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# compute msd command

## Syntax

    compute ID group-ID msd keyword values ...

- ID, group-ID are documented in compute command

- msd = style name of this compute command

- zero or more keyword/value pairs may be appended

- keyword = com or average

      com value = yes or no
      average value = yes or no

## Examples

    compute 1 all msd
    compute 1 upper msd com yes average yes

## Description

Define a computation that calculates the mean-squared displacement (MSD) of the group of atoms, including all effects due to atoms passing through periodic boundaries. For computation of the non-Gaussian parameter of mean-squared displacement, see the compute msd/nongauss command.

A vector of four quantities is calculated by this compute. The first three elements of the vector are the squared dx, dy, and dz displacements, summed and averaged over atoms in the group. The fourth element is the total squared displacement (i.e., \(dx^2 + dy^2 + dz^2\)), summed and averaged over atoms in the group.

The slope of the mean-squared displacement (MSD) versus time is proportional to the diffusion coefficient of the diffusing atoms.

The displacement of an atom is from its reference position. This is normally the original position at the time the compute command was issued, unless the average keyword is set to yes.

If the com option is set to yes then the effect of any drift in the center-of-mass of the group of atoms is subtracted out before the displacement of each atom is calculated.

If the average option is set to yes then the reference position of an atom is based on the average position of that atom, corrected for center-of-mass motion if requested. The average position is a running average over all previous calls to the compute, including the current call. So on the first call it is current position, on the second call it is the arithmetic average of the current position and the position on the first call, and so on. Note that when using this option, the precise value of the mean square displacement will depend on the number of times the compute is called. So, for example, changing the frequency of thermo output may change the computed displacement. Also, the precise values will be changed if a single simulation is broken up into two parts, using either multiple run commands or a restart file. It only makes sense to use this option if the atoms are not diffusing, so that their average positions relative to the center of mass of the system are stationary. The most common case is crystalline solids undergoing thermal motion.

Note

Initial coordinates are stored in “unwrapped” form, by using the image flags associated with each atom. See the dump custom command for a discussion of “unwrapped” coordinates. See the Atoms section of the read_data command for a discussion of image flags and how they are set for each atom. You can reset the image flags (e.g. to 0) before invoking this compute by using the set image command.

Note

If you want the quantities calculated by this compute to be continuous when running from a restart file, then you should use the same ID for this compute, as in the original run. This is so that the fix this compute creates to store per-atom quantities will also have the same ID, and thus be initialized correctly with atom reference positions from the restart file. When average is set to yes, then the atom reference positions are restored correctly, but not the number of samples used obtain them. As a result, the reference positions from the restart file are combined with subsequent positions as if they were from a single sample, instead of many, which will change the values of msd somewhat.

## Output info

This compute calculates a global vector of length 4, which can be accessed by indices 1–4 by any command that uses global vector values from a compute as input. See the Howto output doc page for an overview of LAMMPS output options.

The vector values are “intensive”. The vector values will be in distance\(^2\) units.

## Restrictions

Compute msd cannot be used with a dynamic group and the number of atoms in the compute group must not be changed by some fixes like, for example, fix deposit or fix evaporate.

## Related commands

compute msd/nongauss, compute displace_atom, fix store/state, compute msd/chunk

## Default

The option default are com = no, average = no.