argument in "fix modify"_fix_modify.html and
"thermo_modify"_thermo_modify.html resulting in:

(...)
compute CSequ all temp/cs cores shells
compute thermo_press_lmp all pressure thermo_temp       # pressure for individual particles
thermo_modify temp CSequ press thermo_press_lmp         # modify thermo to regular pressure
fix press_bar all npt temp 300 300 0.04 iso 0 0 0.4
fix_modify press_bar temp CSequ press thermo_press_lmp  # pressure modification for correct kinetic scalar :pre

If "compute temp/cs"_compute_temp_cs.html is used, the decoupled
relative motion of the core and the shell should in theory be
stable.  However numerical fluctuation can introduce a small
momentum to the system, which is noticable over long trajectories.
Therefore it is recommendable to use the "fix
momentum"_fix_momentum.html command in combination with "compute
temp/cs"_compute_temp_cs.html when equilibrating the system to
prevent any drift.

When initializing the velocities of a system with core/shell pairs, it
is also desirable to not introduce energy into the relative motion of
the core/shell particles, but only assign a center-of-mass velocity to
the pairs.  This can be done by using the {bias} keyword of the
"velocity create"_velocity.html command and assigning the "compute
temp/cs"_compute_temp_cs.html command to the {temp} keyword of the
"velocity"_velocity.html command, e.g.

velocity all create 1427 134 bias yes temp CSequ
velocity all scale 1427 temp CSequ :pre

To maintain the correct polarizability of the core/shell pairs, the
kinetic energy of the internal motion shall remain nearly constant.
Therefore the choice of spring force and mass ratio need to ensure
much faster relative motion of the 2 atoms within the core/shell pair
than their center-of-mass velocity. This allows the shells to
effectively react instantaneously to the electrostatic environment and
limits energy transfer to or from the core/shell oscillators.
This fast movement also dictates the timestep that can be used.

The primary literature of the adiabatic core/shell model suggests that
the fast relative motion of the core/shell pairs only allows negligible
energy transfer to the environment.
The mentioned energy transfer will typically lead to a small drift
in total energy over time.  This internal energy can be monitored
using the "compute chunk/atom"_compute_chunk_atom.html and "compute
temp/chunk"_compute_temp_chunk.html commands.  The internal kinetic
energies of each core/shell pair can then be summed using the sum()
special function of the "variable"_variable.html command.  Or they can
be time/averaged and output using the "fix ave/time"_fix_ave_time.html
command.  To use these commands, each core/shell pair must be defined
as a "chunk".  If each core/shell pair is defined as its own molecule,
the molecule ID can be used to define the chunks.  If cores are bonded
to each other to form larger molecules, the chunks can be identified
by the "fix property/atom"_fix_property_atom.html via assigning a
core/shell ID to each atom using a special field in the data file read
by the "read_data"_read_data.html command.  This field can then be
accessed by the "compute property/atom"_compute_property_atom.html
command, to use as input to the "compute
chunk/atom"_compute_chunk_atom.html command to define the core/shell
pairs as chunks.

For example if core/shell pairs are the only molecules:

read_data NaCl_CS_x0.1_prop.data
compute prop all property/atom molecule
compute cs_chunk all chunk/atom c_prop
compute cstherm all temp/chunk cs_chunk temp internal com yes cdof 3.0     # note the chosen degrees of freedom for the core/shell pairs
fix ave_chunk all ave/time 10 1 10 c_cstherm file chunk.dump mode vector :pre

For example if core/shell pairs and other molecules are present:

fix csinfo all property/atom i_CSID                       # property/atom command
read_data NaCl_CS_x0.1_prop.data fix csinfo NULL CS-Info  # atom property added in the data-file
compute prop all property/atom i_CSID
(...) :pre

The additional section in the date file would be formatted like this:

CS-Info         # header of additional section :pre

1   1           # column 1 = atom ID, column 2 = core/shell ID
2   1
3   2
4   2
5   3
6   3
7   4
8   4
(...) :pre

:line

6.27 Drude induced dipoles :link(howto_27),h4

The thermalized Drude model, similarly to the "core-shell"_#howto_26
model, represents induced dipoles by a pair of charges (the core atom
and the Drude particle) connected by a harmonic spring. The Drude
model has a number of features aimed at its use in molecular systems
("Lamoureux and Roux"_#howto-Lamoureux):

Thermostating of the additional degrees of freedom associated with the
induced dipoles at very low temperature, in terms of the reduced
coordinates of the Drude particles with respect to their cores. This
makes the trajectory close to that of relaxed induced dipoles. :ulb,l

Consistent definition of 1-2 to 1-4 neighbors. A core-Drude particle
pair represents a single (polarizable) atom, so the special screening
factors in a covalent structure should be the same for the core and
the Drude particle.  Drude particles have to inherit the 1-2, 1-3, 1-4
special neighbor relations from their respective cores. :l

Stabilization of the interactions between induced dipoles. Drude
dipoles on covalently bonded atoms interact too strongly due to the
short distances, so an atom may capture the Drude particle of a
neighbor, or the induced dipoles within the same molecule may align
too much. To avoid this, damping at short range can be done by Thole
functions (for which there are physical grounds). This Thole damping
is applied to the point charges composing the induced dipole (the
charge of the Drude particle and the opposite charge on the core, not
to the total charge of the core atom). :l
:ule

A detailed tutorial covering the usage of Drude induced dipoles in
LAMMPS is "available here"_tutorial_drude.html.

As with the core-shell model, the cores and Drude particles should
appear in the data file as standard atoms. The same holds for the
springs between them, which are described by standard harmonic bonds.
The nature of the atoms (core, Drude particle or non-polarizable) is
specified via the "fix drude"_fix_drude.html command.  The special
list of neighbors is automatically refactored to account for the
equivalence of core and Drude particles as regards special 1-2 to 1-4
screening. It may be necessary to use the {extra/special/per/atom}
keyword of the "read_data"_read_data.html command. If using "fix
shake"_fix_shake.html, make sure no Drude particle is in this fix
group.

There are two ways to thermostat the Drude particles at a low
temperature: use either "fix langevin/drude"_fix_langevin_drude.html
for a Langevin thermostat, or "fix
drude/transform/*"_fix_drude_transform.html for a Nose-Hoover
thermostat. The former requires use of the command "comm_modify vel
yes"_comm_modify.html. The latter requires two separate integration
fixes like {nvt} or {npt}. The correct temperatures of the reduced
degrees of freedom can be calculated using the "compute
temp/drude"_compute_temp_drude.html. This requires also to use the
command {comm_modify vel yes}.

Short-range damping of the induced dipole interactions can be achieved
using Thole functions through the "pair style
thole"_pair_thole.html in "pair_style hybrid/overlay"_pair_hybrid.html
with a Coulomb pair style. It may be useful to use {coul/long/cs} or
similar from the CORESHELL package if the core and Drude particle come
too close, which can cause numerical issues.

:line
:line

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