# compute ptm/atom command

## Syntax

``` LAMMPS
compute ID group-ID ptm/atom structures threshold group2-ID
```

-   ID, group-ID are documented in [compute](compute) command
-   ptm/atom = style name of this compute command
-   structures = *default* or *all* or any hyphen-separated combination
    of *fcc*, *hcp*, *bcc*, *ico*, *sc*, *dcub*, *dhex*, or *graphene* =
    structure types to search for
-   threshold = lattice distortion threshold (RMSD)
-   group2-ID determines which group is used for neighbor selection
    (optional, default \"all\")

## Examples

``` LAMMPS
compute 1 all ptm/atom default 0.1 all
compute 1 all ptm/atom fcc-hcp-dcub-dhex 0.15 all
compute 1 all ptm/atom all 0
```

## Description

Define a computation that determines the local lattice structure around
an atom using the PTM (Polyhedral Template Matching) method. The PTM
method is described in [(Larsen)](Larsen).

Currently, there are seven lattice structures PTM recognizes:

-   fcc = 1
-   hcp = 2
-   bcc = 3
-   ico (icosahedral) = 4
-   sc (simple cubic) = 5
-   dcub (diamond cubic) = 6
-   dhex (diamond hexagonal) = 7
-   graphene = 8

The value of the PTM structure will be 0 for unknown types and $-1$ for
atoms not in the specified compute group. The choice of structures to
search for can be specified using the \"structures\" argument, which is
a hyphen-separated list of structure keywords. Two convenient pre-set
options are provided:

-   default: fcc-hcp-bcc-ico
-   all: fcc-hcp-bcc-ico-sc-dcub-dhex-graphene

The \'default\' setting detects the same structures as the Common
Neighbor Analysis method. The \'all\' setting searches for all structure
types. A performance penalty is incurred for the diamond and graphene
structures, so it is not recommended to use this option if it is known
that the simulation does not contain these structures.

PTM identifies structures using two steps. First, a graph isomorphism
test is used to identify potential structure matches. Next, the
deviation is computed between the local structure (in the simulation)
and a template of the ideal lattice structure. The deviation is
calculated as:

$$\text{RMSD}(\mathbf{u}, \mathbf{v})
 = \min_{s, \mathbf{Q}} \sqrt{\frac{1}{N} \sum\limits_{i=1}^{N}
{\left\lVert s[\vec{u}_i - \mathbf{\bar{u}}]
              - \mathbf{Q} \cdot \vec{v}_i \right\rVert}^2}$$

Here, $\vec u$ and $\vec v$ contain the coordinates of the local and
ideal structures respectively, $s$ is a scale factor, and $\mathbf Q$ is
a rotation. The best match is identified by the lowest RMSD value, using
the optimal scaling, rotation, and correspondence between the points.

The *threshold* keyword sets an upper limit on the maximum permitted
deviation before a local structure is identified as disordered. Typical
values are in the range 0.1\--0.15, but larger values may be desirable
at higher temperatures. A value of 0 is equivalent to infinity and can
be used if no threshold is desired.

The neighbor list needed to compute this quantity is constructed each
time the calculation is performed (e.g., each time a snapshot of atoms
is dumped). Thus it can be inefficient to compute/dump this quantity too
frequently or to have multiple compute/dump commands, each with a
*ptm/atom* style. By default the compute processes **all** neighbors
unless the optional *group2-ID* argument is given, then only members of
that group are considered as neighbors.

## Output info

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

Results are stored in the per-atom array in the following order:

-   type
-   rmsd
-   interatomic distance
-   qw
-   qx
-   qy
-   qz

The type is a number from $-1$ to 8. The rmsd is a positive real number.
The interatomic distance is computed from the scale factor in the RMSD
equation. The $(qw,qx,qy,qz)$ parameters represent the orientation of
the local structure in quaternion form. The reference coordinates for
each template (from which the orientation is determined) can be found in
the *ptm_constants.h* file in the PTM source directory. For atoms that
are not within the compute group-ID, all values are set to zero.

## Restrictions

This fix is part of the PTM 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 centro/atom](compute_centro_atom) [compute
cna/atom](compute_cna_atom)

## Default

none

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

::: {#Larsen}
**(Larsen)** Larsen, Schmidt, Schiotz, Modelling Simul Mater Sci Eng,
24, 055007 (2016).
:::