# compute msd command

## Syntax

``` LAMMPS
compute ID group-ID msd keyword values ...
```

-   ID, group-ID are documented in [compute](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

``` LAMMPS
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](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*. The value of the
displacement will be 0.0 for atoms not in the specified compute group.

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
::: title
Note
:::

Initial coordinates are stored in \"unwrapped\" form, by using the image
flags associated with each atom. See the [dump custom](dump) command for
a discussion of \"unwrapped\" coordinates. See the Atoms section of the
[read_data](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](set) command.
::::

:::: note
::: title
Note
:::

If you want the quantities calculated by this compute to be continuous
when running from a [restart file](read_restart), 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](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](units).

## Restrictions

Compute *msd* cannot be used with a dynamic group.

## Related commands

[compute msd/nongauss](compute_msd_nongauss), [compute
displace_atom](compute_displace_atom), [fix
store/state](fix_store_state), [compute msd/chunk](compute_msd_chunk)

## Default

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