\(\renewcommand{\AA}{\text{Å}}\)

# compute gyration/chunk command

## Syntax

    compute ID group-ID gyration/chunk chunkID keyword value ...

- ID, group-ID are documented in compute command

- gyration/chunk = style name of this compute command

- chunkID = ID of compute chunk/atom command

- zero or more keyword/value pairs may be appended

- keyword = tensor

      tensor value = none

## Examples

    compute 1 molecule gyration/chunk molchunk
    compute 2 molecule gyration/chunk molchunk tensor

## Description

Define a computation that calculates the radius of gyration \(R_g\) for multiple chunks of atoms.

In LAMMPS, chunks are collections of atoms defined by a compute chunk/atom command, which assigns each atom to a single chunk (or no chunk). The ID for this command is specified as chunkID. For example, a single chunk could be the atoms in a molecule or atoms in a spatial bin. See the compute chunk/atom and Howto chunk doc pages for details of how chunks can be defined and examples of how they can be used to measure properties of a system.

This compute calculates the radius of gyration \(R_g\) for each chunk, which includes all effects due to atoms passing through periodic boundaries.

\(R_g\) is a measure of the size of a chunk, and is computed by the 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 chunk, \(r_{\text{cm}}\) is the center-of-mass position of the chunk, and the sum is over all atoms in the chunk.

Note that only atoms in the specified group contribute to the calculation. The compute chunk/atom command defines its own group; atoms will have a chunk ID = 0 if they are not in that group, signifying they are not assigned to a chunk, and will thus also not contribute to this calculation. You can specify the “all” group for this command if you simply want to include atoms with non-zero chunk IDs.

If the tensor keyword is specified, then the scalar \(R_g\) value is not calculated, but an \(R_g\) tensor is instead calculated for each chunk. 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 tensor are ordered \(xx\), \(yy\), \(zz\), \(xy\), \(xz\), \(yz\).

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.

The simplest way to output the results of the compute gyration/chunk calculation to a file is to use the fix ave/time command, for example:

    compute cc1 all chunk/atom molecule
    compute myChunk all gyration/chunk cc1
    fix 1 all ave/time 100 1 100 c_myChunk file tmp.out mode vector

## Output info

This compute calculates a global vector if the tensor keyword is not specified and a global array if it is. The length of the vector or number of rows in the array = the number of chunks Nchunk as calculated by the specified compute chunk/atom command. If the tensor keyword is specified, the global array has six columns. The vector or array can be accessed by any command that uses global values from a compute as input. See the Howto output page for an overview of LAMMPS output options.

All the vector or array values calculated by this compute are “intensive”. The vector or array values will be in distance units, since they are the square root of values represented by the formula above.

## Restrictions

none

## Related commands

none

compute gyration

## Default

none