# compute hexorder/atom command

## Syntax

``` LAMMPS
compute ID group-ID hexorder/atom keyword values ...
```

-   ID, group-ID are documented in [compute](compute) command

-   hexorder/atom = style name of this compute command

-   one or more keyword/value pairs may be appended

        keyword = *degree* or *nnn* or *cutoff*
          *cutoff* value = distance cutoff
          *nnn* value = number of nearest neighbors
          *degree* value = degree *n* of order parameter

## Examples

``` LAMMPS
compute 1 all hexorder/atom
compute 1 all hexorder/atom degree 4 nnn 4 cutoff 1.2
```

## Description

Define a computation that calculates $q_n$ the bond-orientational order
parameter for each atom in a group. The hexatic (\*n\* = 6) order
parameter was introduced by [Nelson and Halperin](Nelson) as a way to
detect hexagonal symmetry in two-dimensional systems. For each atom,
$q_n$ is a complex number (stored as two real numbers) defined as
follows:

$$q_n = \frac{1}{nnn}\sum_{j = 1}^{nnn} e^{n i \theta({\bf r}_{ij})}$$

where the sum is over the *nnn* nearest neighbors of the central atom.
The angle $\theta$ is formed by the bond vector $r_{ij}$ and the *x*
axis. $\theta$ is calculated only using the *x* and *y* components,
whereas the distance from the central atom is calculated using all three
*x*, *y*, and *z* components of the bond vector. Neighbor atoms not in
the group are included in the order parameter of atoms in the group.

The optional keyword *cutoff* defines the distance cutoff used when
searching for neighbors. The default value, also the maximum allowable
value, is the cutoff specified by the pair style.

The optional keyword *nnn* defines the number of nearest neighbors used
to calculate $q_n$. The default value is 6. If the value is NULL, then
all neighbors up to the distance cutoff are used.

The optional keyword *degree* sets the degree *n* of the order
parameter. The default value is 6. For a perfect hexagonal lattice with
*nnn* = 6, $q_6 = e^{6 i \phi}$ for all atoms, where the constant
$0 < \phi < \frac{\pi}{3}$ depends only on the orientation of the
lattice relative to the *x* axis. In an isotropic liquid, local
neighborhoods may still exhibit weak hexagonal symmetry, but because the
orientational correlation decays quickly with distance, the value of
$\phi$ will be different for different atoms, and so when $q_6$ is
averaged over all the atoms in the system,
$| \left< q_6 \right> | << 1$.

The value of $q_n$ is set to zero for atoms not in the specified compute
group, as well as for atoms that have less than *nnn* neighbors within
the distance cutoff.

The neighbor list needed to compute this quantity is constructed each
time the calculation is performed (i.e. each time a snapshot of atoms is
dumped). Thus it can be inefficient to compute/dump this quantity too
frequently.

:::: note
::: title
Note
:::

If you have a bonded system, then the settings of
[special_bonds](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](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 order parameter. This difficulty can be circumvented by
writing a dump file, and using the [rerun](rerun) command to compute the
order parameter for snapshots in the dump file. The rerun script can use
a [special_bonds](special_bonds) command that includes all pairs in the
neighbor list.
::::

## Output info

This compute calculates a per-atom array with 2 columns, giving the real
and imaginary parts $q_n$, a complex number restricted to the unit disk
of the complex plane (i.e., $\Re(q_n)^2 + \Im(q_n)^2 \le 1$).

These values can be accessed by any command that uses per-atom values
from a compute as input. See the [Howto output](Howto_output) doc page
for an overview of LAMMPS output options.

## 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](Build_package) page for more info.

## Related commands

[compute orientorder/atom](compute_orientorder_atom), [compute
coord/atom](compute_coord_atom), [compute
centro/atom](compute_centro_atom)

## Default

The option defaults are *cutoff* = pair style cutoff, *nnn* = 6,
*degree* = 6

------------------------------------------------------------------------

::: {#Nelson}
**(Nelson)** Nelson, Halperin, Phys Rev B, 19, 2457 (1979).
:::