\(\renewcommand{\AA}{\text{Å}}\)

# compute gyration/shape/chunk command

## Syntax

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

- ID, group-ID are documented in compute command

- gyration/shape/chunk = style name of this compute command

- compute-ID = ID of compute gyration/chunk command

## Examples

    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.,

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

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) while an application to polymer systems can be found in (Theodorou). 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

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 command for a discussion of “unwrapped” coordinates. See the Atoms section of the 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 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 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 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 page for more info.

## Related commands

compute gyration/chunk compute gyration/shape

## Default

none

(Mattice) Mattice, Suter, Conformational Theory of Large Molecules, Wiley, New York, 1994.

(Theodorou) Theodorou, Suter, Macromolecules, 18, 1206 (1985).