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# compute vacf command

## Syntax

    compute ID group-ID vacf

- ID, group-ID are documented in compute command

- vacf = style name of this compute command

## Examples

    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() function:

    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

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 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 doc page for an overview of LAMMPS output options.

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

## Restrictions

none

## Related commands

compute msd, compute vacf/chunk

## Default

none