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### fix gcmc command

Syntax:

    fix ID group-ID gcmc N X M type seed T mu displace keyword values ...

- ID, group-ID are documented in fix command
- gcmc = style name of this fix command
- N = invoke this fix every N steps
- X = average number of GCMC exchanges to attempt every N steps
- M = average number of MC moves to attempt every N steps
- type = atom type for inserted atoms (must be 0 if mol keyword used)
- seed = random # seed (positive integer)
- T = temperature of the ideal gas reservoir (temperature units)
- mu = chemical potential of the ideal gas reservoir (energy units)
- translate = maximum Monte Carlo translation distance (length units)
- zero or more keyword/value pairs may be appended to args

      keyword = mol, region, maxangle, pressure, fugacity_coeff, full_energy, charge, group, grouptype, intra_energy, or tfac_insert
        mol value = template-ID
          template-ID = ID of molecule template specified in a separate molecule command
        shake value = fix-ID
          fix-ID = ID of fix shake command
        region value = region-ID
          region-ID = ID of region where MC moves are allowed
        maxangle value = maximum molecular rotation angle (degrees)
        pressure value = pressure of the gas reservoir (pressure units)
        fugacity_coeff value = fugacity coefficient of the gas reservoir (unitless)
        full_energy = compute the entire system energy when performing MC moves
        charge value = charge of inserted atoms (charge units)
        group value = group-ID
          group-ID = group-ID for inserted atoms (string)
        grouptype values = type group-ID
          type = atom type (int)
          group-ID = group-ID for inserted atoms (string)
        intra_energy value = intramolecular energy (energy units)
        tfac_insert value = scale up/down temperature of inserted atoms (unitless)

Examples:

    fix 2 gas gcmc 10 1000 1000 2 29494 298.0 -0.5 0.01
    fix 3 water gcmc 10 100 100 0 3456543 3.0 -2.5 0.1 mol my_one_water maxangle 180 full_energy
    fix 4 my_gas gcmc 1 10 10 1 123456543 300.0 -12.5 1.0 region disk

Description:

This fix performs grand canonical Monte Carlo (GCMC) exchanges of atoms or molecules of the given type with an imaginary ideal gas reservoir at the specified T and chemical potential (mu) as discussed in (Frenkel). If used with the fix nvt command, simulations in the grand canonical ensemble (muVT, constant chemical potential, constant volume, and constant temperature) can be performed. Specific uses include computing isotherms in microporous materials, or computing vapor-liquid coexistence curves.

Every N timesteps the fix attempts a number of GCMC exchanges (insertions or deletions) of gas atoms or molecules of the given type between the simulation cell and the imaginary reservoir. It also attempts a number of Monte Carlo moves (translations and molecule rotations) of gas of the given type within the simulation cell or region. The average number of attempted GCMC exchanges is X. The average number of attempted MC moves is M. M should typically be chosen to be approximately equal to the expected number of gas atoms or molecules of the given type within the simulation cell or region, which will result in roughly one MC translation per atom or molecule per MC cycle.

For MC moves of molecular gasses, rotations and translations are each attempted with 50% probability. For MC moves of atomic gasses, translations are attempted 100% of the time. For MC exchanges of either molecular or atomic gasses, deletions and insertions are each attempted with 50% probability.

All inserted particles are always assigned to two groups: the default group "all" and the group specified in the fix gcmc command (which can also be "all"). In addition, particles are also added to any groups specified by the group and grouptype keywords. If inserted particles are individual atoms, they are assigned the atom type given by the type argument. If they are molecules, the type argument has no effect and must be set to zero. Instead, the type of each atom in the inserted molecule is specified in the file read by the molecule command.

This fix cannot be used to perform MC insertions of gas atoms or molecules other than the exchanged type, but MC deletions, translations, and rotations can be performed on any atom/molecule in the fix group. All atoms in the simulation cell can be moved using regular time integration translations, e.g. via fix nvt, resulting in a hybrid GCMC+MD simulation. A smaller-than-usual timestep size may be needed when running such a hybrid simulation, especially if the inserted molecules are not well equilibrated.

This command may optionally use the region keyword to define an exchange and move volume. The specified region must have been previously defined with a region command. It must be defined with side = in. Insertion attempts occur only within the specified region. For non-rectangular regions, random trial points are generated within the rectangular bounding box until a point is found that lies inside the region. If no valid point is generated after 1000 trials, no insertion is performed, but it is counted as an attempted insertion. Move and deletion attempt candidates are selected from gas atoms or molecules within the region. If there are no candidates, no move or deletion is performed, but it is counted as an attempt move or deletion. If an attempted move places the atom or molecule center-of-mass outside the specified region, a new attempted move is generated. This process is repeated until the atom or molecule center-of-mass is inside the specified region.

If used with fix nvt, the temperature of the imaginary reservoir, T, should be set to be equivalent to the target temperature used in fix nvt. Otherwise, the imaginary reservoir will not be in thermal equilibrium with the simulation cell. Also, it is important that the temperature used by fix nvt be dynamic, which can be achieved as follows:

    compute mdtemp mdatoms temp
    compute_modify mdtemp dynamic yes
    fix mdnvt mdatoms nvt temp 300.0 300.0 10.0
    fix_modify mdnvt temp mdtemp

Note that neighbor lists are re-built every timestep that this fix is invoked, so you should not set N to be too small. However, periodic rebuilds are necessary in order to avoid dangerous rebuilds and missed interactions. Specifically, avoid performing so many MC translations per timestep that atoms can move beyond the neighbor list skin distance. See the neighbor command for details.

When an atom or molecule is to be inserted, its coordinates are chosen at a random position within the current simulation cell or region, and new atom velocities are randomly chosen from the specified temperature distribution given by T. The effective temperature for new atom velocities can be increased or decreased using the optional keyword tfac_insert (see below). Relative coordinates for atoms in a molecule are taken from the template molecule provided by the user. The center of mass of the molecule is placed at the insertion point. The orientation of the molecule is chosen at random by rotating about this point.

Individual atoms are inserted, unless the mol keyword is used. It specifies a template-ID previously defined using the molecule command, which reads a file that defines the molecule. The coordinates, atom types, charges, etc, as well as any bond/angle/etc and special neighbor information for the molecule can be specified in the molecule file. See the molecule command for details. The only settings required to be in this file are the coordinates and types of atoms in the molecule.

When not using the mol keyword, you should ensure you do not delete atoms that are bonded to other atoms, or LAMMPS will soon generate an error when it tries to find bonded neighbors. LAMMPS will warn you if any of the atoms eligible for deletion have a non-zero molecule ID, but does not check for this at the time of deletion.

If you wish to insert molecules via the mol keyword, that will have their bonds or angles constrained via SHAKE, use the shake keyword, specifying as its value the ID of a separate fix shake command which also appears in your input script.

Optionally, users may specify the maximum rotation angle for molecular rotations using the maxangle keyword and specifying the angle in degrees. Rotations are performed by generating a random point on the unit sphere and a random rotation angle on the range [0,maxangle). The molecule is then rotated by that angle about an axis passing through the molecule center of mass. The axis is parallel to the unit vector defined by the point on the unit sphere. The same procedure is used for randomly rotating molecules when they are inserted, except that the maximum angle is 360 degrees.

Note that fix GCMC does not use configurational bias MC or any other kind of sampling of intramolecular degrees of freedom. Inserted molecules can have different orientations, but they will all have the same intramolecular configuration, which was specified in the molecule command input.

For atomic gasses, inserted atoms have the specified atom type, but deleted atoms are any atoms that have been inserted or that belong to the user-specified fix group. For molecular gasses, exchanged molecules use the same atom types as in the template molecule supplied by the user. In both cases, exchanged atoms/molecules are assigned to two groups: the default group "all" and the group specified in the fix gcmc command (which can also be "all").

The gas reservoir pressure can be specified using the pressure keyword, in which case the user-specified chemical potential is ignored. For non-ideal gas reservoirs, the user may also specify the fugacity coefficient using the fugacity_coeff keyword.

The full_energy option means that fix GCMC will compute the total potential energy of the entire simulated system. The total system energy before and after the proposed GCMC move is then used in the Metropolis criterion to determine whether or not to accept the proposed GCMC move. By default, this option is off, in which case only partial energies are computed to determine the difference in energy that would be caused by the proposed GCMC move.

The full_energy option is needed for systems with complicated potential energy calculations, including the following:

- long-range electrostatics (kspace)
- many-body pair styles
- hybrid pair styles
- eam pair styles
- triclinic systems
- need to include potential energy contributions from other fixes

In these cases, LAMMPS will automatically apply the full_energy keyword and issue a warning message.

When the mol keyword is used, the full_energy option also includes the intramolecular energy of inserted and deleted molecules. If this is not desired, the intra_energy keyword can be used to define an amount of energy that is subtracted from the final energy when a molecule is inserted, and added to the initial energy when a molecule is deleted. For molecules that have a non-zero intramolecular energy, this will ensure roughly the same behavior whether or not the full_energy option is used.

Inserted atoms and molecules are assigned random velocities based on the specified temperature T. Because the relative velocity of all atoms in the molecule is zero, this may result in inserted molecules that are systematically too cold. In addition, the intramolecular potential energy of the inserted molecule may cause the kinetic energy of the molecule to quickly increase or decrease after insertion. The tfac_insert keyword allows the user to counteract these effects by changing the temperature used to assign velocities to inserted atoms and molecules by a constant factor. For a particular application, some experimentation may be required to find a value of tfac_insert that results in inserted molecules that equilibrate quickly to the correct temperature.

Some fixes have an associated potential energy. Examples of such fixes include: efield, gravity, addforce, langevin, restrain, temp/berendsen, temp/rescale, and wall fixes. For that energy to be included in the total potential energy of the system (the quantity used when performing GCMC moves), you MUST enable the fix_modify energy option for that fix. The doc pages for individual fix commands specify if this should be done.

Use the charge option to insert atoms with a user-specified point charge. Note that doing so will cause the system to become non-neutral. LAMMPS issues a warning when using long-range electrostatics (kspace) with non-neutral systems. See the compute group/group documentation for more details about simulating non-neutral systems with kspace on.

Use of this fix typically will cause the number of atoms to fluctuate, therefore, you will want to use the compute_modify command to insure that the current number of atoms is used as a normalizing factor each time temperature is computed. Here is the necessary command:

    compute_modify thermo_temp dynamic yes

If LJ units are used, note that a value of 0.18292026 is used by this fix as the reduced value for Planck's constant. This value was derived from LJ parameters for argon, where h* = h/sqrt(sigma^2 * epsilon * mass), sigma = 3.429 angstroms, epsilon/k = 121.85 K, and mass = 39.948 amu.

The group keyword assigns all inserted atoms to the group of the group-ID value. The grouptype keyword assigns all inserted atoms of the specified type to the group of the group-ID value.

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

This fix writes the state of the fix to binary restart files. This includes information about the random number generator seed, the next timestep for MC exchanges, etc. See the 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.

None of the fix_modify options are relevant to this fix.

This fix computes a global vector of length 8, which can be accessed by various output commands. The vector values are the following global cumulative quantities:

- 1 = translation attempts
- 2 = translation successes
- 3 = insertion attempts
- 4 = insertion successes
- 5 = deletion attempts
- 6 = deletion successes
- 7 = rotation attempts
- 8 = rotation successes

The vector values calculated by this fix are "extensive".

No parameter of this fix can be used with the start/stop keywords of the run command. This fix is not invoked during energy minimization.

Restrictions:

This fix is part of the MC package. It is only enabled if LAMMPS was built with that package. See the Making LAMMPS section for more info.

Do not set "neigh_modify once yes" or else this fix will never be called. Reneighboring is required.

Can be run in parallel, but aspects of the GCMC part will not scale well in parallel. Only usable for 3D simulations.

Note that very lengthy simulations involving insertions/deletions of billions of gas molecules may run out of atom or molecule IDs and trigger an error, so it is better to run multiple shorter-duration simulations. Likewise, very large molecules have not been tested and may turn out to be problematic.

Use of multiple fix gcmc commands in the same input script can be problematic if using a template molecule. The issue is that the user-referenced template molecule in the second fix gcmc command may no longer exist since it might have been deleted by the first fix gcmc command. An existing template molecule will need to be referenced by the user for each subsequent fix gcmc command.

Because molecule insertion does not work in combination with fix rigid, simulataneous use of fix rigid or fix rigid/small with this fix is not allowed.

Related commands:

fix atom/swap, fix nvt, neighbor, fix deposit, fix evaporate, delete_atoms

Default:

The option defaults are mol = no, maxangle = 10, full_energy = no, except for the situations where full_energy is required, as listed above.

(Frenkel) Frenkel and Smit, Understanding Molecular Simulation, Academic Press, London, 2002.