\(\renewcommand{\AA}{\text{Å}}\)

# pair_style tri/lj command

## Syntax

    pair_style tri/lj cutoff

cutoff = global cutoff for interactions (distance units)

## Examples

    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 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 command as in the examples above, or in the data file or restart files read by the read_data or 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 shift, table, and tail options.

This pair style does not write its information to binary restart files.

This pair style can only be used via the pair keyword of the run_style respa 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 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 command.

## Related commands

pair_coeff, pair_style line/lj

## Default

none