# pair_style tri/lj command

## Syntax

``` LAMMPS
pair_style tri/lj cutoff
```

cutoff = global cutoff for interactions (distance units)

## Examples

``` LAMMPS
pair_style tri/lj 3.0
pair_coeff * * 1.0 1.0
pair_coeff 1 1 1.0 1.5 2.5
```

## Description

Style *tri/lj* treats particles which are triangles as a set of small
spherical particles that tile the triangle surface as explained below.
Interactions between two triangles, each with N1 and N2 spherical
particles, are calculated as the pairwise sum of N1\*N2 Lennard-Jones
interactions. Interactions between a triangle with N spherical particles
and a point particle are treated as the pairwise sum of N Lennard-Jones
interactions. See the [pair_style lj/cut](pair_lj) doc page for the
definition of Lennard-Jones interactions.

The cutoff distance for an interaction between 2 triangles, or between a
triangle and a point particle, is calculated from the position of the
triangle (its centroid), not between pairs of individual spheres
comprising the triangle. Thus an interaction is either calculated in its
entirety or not at all.

The set of non-overlapping spherical particles that represent a
triangle, for purposes of this pair style, are generated in the
following manner. Assume the triangle is of type I, and sigma_II has
been specified. We want a set of spheres with centers in the plane of
the triangle, none of them larger in diameter than sigma_II, which
completely cover the triangle\'s area, but with minimal overlap and a
minimal total number of spheres. This is done in a recursive manner.
Place a sphere at the centroid of the original triangle. Calculate what
diameter it must have to just cover all 3 corner points of the triangle.
If that diameter is equal to or smaller than sigma_II, then include a
sphere of the calculated diameter in the set of covering spheres. It the
diameter is larger than sigma_II, then split the triangle into 2
triangles by bisecting its longest side. Repeat the process on each
sub-triangle, recursing as far as needed to generate a set of covering
spheres. When finished, the original criteria are met, and the set of
covering spheres should be near minimal in number and overlap, at least
for input triangles with a reasonable aspect-ratio.

The LJ interaction between 2 spheres on different triangles of types I,J
is computed with an arithmetic mixing of the sigma values of the 2
spheres and using the specified epsilon value for I,J atom types. Note
that because the sigma values for triangles spheres is computed using
only sigma_II values, specific to the triangles\'s type, this means that
any specified sigma_IJ values (for I != J) are effectively ignored.

For style *tri/lj*, the following coefficients must be defined for each
pair of atoms types via the [pair_coeff](pair_coeff) command as in the
examples above, or in the data file or restart files read by the
[read_data](read_data) or [read_restart](read_restart) commands:

-   epsilon (energy units)
-   sigma (distance units)
-   cutoff (distance units)

The last coefficient is optional. If not specified, the global cutoff is
used.

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

## Mixing, shift, table, tail correction, restart, rRESPA info

For atom type pairs I,J and I != J, the epsilon and sigma coefficients
and cutoff distance for all of this pair style can be mixed. The default
mix value is *geometric*. See the \"pair_modify\" command for details.

This pair style does not support the [pair_modify](pair_modify) shift,
table, and tail options.

This pair style does not write its information to [binary restart
files](restart).

This pair style can only be used via the *pair* keyword of the
[run_style respa](run_style) command. It does not support the *inner*,
*middle*, *outer* keywords.

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

## Restrictions

This style is part of the ASPHERE package. It is only enabled if LAMMPS
was built with that package. See the [Build package](Build_package) page
for more info.

Defining particles to be triangles so they participate in tri/tri or
tri/particle interactions requires the use the [atom_style
tri](atom_style) command.

## Related commands

[pair_coeff](pair_coeff), [pair_style line/lj](pair_line_lj)

## Default

none