# compute rdf command

## Syntax

    compute ID group-ID rdf general_keyword general_values Nbin itype1 jtype1 itype2 jtype2 ...

- ID, group-ID are documented in compute command
- rdf = style name of this compute command
- general_keywords general_values are documented in compute
- Nbin = number of RDF bins
- itypeN = central atom type for Nth RDF histogram (see asterisk form below)
- jtypeN = distribution atom type for Nth RDF histogram (see asterisk form below)

## Examples

    compute 1 all rdf 100
    compute 1 all rdf 100 1 1
    compute 1 all rdf 100 * 3
    compute 1 fluid rdf 500 1 1 1 2 2 1 2 2
    compute 1 fluid rdf 500 1*3 2 5 *10

## Description

Define a computation that calculates the radial distribution function (RDF), also called g(r), and the coordination number for a group of particles. Both are calculated in histogram form by binning pairwise distances into Nbin bins from 0.0 to the maximum force cutoff defined by the pair_style command. The bins are of uniform size in radial distance. Thus a single bin encompasses a thin shell of distances in 3d and a thin ring of distances in 2d.

Warning

If you have a bonded system, then the settings of `special_bonds` command can remove pairwise interactions between atoms in the same bond, angle, or dihedral. This is the default setting for the `special_bonds` command, and means those pairwise interactions do not appear in the neighbor list. Because this fix uses the neighbor list, it also means those pairs will not be included in the RDF. One way to get around this, is to write a dump file, and use the `rerun` command to compute the RDF for snapshots in the dump file. The rerun script can use a `special_bonds` command that includes all pairs in the neighbor list.

The itypeN and jtypeN arguments are optional. These arguments must come in pairs. If no pairs are listed, then a single histogram is computed for g(r) between all atom types. If one or more pairs are listed, then a separate histogram is generated for each itype,*jtype* pair.

The itypeN and jtypeN settings can be specified in one of two ways. An explicit numeric value can be used, as in the 4th example above. Or a wild-card asterisk can be used to specify a range of atom types. This takes the form “*” or “n” or “n” or “m*n”. If N = the number of atom types, then an asterisk with no numeric values means all types from 1 to N. A leading asterisk means all types from 1 to n (inclusive). A trailing asterisk means all types from n to N (inclusive). A middle asterisk means all types from m to n (inclusive).

If both itypeN and jtypeN are single values, as in the 4th example above, this means that a g(r) is computed where atoms of type itypeN are the central atom, and atoms of type jtypeN are the distribution atom. If either itypeN and jtypeN represent a range of values via the wild-card asterisk, as in the 5th example above, this means that a g(r) is computed where atoms of any of the range of types represented by itypeN are the central atom, and atoms of any of the range of types represented by jtypeN are the distribution atom.

Pairwise distances are generated by looping over a pairwise neighbor list, just as they would be in a pair_style computation. The distance between two atoms I and J is included in a specific histogram if the following criteria are met:

- atoms I,J are both in the specified compute group
- the distance between atoms I,J is less than the maximum force cutoff
- the type of the I atom matches itypeN (one or a range of types)
- the type of the J atom matches jtypeN (one or a range of types)

It is OK if a particular pairwise distance is included in more than one individual histogram, due to the way the itypeN and jtypeN arguments are specified.

The g(r) value for a bin is calculated from the histogram count by scaling it by the idealized number of how many counts there would be if atoms of type jtypeN were uniformly distributed. Thus it involves the count of itypeN atoms, the count of jtypeN atoms, the volume of the entire simulation box, and the volume of the bin’s thin shell in 3d (or the area of the bin’s thin ring in 2d).

A coordination number coord(r) is also calculated, which is the number of atoms of type jtypeN within the current bin or closer, averaged over atoms of type itypeN. This is calculated as the area- or volume-weighted sum of g(r) values over all bins up to and including the current bin, multiplied by the global average volume density of atoms of type jtypeN.

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

    compute myRDF all rdf 50
    fix 1 all ave/time 100 1 100 c_myRDF file tmp.rdf mode vector

## Output info

This compute calculates a global array with the number of rows = Nbins, and the number of columns = 1 + 2*Npairs, where Npairs is the number of I,J pairings specified. The first column has the bin coordinate (center of the bin), Each successive set of 2 columns has the g(r) and coord(r) values for a specific set of itypeN versus jtypeN interactions, as described above. These values can be used by any command that uses a global values from a compute as input. See Section_howto 15 for an overview of LIGGGHTS(R)-PUBLIC output options.

The array values calculated by this compute are all “intensive”.

The first column of array values will be in distance units. The g(r) columns of array values are normalized numbers >= 0.0. The coordination number columns of array values are also numbers >= 0.0.

## Restrictions

The RDF is not computed for distances longer than the force cutoff, since processors (in parallel) don’t know about atom coordinates for atoms further away than that distance. If you want an RDF for larger distances, you can use the `rerun` command to post-process a dump file. The definition of g(r) used by LIGGGHTS(R)-PUBLIC is only appropriate for characterizing atoms that are uniformly distributed throughout the simulation cell. In such cases, the coordination number is still correct and meaningful. As an example, if a large simulation cell contains only one atom of type itypeN and one of jtypeN, then g(r) will register an arbitrarily large spike at whatever distance they happen to be at, and zero everywhere else. coord(r) will show a step change from zero to one at the location of the spike in g(r).

## Related commands

fix ave/time

Default: none