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### 4. How-to discussions

The following sections describe what commands can be used to perform certain kinds of LAMMPS simulations.

4.1 Restarting a simulation
4.2 2d simulations
4.3 CHARMM and AMBER force fields
4.4 Running multiple simulations from one input script
4.5 Parallel tempering
4.6 Granular models
4.7 TIP3P water model
4.8 TIP4P water model
4.9 SPC water model
4.10 Coupling LAMMPS to other codes
4.11 Visualizing LAMMPS snapshots
4.12 Non-orthogonal simulation boxes
4.13 NEMD simulations
4.14 Extended spherical and aspherical particles
4.15 Output from LAMMPS (thermo, dumps, computes, fixes, variables)
4.16 Thermostatting, barostatting and computing temperature
4.17 Walls

The example input scripts included in the LAMMPS distribution and highlighted in this section also show how to setup and run various kinds of problems.

#### 4.1 Restarting a simulation

There are 3 ways to continue a long LAMMPS simulation. Multiple run 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 command. At a later time, these binary files can be read via a read_restart command in a new script. Or they can be converted to text data files and read by a read_data command in a new script. This section discusses the restart2data tool that is used to perform the conversion.

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 and read_data 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

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

    neighbor	0.4 bin
    neigh_modify	every 1 delay 1

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

    timestep	0.012

    run		50

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 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 using this tool:

    restart2data tmp.restart.50 tmp.restart.data

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

    read_data	tmp.restart.data

    neighbor	0.4 bin
    neigh_modify	every 1 delay 1

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

    timestep	0.012

    reset_timestep	50
    run		50

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 command is used to tell LAMMPS the current timestep. This value is stored in restart files, but not in data files.

#### 4.2 2d simulations

Use the dimension command to specify a 2d simulation.

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

If using the create box 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 1 -10 10 -10 10 -0.25 0.25

If using the read data 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 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.

IMPORTANT NOTE: Some models in LAMMPS treat particles as extended spheres, as opposed to point particles. In 2d, the particles will still be spheres, not disks, meaning their moment of inertia will be the same as in 3d.

#### 4.3 CHARMM and AMBER force fields

There are many different ways to compute forces in the CHARMM and AMBER molecular dynamics codes, only some of which are available as options in LAMMPS. 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. Setting coefficients is done in the input data file via the read_data command or in the input script with commands like pair_coeff or bond_coeff. See this section for additional tools that can use CHARMM or AMBER to assign force field coefficients and convert their output into LAMMPS input.

See (MacKerell) for a description of the CHARMM force field. See (Cornell) for a description of the AMBER force field.

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 harmonic
- angle_style charmm
- dihedral_style charmm
- pair_style lj/charmm/coul/charmm
- pair_style lj/charmm/coul/charmm/implicit
- pair_style lj/charmm/coul/long

- special_bonds charmm
- special_bonds amber

#### 4.4 Running multiple simulations from one input script

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 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

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 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

would run 2 independent simulations, one after the other.

For large numbers of independent simulations, you can use variables and the next and jump 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

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
    next t
    next a
    jump in.polymer

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 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 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.

#### 4.5 Parallel tempering

The temper command can be used to perform a parallel tempering or replica-exchange simulation where multiple copies of a simulation are run at different temperatures on different sets of processors, and Monte Carlo temperature swaps are performed between pairs of copies.

Use the -procs and -in command-line switches to launch LAMMPS on multiple partitions.

In your input script, define a set of temperatures, one for each processor partition, using the variable command:

    variable t world 300.0 310.0 320.0 330.0

Define a fix of style nvt or langevin to control the temperature of each simulation:

    fix myfix all nvt $t $t 100.0

Use the temper command in place of a run command to perform a simulation where tempering exchanges will take place:

    temper 100000 100 $t myfix 3847 58382

#### 4.6 Granular models

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 granular
- fix nve/sphere
- fix gravity

This compute

- compute erotate/sphere

calculates rotational kinetic energy which can be output with thermodynamic info.

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

- pair_style gran/history
- pair_style gran/no_history
- pair_style gran/hertzian

These commands implement fix options specific to granular systems:

- fix freeze
- fix pour
- fix viscous
- fix wall/gran

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 exclude

#### 4.7 TIP3P water model

The TIP3P water model as implemented in CHARMM (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 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).

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

These are the parameters to use for TIP3P with a long-range Coulombic solver (Ewald or PPPM in LAMMPS):

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

#### 4.8 TIP4P water model

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.

Currently, only a four-point model for long-range Coulombics is implemented via the LAMMPS pair style lj/cut/coul/long/tip4p. A cutoff version may be added the future. For both models, the bond lengths and bond angles should be held fixed using the fix shake 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). Note that the OM distance is specified in the pair_style 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

These are the parameters to use for TIP4P with a long-range Coulombic solver (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

#### 4.9 SPC water model

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 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 with long-range Coulombics (Ewald or PPPM in LAMMPS).

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

To use SPC with a long-range Coulombic solver (Ewald or PPPM in LAMMPS), the only parameters that change are the partial charge assignments:

O charge = -0.8476
H charge = 0.4238

#### 4.10 Coupling LAMMPS to other codes

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 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 package that performs constrained rigid-body motion on groups of atoms is hooked to LAMMPS. See the fix_poems command for more details. See this section of the documentation for info on how to add a new fix to LAMMPS.

(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 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 this section 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 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.

This section of the documentation describes how to build LAMMPS as a library. Once this is done, you can interface with LAMMPS either via C++, C, or Fortran (or any other language that supports a vanilla C-like interface, e.g. a scripting language). 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. Library.cpp and library.h contain such a C interface with the functions:

    void lammps_open(int, char **, MPI_Comm, void **);
    void lammps_close(void *);
    void lammps_file(void *, char *);
    char *lammps_command(void *, char *);

The functions contain C++ code you could write in a C++ application that was invoking LAMMPS directly. Note that LAMMPS classes are defined within a LAMMPS namespace (LAMMPS_NS) if you use them from another C++ application.

Two of the routines in library.cpp are of particular note. The lammps_open() function initiates LAMMPS and takes an MPI communicator as an argument. It returns a pointer to a LAMMPS "object". As with C++, 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.

Library.cpp contains a lammps_command() function to which the caller passes a single LAMMPS command (a string). Thus the calling code can read or generate a series of LAMMPS commands (e.g. an input script) one line at a time and pass it thru the library interface to setup a problem and then run it.

A few other sample functions are included in library.cpp, but the key idea is that you can write any functions you wish to define an interface for how your code talks to LAMMPS and add them to library.cpp and library.h. The routines you add can access any LAMMPS data. The examples/couple directory has example C++ and C codes which show how a stand-alone code can link LAMMPS as a library, run LAMMPS on a subset of processors, grab data from LAMMPS, change it, and put it back into LAMMPS.

#### 4.11 Visualizing LAMMPS snapshots

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 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 the xmovie program, included with the LAMMPS package. This produces simple, fast 2d projections of 3d systems, and can be useful for rapid debugging of simulation geometry and atom trajectories.

Several programs included with LAMMPS as auxiliary tools can convert native LAMMPS dump files to other formats. See the Section_tools doc page for details. The first is the ch2lmp tool, which contains a lammps2pdb Perl script which converts LAMMPS dump files into PDB files. The second is the lmp2arc tool which converts LAMMPS dump files into Accelrys' Insight MD program files. The third is the lmp2cfg tool which converts LAMMPS dump files into CFG files which can be read into the AtomEye visualizer.

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 for details. Specifically, Pizza.py can convert LAMMPS dump files into PDB, XYZ, 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.

LAMMPS can create XYZ files directly (via "dump xyz") which is a simple text-based file format used by many visualization programs including VMD.

LAMMPS can create DCD files directly (via "dump dcd") which can be read by VMD in conjunction with a CHARMM PSF file. Using this form of output avoids the need to convert LAMMPS snapshots to PDB files. See the dump command for more information on DCD files.

LAMMPS can create XTC files directly (via "dump xtc") which is GROMACS file format which can also be read by VMD for visualization. See the dump command for more information on XTC files.

#### 4.12 Non-orthogonal simulation boxes

By default, LAMMPS uses an orthogonal simulation box to encompass the particles. The boundary command sets the boundary conditions of the box (periodic, non-periodic, etc). If the box size is xprd by yprd by zprd then the 3 mutually orthogonal edge vectors of an orthogonal simulation box are a = (xprd,0,0), b = (0,yprd,0), and c = (0,0,zprd).

LAMMPS also allows non-orthogonal simulation boxes (triclinic symmetry) to be defined with 3 additional "tilt" parameters which change the edge vectors of the simulation box to be a = (xprd,0,0), b = (xy,yprd,0), and c = (xz,yz,zprd). The xy, xz, and yz parameters can be positive or negative. The simulation box must be periodic in both dimensions associated with a tilt factor. For example, if xz != 0.0, then the x and z dimensions must be periodic.

To avoid extremely tilted boxes (which would be computationally inefficient), 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). 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 all equivalent.

You tell LAMMPS to use a non-orthogonal box when the simulation box is defined. This happens in one of 3 ways. If the create_box command is used with a region of style prism, then a non-orthogonal domain is setup. See the region command for details. If the read_data 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 non-orthogonal domain is setup. See the read_data command for details. Finally, if the read_restart command reads a restart file which was written from a simulation using a triclinic box, then a non-orthogonal box will be enabled for the restarted simulation.

Note that you can define a non-orthogonal box with all 3 tilt factors = 0.0, so that it is initially orthogonal. This is necessary if the box will become non-orthogonal. Alternatively, you can use the change_box command to convert a simulation box from orthogonal to non-orthogonal and vice versa.

One use of non-orthogonal boxes is to model solid-state crystals with triclinic symmetry. The lattice command can be used with non-orthogonal basis vectors to define a lattice that will tile a non-orthogonal simulation box via the create_atoms command. Note that while the box edge vectors a,b,c cannot be arbitrary vectors (e.g. a must be aligned with the x axis), it is possible to rotate any crystal's basis vectors so that they meet these restrictions.

A second use of non-orthogonal boxes is to shear a bulk solid to study the response of the material. The fix deform command can be used for this purpose. It allows dynamic control of the xy, xz, and yz tilt factors as a simulation runs.

Another use of non-orthogonal boxes is to perform non-equilibrium MD (NEMD) simulations, as discussed in the next section.

#### 4.13 NEMD simulations

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 command. The fix nvt/sllod 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 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/spatial 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 can continuously strain a box by an arbitrary amount. As discussed in the fix deform command, when the tilt value reaches a limit, the box is re-shaped 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 should be set to "remap v", since that is what fix nvt/sllod 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 command.

#### 4.14 Extended spherical and aspherical particles

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

##### Atom styles

There are 3 atom styles that allow for definition of finite-size particles: granular, dipole, ellipsoid.

Granular particles 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.

Dipolar particles are typically spheriods with a point dipole and each particle type has a diamater and mass, set by the shape and mass commands. These particles store an angular velocity (omega) and can be acted upon by torque. They also store an orientation for the point dipole (mu) which has a length set by the dipole command. The set command can be used to initialize the orientation of dipole moments.

Ellipsoid particles are aspherical. Each particle type has an ellipsoidal shape and mass, defined by the shape and mass commands. 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. Ellipsoidal particles can also store a dipole moment if an atom_style hybrid ellipsoid dipole is used. The set command can be used to initialize the orientation of ellipsoidal particles and has a brief explanation of quaternions.

Note that if one of these atom styles is used (or multiple styles via the atom_style hybrid command), not all particles in the system are required to be finite-size or aspherical. For example, if the 3 shape parameters are set to the same value, the particle will be a spheroid 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. If the dipole moment is set to zero, the particle will not have a point dipole associated with it. The pair styles used to compute pairwise interactions will typically compute the correct interaction in these simplified (cheaper) cases. Pair_style hybrid can be used to insure the correct interactions are computed for the appropriate style of interactions. Likewise, using groups to partition particles (ellipsoid versus spheroid 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, finite-size spheroids and ellipsoids are still treated as 3d particles, rather than as disks or ellipses. This means they have the same moment of inertia for a 3d extended object. When their temperature is coomputed, the correct degrees of freedom are used for rotation in a 2d versus 3d system.

##### Pair potentials

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

- pair_style gran/history
- pair_style gran/hertzian
- pair_style gran/no_history
- pair_style dipole/cut
- pair_style gayberne
- pair_style resquared
- pair_style lubricate

The granular pair styles are used with atom_style granular. The dipole pair style is used with atom_style dipole. The GayBerne and REsquared potentials require particles have a shape and are designed for ellipsoidal particles. The lubrication potential requires that particles have a shape. It can currently only be used with extended spherical particles.

##### Time integration

There are 3 fixes that perform time integration on extended spherical particles, meaning the integrators update the rotational orientation and angular velocity or angular momentum of the particles:

- fix nve/sphere
- fix nvt/sphere
- fix npt/sphere

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

- fix nve/asphere
- fix nvt/asphere
- fix npt/asphere

The advantage of these fixes is that those which thermostat the particles include the rotational degrees of freedom in the temperature calculation and thermostatting. Other thermostats can be used with fix nve/sphere or fix nve/asphere, such as fix langevin or fix temp/berendsen, but those thermostats only operate on the translational kinetic energy of the extended particles.

Note that for mixtures of point and extended particles, you should only use these integration fixes on groups which contain extended particles.

##### Computes, thermodynamics, and dump output

There are 4 computes that calculate the temperature or rotational energy of extended spherical or aspherical particles:

- compute temp/sphere
- compute temp/asphere
- compute erotate/sphere
- compute erotate/asphere

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 extended particles), then the compute can be defined and the thermo_modify 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 command for details.

The dump custom command can output various attributes of extended particles, including the dipole moment (mu), the angular velocity (omega), the angular momentum (angmom), the quaternion (quat), and the torque (tq) on the particle.

##### Rigid bodies composed of extended particles

The fix rigid 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.

(NOTE: the feature described in the following paragraph has not yet been released. It will be soon.)

If any of the constituent particles of a rigid body are extended particles (spheroids or ellipsoids), 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 extended sphereoids, even if the two particles have the same mass. Extended 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 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.

#### 4.15 Output from LAMMPS (thermo, dumps, computes, fixes, variables)

There are four basic kinds of LAMMPS output:

- Thermodynamic output, which is a list of quantities printed every few timesteps to the screen and logfile.
- Dump files, which contain snapshots of atoms and various per-atom values and are written at a specified frequency.
- Certain fixes can output user-specified quantities to files: fix ave/time for time averaging, fix ave/spatial for spatial averaging, and fix print for single-line output of variables. Fix print can also output to the screen.
- Restart files.

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 and fix 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 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
- Scalar/vector/array data
- Thermodynamic output
- Dump file output
- Fixes that write output files
- Computes that process output quantities
- Fixes that process output quantities
- Computes that generate values to output
- Fixes that generate values to output
- Variables that generate values to output
- Summary table of output options and data flow between commands

##### Global/per-atom/local data

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

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

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

The frequency and format of thermodynamic output is set by the thermo, thermo_style, and thermo_modify commands. The thermo_style 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 or fix or variable 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 command.

##### Dump file output

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

There is also a dump custom 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 or fix or variable 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 command.

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

##### Fixes that write output files

Three fixes take various quantities as input and can write output files: fix ave/time, fix ave/spatial, and fix print.

The fix ave/time 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 values, global fix values, or variables 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 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/spatial command enables direct output to a file of spatial-averaged per-atom quantities like those output in dump files, within 1d layers of the simulation box. 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, by a fix, or by an atom-style variable. The spatial-averaged output of this fix can also be used as input to other output commands.

The fix ave/histo 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 print 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 values for any style variable except the atom style). As explained above, variables themselves can contain references to global values generated by thermodynamic keywords, computes, fixes, or other variables, or to per-atom values for a specific atom. Thus the fix print command is a means to output a wide variety of quantities separate from normal thermodynamic or dump file output.

##### Computes that process output quantities

The compute reduce and compute reduce/region commands take one or more 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 property/atom 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 command.

The compute property/local 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

The fix ave/atom 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, by a fix, or by an atom-style variable. The time-averaged per-atom output of this fix can be used as input to other output commands.

##### Computes that generate values to output

Every compute 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

Some fixes 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

Every variables defined in an input script generates either a global scalar value or a per-atom vector (only atom-style variables) when it is accessed. The formulas used to define equal- and atom-style 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 output using the other commands described in this section.

##### Summary table of output options and data flow between commands

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 | global scalars | screen, log file |
dump custom | per-atom vectors | dump file |
dump local | local vectors | dump file |
fix print | global scalar from variable | screen, file |
print | global scalar from variable | screen |
computes | N/A | global/per-atom/local scalar/vector/array |
fixes | N/A | global/per-atom/local scalar/vector/array |
variables | global scalars, per-atom vectors | global scalar, per-atom vector |
compute reduce | global/per-atom/local vectors | global scalar/vector |
compute property/atom | per-atom vectors | per-atom vector/array |
compute property/local | local vectors | local vector/array |
fix ave/atom | per-atom vectors | per-atom vector/array |
fix ave/time | global scalars/vectors | global scalar/vector/array, file |
fix ave/spatial | per-atom vectors | global array, file |
fix ave/histo | global/per-atom/local scalars and vectors | global array, file |

#### 4.16 Thermostatting, barostatting, and computing temperature

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 motiion 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 calculate temperature, and the compute pressure command calculates pressure.

- compute temp
- compute temp/sphere
- compute temp/asphere
- compute temp/com
- compute temp/deform
- compute temp/partial
- compute temp/profile
- compute temp/ramp
- compute temp/region

All but the first 3 calculate velocity biases (i.e. advection velocities) that are removed when computing the thermal temperature. Fix temp/sphere and fix temp/asphere compute kinetic energy for extended particles that includes rotational degrees of freedom. They both allow, as an extra argument, which is another temperature compute that subtracts a velocity bias. This allows the translational velocity of extended spherical or aspherical particles to be adjusted in prescribed ways.

Thermostatting in LAMMPS is performed by fixes. Four thermostatting fixes are currently available: Nose-Hoover (nvt), Berendsen, Langevin, and direct rescaling (temp/rescale):

- fix nvt
- fix nvt/sphere
- fix nvt/asphere
- fix nvt/sllod
- fix temp/berendsen
- fix langevin
- fix temp/rescale

Fix nvt only thermostats the translational velocity of particles. Fix nvt/sllod 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 section of this page for further details. Fix nvt/sphere and fix nvt/asphere thermostat not only translation velocities but also rotational velocities for spherical and aspherical particles.

Any of these fixes can use temperature computes that remove bias for two purposes: (a) computing the current temperature to compare to the requested target temperature, and (b) adjusting only the thermal temperature component of the particle's velocities. See the doc pages for the individual fixes and for the fix_modify 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.

IMPORTANT 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/sphere
- fix nve/asphere

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

- fix npt
- fix npt/sphere
- fix npt/asphere
- fix nph
- fix press/berendsen

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

As with the thermostats, fix npt and fix nph only use translational motion of the particles in computing T and P and performing thermo/barostatting. Fix npt/sphere and fix npt/asphere 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 to calculate a current pressure. By default, this compute is created with a simple compute temp (see the last argument of the compute pressure command), which is used to calculated the kinetic componenet of the pressure. The barostatting fixes can also use temperature computes that remove bias for the purpose of computing the kinetic componenet which contributes to the current pressure. See the doc pages for the individual fixes and for the fix_modify command for instructions on how to assign a temperature or pressure compute to a barostatting fix.

IMPORTANT NOTE: As with the thermostats, the Nose/Hoover methods (fix npt and fix nph) perform time integration. Fix press/berendsen 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 command, often includes temperature and pressure values. As explained on the doc page for the thermo_style 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 command. Or you can use the thermo_modify command to re-define what temperature or pressure compute is used for default thermodynamic output.

#### 4.16 Walls

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 and create_atoms commands, or read in via the read_data 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 or fix nvt is not used with the group that contains wall particles, their positions and velocities will not be updated.

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

The fix move command offers the most generality, since the motion of individual particles can be specified with variable 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 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. The bonded particles do interact with other mobile particles.

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

- fix wall/reflect - reflective flat walls
- fix wall/lj93 - flat walls, with Lennard-Jones 9/3 potential
- fix wall/lj126 - flat walls, with Lennard-Jones 12/6 potential
- fix wall/colloid - flat walls, with pair_style colloid potential
- fix wall/harmonic - flat walls, with repulsive harmonic spring potential
- fix wall/region - use region surface as wall
- fix wall/gran - flat or curved walls with pair_style granular potential

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 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 can also specify a volume "interior" or "exterior" to the specified primitive shape or union or intersection. Regions 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 command. At some point we plan to allow regoin surfaces to be used as frictional walls, as well as triangulated surfaces.

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