## Syntax

compute ID group-ID adf Nbin itype1 jtype1 ktype1 Rjinner1 Rjouter1 Rkinner1 Rkouter1 ...

• ID, group-ID are documented in compute command

• adf = style name of this compute command

• Nbin = number of ADF bins

• itypeN = central atom type for Nth ADF histogram (see asterisk form below)

• jtypeN = J atom type for Nth ADF histogram (see asterisk form below)

• ktypeN = K atom type for Nth ADF histogram (see asterisk form below)

• RjinnerN = inner radius of J atom shell for Nth ADF histogram (distance units)

• RjouterN = outer radius of J atom shell for Nth ADF histogram (distance units)

• RkinnerN = inner radius of K atom shell for Nth ADF histogram (distance units)

• RkouterN = outer radius of K atom shell for Nth ADF histogram (distance units)

• zero or one keyword/value pairs may be appended

• keyword = ordinate

ordinate value = degree or radian or cosine
Choose the ordinate parameter for the histogram

## Examples

compute 1 fluid adf 32 1 1 1 0.0 1.2 0.0 1.2 &
1 1 2 0.0 1.2 0.0 1.5 &
1 2 2 0.0 1.5 0.0 1.5 &
2 1 1 0.0 1.2 0.0 1.2 &
2 1 2 0.0 1.5 2.0 3.5 &
2 2 2 2.0 3.5 2.0 3.5
compute 1 fluid adf 32 1*2 1*2 1*2 0.5 3.5
compute 1 fluid adf 32

## Description

Define a computation that calculates one or more angular distribution functions (ADF) for a group of particles. Each ADF is calculated in histogram form by measuring the angle formed by a central atom and two neighbor atoms and binning these angles into Nbin bins. Only neighbors for which Rinner < R < Router are counted, where Rinner and Router are specified separately for the first and second neighbor atom in each requested ADF.

Note

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 a neighbor list, it also means those pairs will not be included in the ADF. This does not apply when using long-range coulomb interactions (coul/long, coul/msm, coul/wolf or similar. One way to get around this would be to set special_bond scaling factors to very tiny numbers that are not exactly zero (e.g. 1.0e-50). Another workaround is to write a dump file, and use the rerun command to compute the ADF for snapshots in the dump file. The rerun script can use a special_bonds command that includes all pairs in the neighbor list.

Note

If you request any outer cutoff Router > force cutoff, or if no pair style is defined, e.g. the rerun command is being used to post-process a dump file of snapshots you must insure ghost atom information out to the largest value of Router + skin is communicated, via the comm_modify cutoff command, else the ADF computation cannot be performed, and LAMMPS will give an error message. The skin value is what is specified with the neighbor command.

The itypeN,jtypeN,ktypeN settings can be specified in one of two ways. An explicit numeric value can be used, as in the 1st example above. Or a wild-card asterisk can be used to specify a range of atom types as in the 2nd example above. 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 itypeN, jtypeN, and ktypeN are single values, as in the 1st example above, this means that the ADF is computed where atoms of type itypeN are the central atom, and neighbor atoms of type jtypeN and ktypeN are forming the angle. If any of itypeN, jtypeN, or ktypeN represent a range of values via the wild-card asterisk, as in the 2nd example above, this means that the ADF is computed where atoms of any of the range of types represented by itypeN are the central atom, and the angle is formed by two neighbors, one neighbor in the range of types represented by jtypeN and another neighbor in the range of types represented by ktypeN.

If no itypeN, jtypeN, ktypeN settings are specified, then LAMMPS will generate a single ADF for all atoms in the group. The inner cutoff is set to zero and the outer cutoff is set to the force cutoff. If no pair_style is specified, there is no force cutoff and LAMMPS will give an error message. Note that in most cases, generating an ADF for all atoms is not a good thing. Such an ADF is both uninformative and extremely expensive to compute. For example, with liquid water with a 10 A force cutoff, there are 80,000 angles per atom. In addition, most of the interesting angular structure occurs for neighbors that are the closest to the central atom, involving just a few dozen angles.

Angles for each ADF are generated by double-looping over the list of neighbors of each central atom I, just as they would be in the force calculation for a three-body potential such as Stillinger-Weber. The angle formed by central atom I and neighbor atoms J and K is included in an ADF if the following criteria are met:

• atoms I,J,K are all in the specified compute group

• the distance between atoms I,J is between Rjinner and Rjouter

• the distance between atoms I,K is between Rkinner and Rkouter

• the type of the I atom matches itypeN (one or a range of types)

• atoms I,J,K are distinct

• the type of the J atom matches jtypeN (one or a range of types)

• the type of the K atom matches ktypeN (one or a range of types)

Each unique angle satisfying the above criteria is counted only once, regardless of whether either or both of the neighbor atoms making up the angle appear in both the J and K lists. It is OK if a particular angle is included in more than one individual histogram, due to the way the itypeN, jtypeN, ktypeN arguments are specified.

The first ADF value for a bin is calculated from the histogram count by dividing by the total number of triples satisfying the criteria, so that the integral of the ADF w.r.t. angle is 1, i.e. the ADF is a probability density function.

The second ADF value is reported as a cumulative sum of all bins up to the current bins, averaged over atoms of type itypeN. It represents the number of angles per central atom with angle less than or equal to the angle of the current bin, analogous to the coordination number radial distribution function.

The ordinate optional keyword determines whether the bins are of uniform angular size from zero to 180 (degree), zero to Pi (radian), or the cosine of the angle uniform in the range [-1,1] (cosine). cosine has the advantage of eliminating the acos() function call, which speeds up the compute by 2-3x, and it is also preferred on physical grounds, because the for uniformly distributed particles in 3D, the angular probability density w.r.t dtheta is sin(theta)/2, while for d(cos(theta)), it is 1/2, Regardless of which ordinate is chosen, the first column of ADF values is normalized w.r.t. the range of that ordinate, so that the integral is 1.

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

compute myADF all adf 32 2 2 2 0.5 3.5 0.5 3.5
fix 1 all ave/time 100 1 100 c_myADF[*] file tmp.adf mode vector

Output info:

This compute calculates a global array with the number of rows = Nbins, and the number of columns = 1 + 2*Ntriples, where Ntriples is the number of I,J,K triples specified. The first column has the bin coordinate (angle-related ordinate at midpoint of bin). Each subsequent column has the two ADF values for a specific set of (itypeN,jtypeN,ktypeN) interactions, as described above. These values can be used by any command that uses a global values from a compute as input. See the Howto output doc page for an overview of LAMMPS output options.

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

The first column of array values is the angle-related ordinate, either the angle in degrees or radians, or the cosine of the angle. Each subsequent pair of columns gives the first and second kinds of ADF for a specific set of (itypeN,jtypeN,ktypeN). The values in the first ADF column are normalized numbers >= 0.0, whose integral w.r.t. the ordinate is 1, i.e. the first ADF is a normalized probability distribution. The values in the second ADF column are also numbers >= 0.0. They are the cumulative density distribution of angles per atom. By definition, this ADF is monotonically increasing from zero to a maximum value equal to the average total number of angles per atom satisfying the ADF criteria.

## Restrictions

The ADF is not computed for neighbors outside the force cutoff, since processors (in parallel) don’t know about atom coordinates for atoms further away than that distance. If you want an ADF for larger distances, you can use the rerun command to post-process a dump file and set the cutoff for the potential to be longer in the rerun script. Note that in the rerun context, the force cutoff is arbitrary, since you aren’t running dynamics and thus are not changing your model.

## Default

The keyword default is ordinate = degree.