.. index:: fix rigid
.. index:: fix rigid/omp
.. index:: fix rigid/nve
.. index:: fix rigid/nve/omp
.. index:: fix rigid/nvt
.. index:: fix rigid/nvt/omp
.. index:: fix rigid/npt
.. index:: fix rigid/npt/omp
.. index:: fix rigid/nph
.. index:: fix rigid/nph/omp
.. index:: fix rigid/small
.. index:: fix rigid/small/omp
.. index:: fix rigid/nve/small
.. index:: fix rigid/nvt/small
.. index:: fix rigid/npt/small
.. index:: fix rigid/nph/small

fix rigid command
=================

Accelerator Variants: *rigid/omp*

fix rigid/nve command
=====================

Accelerator Variants: *rigid/nve/omp*

fix rigid/nvt command
=====================

Accelerator Variants: *rigid/nvt/omp*

fix rigid/npt command
=====================

Accelerator Variants: *rigid/npt/omp*

fix rigid/nph command
=====================

Accelerator Variants: *rigid/nph/omp*

fix rigid/small command
=======================

Accelerator Variants: *rigid/small/omp*

fix rigid/nve/small command
===========================

fix rigid/nvt/small command
===========================

fix rigid/npt/small command
===========================

fix rigid/nph/small command
===========================

Syntax
""""""

.. code-block:: LAMMPS

   fix ID group-ID style bodystyle args keyword values ...

* ID, group-ID are documented in :doc:`fix <fix>` command
* style = *rigid* or *rigid/nve* or *rigid/nvt* or *rigid/npt* or *rigid/nph* or *rigid/small* or *rigid/nve/small* or *rigid/nvt/small* or *rigid/npt/small* or *rigid/nph/small*
* bodystyle = *single* or *molecule* or *group*

  .. parsed-literal::

       *single* args = none
       *molecule* args = none
       *custom* args = *i_propname* or *v_varname*
         i_propname = a custom integer vector defined via fix property/atom
         v_varname  = an atom-style or atomfile-style variable
       *group* args = N groupID1 groupID2 ...
         N = # of groups
         groupID1, groupID2, ... = list of N group IDs

* zero or more keyword/value pairs may be appended
* keyword = *langevin* or *reinit* or *temp* or *iso* or *aniso* or *x* or *y* or *z* or *couple* or *tparam* or *pchain* or *dilate* or *force* or *torque* or *infile* or *gravity*

  .. parsed-literal::

       *langevin* values = Tstart Tstop Tperiod seed
         Tstart,Tstop = desired temperature at start/stop of run (temperature units)
         Tdamp = temperature damping parameter (time units)
         seed = random number seed to use for white noise (positive integer)
       *reinit* value = *yes* or *no*
       *temp* values = Tstart Tstop Tdamp
         Tstart,Tstop = desired temperature at start/stop of run (temperature units)
         Tdamp = temperature damping parameter (time units)
       *iso* or *aniso* values = Pstart Pstop Pdamp
         Pstart,Pstop = scalar external pressure at start/end of run (pressure units)
         Pdamp = pressure damping parameter (time units)
       *x* or *y* or *z* values = Pstart Pstop Pdamp
         Pstart,Pstop = external stress tensor component at start/end of run (pressure units)
         Pdamp = stress damping parameter (time units)
       *couple* value = *none* or *xyz* or *xy* or *yz* or *xz*
       *tparam* values = Tchain Titer Torder
         Tchain = length of Nose/Hoover thermostat chain
         Titer = number of thermostat iterations performed
         Torder = 3 or 5 = Yoshida-Suzuki integration parameters
       *pchain* values = Pchain
         Pchain = length of the Nose/Hoover thermostat chain coupled with the barostat
       *dilate* value = dilate-group-ID
         dilate-group-ID = only dilate atoms in this group due to barostat volume changes
       *force* values = M xflag yflag zflag
         M = which rigid body from 1-Nbody (see asterisk form below)
         xflag,yflag,zflag = off/on if component of center-of-mass force is active
       *torque* values = M xflag yflag zflag
         M = which rigid body from 1-Nbody (see asterisk form below)
         xflag,yflag,zflag = off/on if component of center-of-mass torque is active
       *infile* filename
         filename = file with per-body values of mass, center-of-mass, moments of inertia
       *gravity* values = gravity-ID
         gravity-ID = ID of fix gravity command to add gravitational forces

..
    FIXME These don't seem to be included in the source code
       *mol* value = template-ID
         template-ID = ID of molecule template specified in a separate :doc:`molecule <molecule>` command

Examples
""""""""

.. code-block:: LAMMPS

   fix 1 clump rigid single reinit yes
   fix 1 clump rigid/small molecule
   fix 1 clump rigid single force 1 off off on langevin 1.0 1.0 1.0 428984
   fix 1 polychains rigid/nvt molecule temp 1.0 1.0 5.0 reinit no
   fix 1 polychains rigid molecule force 1*5 off off off force 6*10 off off on
   fix 1 polychains rigid/small molecule langevin 1.0 1.0 1.0 428984
   fix 2 fluid rigid group 3 clump1 clump2 clump3 torque * off off off
   fix 1 rods rigid/npt molecule temp 300.0 300.0 100.0 iso 0.5 0.5 10.0
   fix 1 particles rigid/npt molecule temp 1.0 1.0 5.0 x 0.5 0.5 1.0 z 0.5 0.5 1.0 couple xz
   fix 1 water rigid/nph molecule iso 0.5 0.5 1.0
   fix 1 particles rigid/npt/small molecule temp 1.0 1.0 1.0 iso 0.5 0.5 1.0

   variable bodyid atom 1.0*gmask(clump1)+2.0*gmask(clump2)+3.0*gmask(clump3)
   fix 1 clump rigid custom v_bodyid

   variable bodyid atomfile bodies.txt
   fix 1 clump rigid custom v_bodyid

   fix 0 all property/atom i_bodyid
   read_restart data.rigid fix 0 NULL Bodies
   fix 1 clump rigid/small custom i_bodyid

Description
"""""""""""

Treat one or more sets of atoms as independent rigid bodies.  This
means that each timestep the total force and torque on each rigid body
is computed as the sum of the forces and torques on its constituent
particles.  The coordinates, velocities, and orientations of the atoms
in each body are then updated so that the body moves and rotates as a
single entity.  This is implemented by creating internal data structures
for each rigid body and performing time integration on these data
structures.  Positions, velocities, and orientations of the constituent
particles are regenerated from the rigid body data structures in every
time step. This restricts which operations and fixes can be applied to
rigid bodies. See below for a detailed discussion.

Examples of large rigid bodies are a colloidal particle, or portions
of a biomolecule such as a protein.

Example of small rigid bodies are patchy nanoparticles, such as those
modeled in :ref:`this paper <Zhang1>` by Sharon Glotzer's group, clumps of
granular particles, lipid molecules consisting of one or more point
dipoles connected to other spheroids or ellipsoids, irregular
particles built from line segments (2d) or triangles (3d), and
coarse-grain models of nano or colloidal particles consisting of a
small number of constituent particles.  Note that the :doc:`fix shake <fix_shake>` command can also be used to rigidify small
molecules of 2, 3, or 4 atoms, e.g. water molecules.  That fix treats
the constituent atoms as point masses.

These fixes also update the positions and velocities of the atoms in
each rigid body via time integration, in the NVE, NVT, NPT, or NPH
ensemble, as described below.

There are two main variants of this fix, fix rigid and fix
rigid/small.  The NVE/NVT/NPT/NHT versions belong to one of the two
variants, as their style names indicate.

.. note::

   Not all of the *bodystyle* options and keyword/value options are
   available for both the *rigid* and *rigid/small* variants.  See
   details below.

The *rigid* styles are typically the best choice for a system with a
small number of large rigid bodies, each of which can extend across
the domain of many processors.  It operates by creating a single
global list of rigid bodies, which all processors contribute to.
MPI_Allreduce operations are performed each timestep to sum the
contributions from each processor to the force and torque on all the
bodies.  This operation will not scale well in parallel if large
numbers of rigid bodies are simulated.

The *rigid/small* styles are typically best for a system with a large
number of small rigid bodies.  Each body is assigned to the atom
closest to the geometrical center of the body.  The fix operates using
local lists of rigid bodies owned by each processor and information is
exchanged and summed via local communication between neighboring
processors when ghost atom info is accumulated.

.. note::

   To use the *rigid/small* styles the ghost atom cutoff must be
   large enough to span the distance between the atom that owns the body
   and every other atom in the body.  This distance value is printed out
   when the rigid bodies are defined.  If the
   :doc:`pair_style <pair_style>` cutoff plus neighbor skin does not span
   this distance, then you should use the :doc:`comm_modify cutoff <comm_modify>` command with a setting epsilon larger than
   the distance.

Which of the two variants is faster for a particular problem is hard
to predict.  The best way to decide is to perform a short test run.
Both variants should give identical numerical answers for short runs.
Long runs should give statistically similar results, but round-off
differences may accumulate to produce divergent trajectories.

.. note::

   You should not update the atoms in rigid bodies via other
   time-integration fixes (e.g. :doc:`fix nve <fix_nve>`, :doc:`fix nvt <fix_nh>`, :doc:`fix npt <fix_nh>`, :doc:`fix move <fix_move>`),
   or you will have conflicting updates to positions and velocities
   resulting in unphysical behavior in most cases. When performing a hybrid
   simulation with some atoms in rigid bodies, and some not, a separate
   time integration fix like :doc:`fix nve <fix_nve>` or :doc:`fix nvt <fix_nh>` should be used for the non-rigid particles.

.. note::

   These fixes are overkill if you simply want to hold a collection
   of atoms stationary or have them move with a constant velocity.  A
   simpler way to hold atoms stationary is to not include those atoms in
   your time integration fix.  E.g. use "fix 1 mobile nve" instead of
   "fix 1 all nve", where "mobile" is the group of atoms that you want to
   move.  You can move atoms with a constant velocity by assigning them
   an initial velocity (via the :doc:`velocity <velocity>` command),
   setting the force on them to 0.0 (via the :doc:`fix setforce <fix_setforce>` command), and integrating them as usual
   (e.g. via the :doc:`fix nve <fix_nve>` command).

.. warning::

   The aggregate properties of each rigid body are
   calculated at the start of a simulation run and are maintained in
   internal data structures. The properties include the position and
   velocity of the center-of-mass of the body, its moments of inertia, and
   its angular momentum.  This is done using the properties of the
   constituent atoms of the body at that point in time (or see the *infile*
   keyword option).  Thereafter, changing these properties of individual
   atoms in the body will have no effect on a rigid body's dynamics, unless
   they effect any computation of per-atom forces or torques. If the
   keyword *reinit* is set to *yes* (the default), the rigid body data
   structures will be recreated at the beginning of each *run* command;
   if the keyword *reinit* is set to *no*, the rigid body data structures
   will be built only at the very first *run* command and maintained for
   as long as the rigid fix is defined. For example, you might think you
   could displace the atoms in a body or add a large velocity to each atom
   in a body to make it move in a desired direction before a second run is
   performed, using the :doc:`set <set>` or
   :doc:`displace_atoms <displace_atoms>` or :doc:`velocity <velocity>`
   commands.  But these commands will not affect the internal attributes
   of the body unless *reinit* is set to *yes*\ . With *reinit* set to *no*
   (or using the *infile* option, which implies *reinit* *no*\ ) the position
   and velocity of individual atoms in the body will be reset when time
   integration starts again.

----------

Each rigid body must have two or more atoms.  An atom can belong to at
most one rigid body.  Which atoms are in which bodies can be defined
via several options.

.. note::

   With the *rigid/small* styles, which require that *bodystyle* be
   specified as *molecule* or *custom*, you can define a system that has
   no rigid bodies initially.  This is useful when you are using the
   *mol* keyword in conjunction with another fix that is adding rigid
   bodies on-the-fly as molecules, such as :doc:`fix deposit <fix_deposit>`
   or :doc:`fix pour <fix_pour>`.

For bodystyle *single* the entire fix group of atoms is treated as one
rigid body.  This option is only allowed for the *rigid* styles.

For bodystyle *molecule*, atoms are grouped into rigid bodies by their
respective molecule IDs: each set of atoms in the fix group with the
same molecule ID is treated as a different rigid body.  This option is
allowed for both the *rigid* and *rigid/small* styles.  Note that
atoms with a molecule ID = 0 will be treated as a single rigid body.
For a system with atomic solvent (typically this is atoms with
molecule ID = 0) surrounding rigid bodies, this may not be what you
want.  Thus you should be careful to use a fix group that only
includes atoms you want to be part of rigid bodies.

Bodystyle *custom* is similar to bodystyle *molecule* except that it
is more flexible in using other per-atom properties to define the sets
of atoms that form rigid bodies.  A custom per-atom integer vector
defined by the :doc:`fix property/atom <fix_property_atom>` command
can be used.  Or an :doc:`atom-style or atomfile-style variable
<variable>` can be used; the floating-point value produced by the
variable is rounded to an integer.  As with bodystyle *molecule*\ ,
each set of atoms in the fix groups with the same integer value is
treated as a different rigid body.  Since fix property/atom custom
vectors and atom-style variables produce values for all atoms, you
should be careful to use a fix group that only includes atoms you want
to be part of rigid bodies.

.. note::

   To compute the initial center-of-mass position and other
   properties of each rigid body, the image flags for each atom in the
   body are used to "unwrap" the atom coordinates.  Thus you must ensure
   that these image flags are consistent so that the unwrapping creates a
   valid rigid body (one where the atoms are close together),
   particularly if the atoms in a single rigid body straddle a periodic
   boundary.  This means the input data file or restart file must define
   the image flags for each atom consistently or that you have used the
   :doc:`set <set>` command to specify them correctly.  If a dimension is
   non-periodic then the image flag of each atom must be 0 in that
   dimension, else an error is generated.

The *force* and *torque* keywords discussed next are only allowed for
the *rigid* styles.

By default, each rigid body is acted on by other atoms which induce an
external force and torque on its center of mass, causing it to
translate and rotate.  Components of the external center-of-mass force
and torque can be turned off by the *force* and *torque* keywords.
This may be useful if you wish a body to rotate but not translate, or
vice versa, or if you wish it to rotate or translate continuously
unaffected by interactions with other particles.  Note that if you
expect a rigid body not to move or rotate by using these keywords, you
must ensure its initial center-of-mass translational or angular
velocity is 0.0.  Otherwise the initial translational or angular
momentum the body has will persist.

An xflag, yflag, or zflag set to *off* means turn off the component of
force of torque in that dimension.  A setting of *on* means turn on
the component, which is the default.  Which rigid body(s) the settings
apply to is determined by the first argument of the *force* and
*torque* keywords.  It can be an integer M from 1 to Nbody, where
Nbody is the number of rigid bodies defined.  A wild-card asterisk can
be used in place of, or in conjunction with, the M argument to set the
flags for multiple rigid bodies.  This takes the form "\*" or "\*n" or
"n\*" or "m\*n".  If N = the number of rigid bodies, then an asterisk
with no numeric values means all bodies from 1 to N.  A leading
asterisk means all bodies from 1 to n (inclusive).  A trailing
asterisk means all bodies from n to N (inclusive).  A middle asterisk
means all types from m to n (inclusive).  Note that you can use the
*force* or *torque* keywords as many times as you like.  If a
particular rigid body has its component flags set multiple times, the
settings from the final keyword are used.

.. note::

   For computational efficiency, you may wish to turn off pairwise
   and bond interactions within each rigid body, as they no longer
   contribute to the motion.  The :doc:`neigh_modify exclude <neigh_modify>` and :doc:`delete_bonds <delete_bonds>`
   commands are used to do this.  If the rigid bodies have strongly
   overlapping atoms, you may need to turn off these interactions to
   avoid numerical problems due to large equal/opposite intra-body forces
   swamping the contribution of small inter-body forces.

For computational efficiency, you should typically define one fix
rigid or fix rigid/small command which includes all the desired rigid
bodies.  LAMMPS will allow multiple rigid fixes to be defined, but it
is more expensive.

----------

The constituent particles within a rigid body can be point particles
(the default in LAMMPS) or finite-size particles, such as spheres or
ellipsoids or line segments or triangles.  See the :doc:`atom_style sphere and ellipsoid and line and tri <atom_style>` commands for more
details on these kinds of particles.  Finite-size particles contribute
differently to the moment of inertia of a rigid body than do point
particles.  Finite-size particles can also experience torque (e.g. due
to :doc:`frictional granular interactions <pair_gran>`) and have an
orientation.  These contributions are accounted for by these fixes.

Forces between particles within a body do not contribute to the
external force or torque on the body.  Thus for computational
efficiency, you may wish to turn off pairwise and bond interactions
between particles within each rigid body.  The :doc:`neigh_modify exclude <neigh_modify>` and :doc:`delete_bonds <delete_bonds>`
commands are used to do this.  For finite-size particles this also
means the particles can be highly overlapped when creating the rigid
body.

----------

The *rigid*, *rigid/nve*, *rigid/small*, and *rigid/small/nve* styles
perform constant NVE time integration.  They are referred to below as
the 4 NVE rigid styles.  The only difference is that the *rigid* and
*rigid/small* styles use an integration technique based on Richardson
iterations.  The *rigid/nve* and *rigid/small/nve* styles uses the
methods described in the paper by :ref:`Miller <Miller3>`, which are thought
to provide better energy conservation than an iterative approach.

The *rigid/nvt* and *rigid/nvt/small* styles performs constant NVT
integration using a Nose/Hoover thermostat with chains as described
originally in :ref:`(Hoover) <Hoover>` and :ref:`(Martyna) <Martyna2>`, which
thermostats both the translational and rotational degrees of freedom
of the rigid bodies.  They are referred to below as the 2 NVT rigid
styles.  The rigid-body algorithm used by *rigid/nvt* is described in
the paper by :ref:`Kamberaj <Kamberaj>`.

The *rigid/npt*, *rigid/nph*, *rigid/npt/small*, and *rigid/nph/small*
styles perform constant NPT or NPH integration using a Nose/Hoover
barostat with chains.  They are referred to below as the 4 NPT and NPH
rigid styles.  For the NPT case, the same Nose/Hoover thermostat is
also used as with *rigid/nvt* and *rigid/nvt/small*\ .

The barostat parameters are specified using one or more of the *iso*,
*aniso*, *x*, *y*, *z* and *couple* keywords.  These keywords give you
the ability to specify 3 diagonal components of the external stress
tensor, and to couple these components together so that the dimensions
they represent are varied together during a constant-pressure
simulation.  The effects of these keywords are similar to those
defined in :doc:`fix npt/nph <fix_nh>`

.. note::

   Currently the *rigid/npt*, *rigid/nph*, *rigid/npt/small*, and
   *rigid/nph/small* styles do not support triclinic (non-orthogonal)
   boxes.

The target pressures for each of the 6 components of the stress tensor
can be specified independently via the *x*, *y*, *z* keywords, which
correspond to the 3 simulation box dimensions.  For each component,
the external pressure or tensor component at each timestep is a ramped
value during the run from *Pstart* to *Pstop*\ . If a target pressure is
specified for a component, then the corresponding box dimension will
change during a simulation.  For example, if the *y* keyword is used,
the y-box length will change.  A box dimension will not change if that
component is not specified, although you have the option to change
that dimension via the :doc:`fix deform <fix_deform>` command.

For all barostat keywords, the *Pdamp* parameter operates like the
*Tdamp* parameter, determining the time scale on which pressure is
relaxed.  For example, a value of 10.0 means to relax the pressure in
a timespan of (roughly) 10 time units (e.g. :math:`\tau` or fs or ps
- see the :doc:`units <units>` command).

Regardless of what atoms are in the fix group (the only atoms which
are time integrated), a global pressure or stress tensor is computed
for all atoms.  Similarly, when the size of the simulation box is
changed, all atoms are re-scaled to new positions, unless the keyword
*dilate* is specified with a *dilate-group-ID* for a group that
represents a subset of the atoms.  This can be useful, for example, to
leave the coordinates of atoms in a solid substrate unchanged and
controlling the pressure of a surrounding fluid.  Another example is a
system consisting of rigid bodies and point particles where the
barostat is only coupled with the rigid bodies.  This option should be
used with care, since it can be unphysical to dilate some atoms and
not others, because it can introduce large, instantaneous
displacements between a pair of atoms (one dilated, one not) that are
far from the dilation origin.

The *couple* keyword allows two or three of the diagonal components of
the pressure tensor to be "coupled" together.  The value specified
with the keyword determines which are coupled.  For example, *xz*
means the *Pxx* and *Pzz* components of the stress tensor are coupled.
*Xyz* means all 3 diagonal components are coupled.  Coupling means two
things: the instantaneous stress will be computed as an average of the
corresponding diagonal components, and the coupled box dimensions will
be changed together in lockstep, meaning coupled dimensions will be
dilated or contracted by the same percentage every timestep.  The
*Pstart*, *Pstop*, *Pdamp* parameters for any coupled dimensions must
be identical.  *Couple xyz* can be used for a 2d simulation; the *z*
dimension is simply ignored.

The *iso* and *aniso* keywords are simply shortcuts that are
equivalent to specifying several other keywords together.

The keyword *iso* means couple all 3 diagonal components together when
pressure is computed (hydrostatic pressure), and dilate/contract the
dimensions together.  Using "iso Pstart Pstop Pdamp" is the same as
specifying these 4 keywords:

.. parsed-literal::

   x Pstart Pstop Pdamp
   y Pstart Pstop Pdamp
   z Pstart Pstop Pdamp
   couple xyz

The keyword *aniso* means *x*, *y*, and *z* dimensions are controlled
independently using the *Pxx*, *Pyy*, and *Pzz* components of the
stress tensor as the driving forces, and the specified scalar external
pressure.  Using "aniso Pstart Pstop Pdamp" is the same as specifying
these 4 keywords:

.. parsed-literal::

   x Pstart Pstop Pdamp
   y Pstart Pstop Pdamp
   z Pstart Pstop Pdamp
   couple none

----------

The keyword/value option pairs are used in the following ways.

The *reinit* keyword determines, whether the rigid body properties
are re-initialized between run commands. With the option *yes* (the
default) this is done, with the option *no* this is not done. Turning
off the re-initialization can be helpful to protect rigid bodies against
unphysical manipulations between runs or when properties cannot be
easily re-computed (e.g. when read from a file). When using the *infile*
keyword, the *reinit* option is automatically set to *no*\ .

The *langevin* and *temp* and *tparam* keywords perform thermostatting
of the rigid bodies, altering both their translational and rotational
degrees of freedom.  What is meant by "temperature" of a collection of
rigid bodies and how it can be monitored via the fix output is
discussed below.

The *langevin* keyword applies a Langevin thermostat to the constant
NVE time integration performed by any of the 4 NVE rigid styles:
*rigid*, *rigid/nve*, *rigid/small*, *rigid/small/nve*\ .  It cannot be
used with the 2 NVT rigid styles: *rigid/nvt*, *rigid/small/nvt*\ .  The
desired temperature at each timestep is a ramped value during the run
from *Tstart* to *Tstop*\ .  The *Tdamp* parameter is specified in time
units and determines how rapidly the temperature is relaxed.  For
example, a value of 100.0 means to relax the temperature in a timespan
of (roughly) 100 time units (:math:`\tau` or fs or ps - see the
:doc:`units <units>` command).  The random # *seed* must be a positive
integer.

The way that Langevin thermostatting operates is explained on the :doc:`fix langevin <fix_langevin>` doc page.  If you wish to simply viscously
damp the rotational motion without thermostatting, you can set
*Tstart* and *Tstop* to 0.0, which means only the viscous drag term in
the Langevin thermostat will be applied.  See the discussion on the
:doc:`fix viscous <fix_viscous>` page for details.

.. note::

   When the *langevin* keyword is used with fix rigid versus fix
   rigid/small, different dynamics will result for parallel runs.  This
   is because of the way random numbers are used in the two cases.  The
   dynamics for the two cases should be statistically similar, but will
   not be identical, even for a single timestep.

The *temp* and *tparam* keywords apply a Nose/Hoover thermostat to the
NVT time integration performed by the 2 NVT rigid styles.  They cannot
be used with the 4 NVE rigid styles.  The desired temperature at each
timestep is a ramped value during the run from *Tstart* to *Tstop*\ .
The *Tdamp* parameter is specified in time units and determines how
rapidly the temperature is relaxed.  For example, a value of 100.0
means to relax the temperature in a timespan of (roughly) 100 time
units (tau or fs or ps - see the :doc:`units <units>` command).

Nose/Hoover chains are used in conjunction with this thermostat.  The
*tparam* keyword can optionally be used to change the chain settings
used.  *Tchain* is the number of thermostats in the Nose Hoover chain.
This value, along with *Tdamp* can be varied to dampen undesirable
oscillations in temperature that can occur in a simulation.  As a rule
of thumb, increasing the chain length should lead to smaller
oscillations. The keyword *pchain* specifies the number of
thermostats in the chain thermostatting the barostat degrees of
freedom.

.. note::

   There are alternate ways to thermostat a system of rigid bodies.
   You can use :doc:`fix langevin <fix_langevin>` to treat the individual
   particles in the rigid bodies as effectively immersed in an implicit
   solvent, e.g. a Brownian dynamics model.  For hybrid systems with both
   rigid bodies and solvent particles, you can thermostat only the
   solvent particles that surround one or more rigid bodies by
   appropriate choice of groups in the compute and fix commands for
   temperature and thermostatting.  The solvent interactions with the
   rigid bodies should then effectively thermostat the rigid body
   temperature as well without use of the Langevin or Nose/Hoover options
   associated with the fix rigid commands.

----------

The *mol* keyword can only be used with the *rigid/small* styles.  It
must be used when other commands, such as :doc:`fix deposit <fix_deposit>` or :doc:`fix pour <fix_pour>`, add rigid
bodies on-the-fly during a simulation.  You specify a *template-ID*
previously defined using the :doc:`molecule <molecule>` command, which
reads a file that defines the molecule.  You must use the same
*template-ID* that the other fix which is adding rigid bodies uses.
The coordinates, atom types, atom diameters, center-of-mass, and
moments of inertia can be specified in the molecule file.  See the
:doc:`molecule <molecule>` command for details.  The only settings
required to be in this file are the coordinates and types of atoms in
the molecule, in which case the molecule command calculates the other
quantities itself.

Note that these other fixes create new rigid bodies, in addition to
those defined initially by this fix via the *bodystyle* setting.

Also note that when using the *mol* keyword, extra restart information
about all rigid bodies is written out whenever a restart file is
written out.  See the NOTE in the next section for details.

----------

The *infile* keyword allows a file of rigid body attributes to be read
in from a file, rather then having LAMMPS compute them.  There are 5
such attributes: the total mass of the rigid body, its center-of-mass
position, its 6 moments of inertia, its center-of-mass velocity, and
the 3 image flags of the center-of-mass position.  For rigid bodies
consisting of point particles or non-overlapping finite-size
particles, LAMMPS can compute these values accurately.

However, for rigid bodies consisting of finite-size particles which
overlap each other, LAMMPS will ignore the overlaps when computing
these 4 attributes, which means the dynamics of the bodies will be
incorrect.  The amount of error this induces depends on the amount of
overlap.  To avoid this issue, the values can be pre-computed
(e.g. using Monte Carlo integration).

The format of the file is as follows.  Note that the file does not
have to list attributes for every rigid body integrated by fix rigid.
Only bodies which the file specifies will have their computed
attributes overridden.  The file can contain initial blank lines or
comment lines starting with "#" which are ignored.  The first
non-blank, non-comment line should list N = the number of lines to
follow.  The N successive lines contain the following information:

.. parsed-literal::

   ID1 masstotal xcm ycm zcm ixx iyy izz ixy ixz iyz vxcm vycm vzcm lx ly lz ixcm iycm izcm
   ID2 masstotal xcm ycm zcm ixx iyy izz ixy ixz iyz vxcm vycm vzcm lx ly lz ixcm iycm izcm
   ...
   IDN masstotal xcm ycm zcm ixx iyy izz ixy ixz iyz vxcm vycm vzcm lx ly lz ixcm iycm izcm

The rigid body IDs are all positive integers.  For the *single*
bodystyle, only an ID of 1 can be used.  For the *group* bodystyle,
IDs from 1 to Ng can be used where Ng is the number of specified
groups.  For the *molecule* bodystyle, use the molecule ID for the
atoms in a specific rigid body as the rigid body ID.

The masstotal and center-of-mass coordinates (xcm,ycm,zcm) are
self-explanatory.  The center-of-mass should be consistent with what
is calculated for the position of the rigid body with all its atoms
unwrapped by their respective image flags.  If this produces a
center-of-mass that is outside the simulation box, LAMMPS wraps it
back into the box.

The 6 moments of inertia (ixx,iyy,izz,ixy,ixz,iyz) should be the
values consistent with the current orientation of the rigid body
around its center of mass.  The values are with respect to the
simulation box XYZ axes, not with respect to the principal axes of the
rigid body itself.  LAMMPS performs the latter calculation internally.

The (vxcm,vycm,vzcm) values are the velocity of the center of mass.
The (lx,ly,lz) values are the angular momentum of the body.  The
(vxcm,vycm,vzcm) and (lx,ly,lz) values can simply be set to 0 if you
wish the body to have no initial motion.

The (ixcm,iycm,izcm) values are the image flags of the center of mass
of the body.  For periodic dimensions, they specify which image of the
simulation box the body is considered to be in.  An image of 0 means
it is inside the box as defined.  A value of 2 means add 2 box lengths
to get the true value.  A value of -1 means subtract 1 box length to
get the true value.  LAMMPS updates these flags as the rigid bodies
cross periodic boundaries during the simulation.

.. note::

   If you use the *infile* or *mol* keywords and write restart
   files during a simulation, then each time a restart file is written,
   the fix also write an auxiliary restart file with the name
   rfile.rigid, where "rfile" is the name of the restart file,
   e.g. tmp.restart.10000 and tmp.restart.10000.rigid.  This auxiliary
   file is in the same format described above.  Thus it can be used in a
   new input script that restarts the run and re-specifies a rigid fix
   using an *infile* keyword and the appropriate filename.  Note that the
   auxiliary file will contain one line for every rigid body, even if the
   original file only listed a subset of the rigid bodies.

If the system has rigid bodies with finite-size overlapping particles
and the model uses the :doc:`fix gravity <fix_gravity>` command to
apply a gravitational force to the rigid bodies, then the *gravity*
keyword should be used in the following manner.

First, the group specified for the :doc:`fix gravity <fix_gravity>`
command should not include any atoms in rigid bodies which have
overlapping particles.  It can be empty (see the :doc:`group empty
<group>` command) or only contain single particles not in rigid
bodies, e.g. background particles.

Second, the *infile* keyword should be used to specify the total mass
and other properties of the rigid bodies with overlaps, so that their
dynamics will be modeled correctly, as explained above.

Third, the *gravity* keyword should be used the with the ID of the
:doc:`fix gravity <fix_gravity>` command as its argument.  The rigid
fixes will access the gravity fix to extract the current direction of
the gravity vector at each timestep (which can be static or dynamic).
A gravity force will then be applied to each rigid body at its
center-of-mass position using its total mass.

----------

If you use a :doc:`temperature compute <compute>` with a group that
includes particles in rigid bodies, the degrees-of-freedom removed by
each rigid body are accounted for in the temperature (and pressure)
computation, but only if the temperature group includes all the
particles in a particular rigid body.

A 3d rigid body has 6 degrees of freedom (3 translational, 3
rotational), except for a collection of point particles lying on a
straight line, which has only 5, e.g a dimer.  A 2d rigid body has 3
degrees of freedom (2 translational, 1 rotational).

.. note::

   You may wish to explicitly subtract additional
   degrees-of-freedom if you use the *force* and *torque* keywords to
   eliminate certain motions of one or more rigid bodies.  LAMMPS does
   not do this automatically.

The rigid body contribution to the pressure of the system (virial) is
also accounted for by this fix.

----------

If your simulation is a hybrid model with a mixture of rigid bodies and
non-rigid particles (e.g. solvent) there are several ways these rigid
fixes can be used in tandem with :doc:`fix nve <fix_nve>`, :doc:`fix nvt
<fix_nh>`, :doc:`fix npt <fix_nh>`, and :doc:`fix nph <fix_nh>`.

If you wish to perform NVE dynamics (no thermostatting or
barostatting), use one of 4 NVE rigid styles to integrate the rigid
bodies, and :doc:`fix nve <fix_nve>` to integrate the non-rigid
particles.

If you wish to perform NVT dynamics (thermostatting, but no
barostatting), you can use one of the 2 NVT rigid styles for the rigid
bodies, and any thermostatting fix for the non-rigid particles
(:doc:`fix nvt <fix_nh>`, :doc:`fix langevin <fix_langevin>`, :doc:`fix
temp/berendsen <fix_temp_berendsen>`).  You can also use one of the 4
NVE rigid styles for the rigid bodies and thermostat them using
:doc:`fix langevin <fix_langevin>` on the group that contains all the
particles in the rigid bodies.  The net force added by :doc:`fix
langevin <fix_langevin>` to each rigid body effectively thermostats its
translational center-of-mass motion.  Not sure how well it does at
thermostatting its rotational motion.

If you wish to perform NPT or NPH dynamics (barostatting), you cannot
use both :doc:`fix npt <fix_nh>` and the NPT or NPH rigid styles.  This
is because there can only be one fix which monitors the global
pressure and changes the simulation box dimensions.  So you have 3
choices:

#. Use one of the 4 NPT or NPH styles for the rigid bodies.  Use the
   *dilate* all option so that it will dilate the positions of the
   non-rigid particles as well.  Use :doc:`fix nvt <fix_nh>` (or any
   other thermostat) for the non-rigid particles.
#. Use :doc:`fix npt <fix_nh>` for the group of non-rigid particles.  Use
   the *dilate* all option so that it will dilate the center-of-mass
   positions of the rigid bodies as well.  Use one of the 4 NVE or 2 NVT
   rigid styles for the rigid bodies.
#. Use :doc:`fix press/berendsen <fix_press_berendsen>` to compute the
   pressure and change the box dimensions.  Use one of the 4 NVE or 2 NVT
   rigid styles for the rigid bodies.  Use :doc:`fix nvt <fix_nh>` (or
   any other thermostat) for the non-rigid particles.

In all case, the rigid bodies and non-rigid particles both contribute
to the global pressure and the box is scaled the same by any of the
barostatting fixes.

You could even use the second and third options for a non-hybrid
simulation consisting of only rigid bodies, assuming you give :doc:`fix
npt <fix_nh>` an empty group, though it's an odd thing to do.  The
barostatting fixes (:doc:`fix npt <fix_nh>` and :doc:`fix press/berensen
<fix_press_berendsen>`) will monitor the pressure and change the box
dimensions, but not time integrate any particles.  The integration of
the rigid bodies will be performed by fix rigid/nvt.

----------

.. include:: accel_styles.rst

----------

Restart, fix_modify, output, run start/stop, minimize info
"""""""""""""""""""""""""""""""""""""""""""""""""""""""""""

No information about the 4 NVE rigid styles is written to :doc:`binary
restart files <restart>`.  The exception is if the *infile* or *mol*
keyword is used, in which case an auxiliary file is written out with
rigid body information each time a restart file is written, as
explained above for the *infile* keyword.  For the 2 NVT rigid styles,
the state of the Nose/Hoover thermostat is written to :doc:`binary
restart files <restart>`.  Ditto for the 4 NPT and NPH rigid styles,
and the state of the Nose/Hoover barostat.  See the :doc:`read_restart
<read_restart>` command for info on how to re-specify a fix in an
input script that reads a restart file, so that the operation of the
fix continues in an uninterrupted fashion.

The :doc:`fix_modify <fix_modify>` *temp* and *press* options are
supported by the 4 NPT and NPH rigid styles to change the computes
used to calculate the instantaneous pressure tensor.  Note that the 2
NVT rigid fixes do not use any external compute to compute
instantaneous temperature.

The :doc:`fix_modify <fix_modify>` *bodyforces* option is supported by
all rigid styles to set whether per-body forces and torques are
computed early or late in a timestep, i.e. at the post-force stage or
at the final-integrate stage or the timestep, respectively.

The cumulative energy change in the system imposed by the 6 NVT, NPT,
NPH rigid fixes, via either thermostatting and/or barostatting, is
included in the :doc:`thermodynamic output <thermo_style>` keywords
*ecouple* and *econserve*.  See the :doc:`thermo_style <thermo_style>`
doc page for details.

The 2 NVE rigid fixes compute a global scalar which can be accessed by
various :doc:`output commands <Howto_output>`.  The scalar value
calculated by these fixes is "intensive".  The scalar is the current
temperature of the collection of rigid bodies.  This is averaged over
all rigid bodies and their translational and rotational degrees of
freedom.  The translational energy of a rigid body is 1/2 m v\^2, where
m = total mass of the body and v = the velocity of its center of mass.
The rotational energy of a rigid body is 1/2 I w\^2, where I = the
moment of inertia tensor of the body and w = its angular velocity.
Degrees of freedom constrained by the *force* and *torque* keywords
are removed from this calculation, but only for the *rigid* and
*rigid/nve* fixes.

The 6 NVT, NPT, NPH rigid fixes compute a global scalar which can be
accessed by various :doc:`output commands <Howto_output>`.  The scalar
is the same cumulative energy change due to these fixes described
above.  The scalar value calculated by this fix is "extensive".

The :doc:`fix_modify <fix_modify>` *virial* option is supported by
these fixes to add the contribution due to the added forces on atoms
to both the global pressure and per-atom stress of the system via the
:doc:`compute pressure <compute_pressure>` and :doc:`compute
stress/atom <compute_stress_atom>` commands.  The former can be
accessed by :doc:`thermodynamic output <thermo_style>`.  The default
setting for this fix is :doc:`fix_modify virial yes <fix_modify>`.

All of the *rigid* styles (not the *rigid/small* styles) compute a
global array of values which can be accessed by various :doc:`output
commands <Howto_output>`.  Similar information about the bodies
defined by the *rigid/small* styles can be accessed via the
:doc:`compute rigid/local <compute_rigid_local>` command.

The number of rows in the array is equal to the number of rigid
bodies.  The number of columns is 15.  Thus for each rigid body, 15
values are stored: the xyz coords of the center of mass (COM), the xyz
components of the COM velocity, the xyz components of the force acting
on the COM, the xyz components of the torque acting on the COM, and
the xyz image flags of the COM.

The center of mass (COM) for each body is similar to unwrapped
coordinates written to a dump file.  It will always be inside (or
slightly outside) the simulation box.  The image flags have the same
meaning as image flags for atom positions (see the "dump" command).
This means you can calculate the unwrapped COM by applying the image
flags to the COM, the same as when unwrapped coordinates are written
to a dump file.

The force and torque values in the array are not affected by the
*force* and *torque* keywords in the fix rigid command; they reflect
values before any changes are made by those keywords.

The ordering of the rigid bodies (by row in the array) is as follows.
For the *single* keyword there is just one rigid body.  For the
*molecule* keyword, the bodies are ordered by ascending molecule ID.
For the *group* keyword, the list of group IDs determines the ordering
of bodies.

The array values calculated by these fixes are "intensive", meaning
they are independent of the number of atoms in the simulation.

No parameter of these fixes can be used with the *start/stop* keywords
of the :doc:`run <run>` command.  These fixes are not invoked during
:doc:`energy minimization <minimize>`.

----------

Restrictions
""""""""""""

These fixes are all part of the RIGID package.  It is only enabled if
LAMMPS was built with that package.  See the :doc:`Build package <Build_package>` page for more info.

Assigning a temperature via the :doc:`velocity create <velocity>`
command to a system with :doc:`rigid bodies <fix_rigid>` may not have
the desired outcome for two reasons.  First, the velocity command can
be invoked before the rigid-body fix is invoked or initialized and the
number of adjusted degrees of freedom (DOFs) is known.  Thus it is not
possible to compute the target temperature correctly.  Second, the
assigned velocities may be partially canceled when constraints are
first enforced, leading to a different temperature than desired.  A
workaround for this is to perform a :doc:`run 0 <run>` command, which
ensures all DOFs are accounted for properly, and then rescale the
temperature to the desired value before performing a simulation.  For
example:

.. code-block:: LAMMPS

   velocity all create 300.0 12345
   run 0                             # temperature may not be 300K
   velocity all scale 300.0          # now it should be

Related commands
""""""""""""""""

:doc:`delete_bonds <delete_bonds>`, :doc:`neigh_modify <neigh_modify>`
exclude, :doc:`fix shake <fix_shake>`

Default
"""""""

The option defaults are force \* on on on and torque \* on on on,
meaning all rigid bodies are acted on by center-of-mass force and
torque.  Also Tchain = Pchain = 10, Titer = 1, Torder = 3, reinit = yes.

----------

.. _Hoover:

**(Hoover)** Hoover, Phys Rev A, 31, 1695 (1985).

.. _Kamberaj:

**(Kamberaj)** Kamberaj, Low, Neal, J Chem Phys, 122, 224114 (2005).

.. _Martyna2:

**(Martyna)** Martyna, Klein, Tuckerman, J Chem Phys, 97, 2635 (1992);
Martyna, Tuckerman, Tobias, Klein, Mol Phys, 87, 1117.

.. _Miller3:

**(Miller)** Miller, Eleftheriou, Pattnaik, Ndirango, and Newns,
J Chem Phys, 116, 8649 (2002).

.. _Zhang1:

**(Zhang)** Zhang, Glotzer, Nanoletters, 4, 1407-1413 (2004).
