# compute vacf command

## Syntax

``` LAMMPS
compute ID group-ID vacf
```

-   ID, group-ID are documented in [compute](compute) command
-   vacf = style name of this compute command

## Examples

``` LAMMPS
compute 1 all vacf
compute 1 upper vacf
```

## Description

Define a computation that calculates the velocity auto-correlation
function (VACF), averaged over a group of atoms. Each atom\'s
contribution to the VACF is its current velocity vector dotted into its
initial velocity vector at the time the compute was specified.

A vector of four quantities is calculated by this compute. The first
three elements of the vector are $v_x v_{x,0}$ (and similar for the $y$
and $z$ components), summed and averaged over atoms in the group, where
$v_x$ is the current $x$-component of the velocity of the atom and
$v_{x,0}$ is the initial $x$-component of the velocity of the atom. The
fourth element of the vector is the total VACF (i.e.,
$(v_x v_{x,0} + v_y v_{y,0} + v_z v_{z,0})$), summed and averaged over
atoms in the group.

The integral of the VACF versus time is proportional to the diffusion
coefficient of the diffusing atoms. This can be computed in the
following manner, using the [variable trap()](variable) function:

``` LAMMPS
compute         2 all vacf
fix             5 all vector 1 c_2[4]
variable        diff equal dt*trap(f_5)
thermo_style    custom step v_diff
```

:::: 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 time=0 atom
velocities from the restart file.
::::

## 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
velocity$^2$ [units](units).

## Restrictions

> none

## Related commands

[compute msd](compute_msd)

## Default

none