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# compute msd/nongauss command¶

## Syntax¶

compute ID group-ID msd/nongauss keyword values ...

• ID, group-ID are documented in compute command

• msd/nongauss = style name of this compute command

• zero or more keyword/value pairs may be appended

• keyword = com

com value = yes or no

## Examples¶

compute 1 all msd/nongauss
compute 1 upper msd/nongauss com yes


## Description¶

Define a computation that calculates the mean-squared displacement (MSD) and non-Gaussian parameter (NGP) of the group of atoms, including all effects due to atoms passing through periodic boundaries.

A vector of three quantities is calculated by this compute. The first element of the vector is the total squared displacement, $$dr^2 = dx^2 + dy^2 + dz^2$$, of the atoms, and the second is the fourth power of these displacements, $$dr^4 = (dx^2 + dy^2 + dz^2)^2$$, summed and averaged over atoms in the group. The third component is the non-Gaussian diffusion parameter NGP,

$\text{NGP}(t) = \frac{3\left\langle(r(t)-r(0))^4\right\rangle} {5\left\langle(r(t)-r(0))^2\right\rangle^2} - 1.$

The NGP is a commonly used quantity in studies of dynamical heterogeneity. Its minimum theoretical value $$(-0.4)$$ occurs when all atoms have the same displacement magnitude. $$\text{NGP}=0$$ for Brownian diffusion, while $$\text{NGP} > 0$$ when some mobile atoms move faster than others.

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.

See the compute msd page for further important NOTEs, which also apply to this compute.

## Output info¶

This compute calculates a global vector of length 3, which can be accessed by indices 1–3 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 first vector value will be in distance$$^2$$ units, the second is in distance$$^4$$ units, and the third is dimensionless.

## Restrictions¶

Compute msd/nongauss cannot be used with a dynamic group.

This compute is part of the EXTRA-COMPUTE package. It is only enabled if LAMMPS was built with that package. See the Build package page for more info.

## Default¶

The option default is com = no.