# compute gyration/shape/chunk command

## Syntax

``` LAMMPS
compute ID group-ID gyration/shape/chunk compute-ID
```

-   ID, group-ID are documented in [compute](compute) command
-   gyration/shape/chunk = style name of this compute command
-   compute-ID = ID of [compute gyration/chunk](compute_gyration_chunk)
    command

## Examples

``` LAMMPS
compute 1 molecule gyration/shape/chunk pe
```

## Description

Define a computation that calculates the eigenvalues of the gyration
tensor and three shape parameters of multiple chunks of atoms. The
computation includes all effects due to atoms passing through periodic
boundaries.

The three computed shape parameters are the asphericity, $b$, the
acylindricity, $c$, and the relative shape anisotropy, $k$, viz.,

$$\begin{aligned}
b &= l_z - \frac12(l_y+l_x) \\
c &= l_y - l_x \\
k &= \frac{3}{2} \frac{l_x^2+l_y^2+l_z^2}{(l_x+l_y+l_z)^2} - \frac{1}{2}
\end{aligned}$$

where $l_x \le l_y \le l_z$ are the three eigenvalues of the gyration
tensor. A general description of these parameters is provided in
[(Mattice)](Mattice2) while an application to polymer systems can be
found in [(Theodorou)](Theodorou2). The asphericity is always
non-negative and zero only when the three principal moments are equal.
This zero condition is met when the distribution of particles is
spherically symmetric (hence the name asphericity) but also whenever the
particle distribution is symmetric with respect to the three coordinate
axes (e.g., when the particles are distributed uniformly on a cube,
tetrahedron, or other Platonic solid). The acylindricity is always
non-negative and zero only when the two principal moments are equal.
This zero condition is met when the distribution of particles is
cylindrically symmetric (hence the name, acylindricity), but also
whenever the particle distribution is symmetric with respect to the two
coordinate axes (e.g., when the particles are distributed uniformly on a
regular prism). The relative shape anisotropy is bounded between 0 (if
all points are spherically symmetric) and 1 (if all points lie on a
line).

The tensor keyword must be specified in the compute gyration/chunk
command.

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

The coordinates of an atom contribute to the gyration tensor 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.
::::

## Output info

This compute calculates a global array with six columns, which can be
accessed by indices 1\--6. The first three columns are the eigenvalues
of the gyration tensor followed by the asphericity, the acylindricity
and the relative shape anisotropy. The computed values can be used by
any command that uses global array values from a compute as input. See
the [Howto output](Howto_output) page for an overview of LAMMPS output
options.

The array calculated by this compute is \"intensive\". The first five
columns will be in distance$^2$ [units](units) while the sixth one is
dimensionless.

## Restrictions

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

## Related commands

[compute gyration/chunk](compute_gyration_chunk) [compute
gyration/shape](compute_gyration_shape)

## Default

none

------------------------------------------------------------------------

::: {#Mattice2}
**(Mattice)** Mattice, Suter, Conformational Theory of Large Molecules,
Wiley, New York, 1994.
:::

::: {#Theodorou2}
**(Theodorou)** Theodorou, Suter, Macromolecules, 18, 1206 (1985).
:::