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# compute gyration command

## Syntax

    compute ID group-ID gyration

- ID, group-ID are documented in compute command

- gyration = style name of this compute command

## Examples

    compute 1 molecule gyration

## Description

Define a computation that calculates the radius of gyration \(R_g\) of the group of atoms, including all effects due to atoms passing through periodic boundaries.

\(R_g\) is a measure of the size of the group of atoms, and is computed as the square root of the \(R_g^2\) value in this formula

\[R_g^2 = \frac{1}{M} \sum_i m_i (r_i - r_{\text{cm}})^2\]

where \(M\) is the total mass of the group, \(r_{\text{cm}}\) is the center-of-mass position of the group, and the sum is over all atoms in the group.

A \(R_g^2\) tensor, stored as a 6-element vector, is also calculated by this compute. The formula for the components of the tensor is the same as the above formula, except that \((r_i - r_{\text{cm}})^2\) is replaced by \((r_{i,x} - r_{\text{cm},x}) \cdot (r_{i,y} - r_{\text{cm},y})\) for the \(xy\) component, and so on. The six components of the vector are ordered \(xx\), \(yy\), \(zz\), \(xy\), \(xz\), \(yz\). Note that unlike the scalar \(R_g\), each of the six values of the tensor is effectively a “squared” value, since the cross-terms may be negative and taking a square root would be invalid.

Note

The coordinates of an atom contribute to \(R_g\) 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 scalar (\(R_g\)) and a global vector of length 6 (\(R_g^2\) tensor), which can be accessed by indices 1–6. These values can be used by any command that uses a global scalar value or vector values from a compute as input. See the Howto output page for an overview of LAMMPS output options.

The scalar and vector values calculated by this compute are “intensive”. The scalar and vector values will be in distance and distance\(^2\) units, respectively.

## Restrictions

none

## Related commands

compute gyration/chunk, compute gyration/shape

## Default

none