# compute gyration/shape command

## Syntax

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

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

## Examples

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

## Description

Define a computation that calculates the eigenvalues of the gyration
tensor of a group of atoms and three shape parameters. 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)](Mattice1) while an application to polymer systems can be
found in [(Theodorou)](Theodorou1). 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 zero
(if all points are spherically symmetric) and one (if all points lie on
a line).

:::: 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 vector of length 6, which can be
accessed by indices 1\--6. The first three values 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 vector values from a compute as input. See the
[Howto output](Howto_output) page for an overview of LAMMPS output
options.

The vector values calculated by this compute are \"intensive\". The
first five vector values 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](compute_gyration)

## Default

none

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

::: {#Mattice1}
**(Mattice)** Mattice, Suter, Conformational Theory of Large Molecules,
Wiley, New York, 1994.
:::

::: {#Theodorou1}
**(Theodorou)** Theodorou, Suter, Macromolecules, 18, 1206 (1985).
:::