\(\renewcommand{\AA}{\text{Å}}\)

# pair_style lj/cut/sphere command

Accelerator Variant: lj/cut/sphere/omp

## Syntax

    pair_style style args

- style = lj/cut/sphere

- args = list of arguments for a particular style

    lj/cut/sphere args = cutoff ratio
      cutoff = global cutoff ratio for Lennard Jones interactions (unitless)

## Examples

    pair_style lj/cut/sphere 2.5
    pair_coeff * * 1.0
    pair_coeff 1 1 1.1 2.8

## Description

Added in version 15Jun2023.

The lj/cut/sphere style compute the standard 12/6 Lennard-Jones potential, given by

\[E = 4 \epsilon \left[ \left(\frac{\sigma_{ij}}{r}\right)^{12} - \left(\frac{\sigma_{ij}}{r}\right)^6 \right] \qquad r < r_c * \sigma_{ij}\]

\(r_c\) is the cutoff ratio.

This is the same potential function used by the lj/cut pair style, but the \(\sigma_{ij}\) parameter is not set as a per-type parameter via the pair_coeff command. Instead it is calculated individually for each pair using the per-atom diameter attribute of atom_style sphere for the two atoms as \(\sigma_{i}\) and \(\sigma_{j}\); \(\sigma_{ij}\) is then computed by the mixing rule for pair coefficients as set by the pair_modify mix command (defaults to geometric mixing). The cutoff is not specified as a distance, but as ratio that is internally multiplied by \(\sigma_{ij}\) to obtain the actual cutoff for each pair of atoms.

Note that \(\sigma_{ij}\) is defined in the LJ formula above as the zero-crossing distance for the potential, not as the energy minimum which is at \(2^{\frac{1}{6}} \sigma_{ij}\).

Notes on cutoffs, neighbor lists, and efficiency

If your system is mildly polydisperse, meaning the ratio of the diameter of the largest particle to the smallest is less than 2.0, then the neighbor lists built by the code should be reasonably efficient. Which means they will not contain too many particle pairs that do not interact. However, if your system is highly polydisperse (ratio > 2.0), the neighbor list build and force computations may be inefficient. There are two ways to try and speed up the simulations.

The first is to assign atoms to different atom types so that atoms of each type are similar in size. E.g. if particle diameters range from 1 to 5 use 4 atom types, ensuring atoms of type 1 have diameters from 1.0-2.0, type 2 from 2.0-3.0, etc. This will reduce the number of non-interacting pairs in the neighbor lists and thus reduce the time spent on computing pairwise interactions.

The second is to use the neighbor multi command which enabled a different algorithm for building neighbor lists. This will also require that you assign multiple atom types according to diameters, but will in addition use a more efficient size-dependent strategy to construct the neighbor lists and thus reduce the time spent on building neighbor lists.

Here are example input script commands using both ideas for a highly polydisperse system:

    units           lj
    atom_style      sphere
    lattice         fcc 0.8442
    region          box block 0 10 0 10 0 10
    create_box      2 box
    create_atoms    1 box

    # create atoms with random diameters from bimodal distribution
    variable switch atom random(0.0,1.0,345634)
    variable diam atom (v_switch<0.75)*normal(0.4,0.075,325)+(v_switch>=0.7)*normal(1.2,0.2,453)
    set group all diameter v_diam

    # assign type 2 to atoms with diameter > 0.6
    variable large atom (2.0*radius)>0.6
    group large variable large
    set group large type 2

    pair_style      lj/cut/sphere 2.5
    pair_coeff      * * 1.0

    neighbor 0.3 multi

Using multiple atom types speeds up the calculation for this example by more than a factor of 2, and using the multi-style neighbor list build causes an additional speedup of about 20 percent.

## Coefficients

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, or by mixing as described below:

- \(\epsilon\) (energy units)

- LJ cutoff ratio (unitless) (optional)

The last coefficient is optional. If not specified, the global LJ cutoff ratio specified in the pair_style command is used.

If a repulsive only LJ interaction is desired, the coefficient for the cutoff ratio should be set to the minimum of the LJ potential using `$(2.0^(1.0/6.0))`

Styles with a gpu, intel, kk, omp, or opt suffix are functionally the same as the corresponding style without the suffix. They have been optimized to run faster, depending on your available hardware, as discussed on the Accelerator packages page. The accelerated styles take the same arguments and should produce the same results, except for round-off and precision issues.

These accelerated styles are part of the GPU, INTEL, KOKKOS, OPENMP, and OPT packages, respectively. They are only enabled if LAMMPS was built with those packages. See the Build package page for more info.

You can specify the accelerated styles explicitly in your input script by including their suffix, or you can use the -suffix command-line switch when you invoke LAMMPS, or you can use the suffix command in your input script.

See the Accelerator packages page for more instructions on how to use the accelerated styles effectively.

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

For atom type pairs I,J and I != J, the epsilon coefficients and cutoff ratio for the lj/cut/sphere pair style can be mixed. The default mixing style is geometric. See the pair_modify command for details.

The lj/cut/sphere pair style supports the pair_modify shift option for the energy of the Lennard-Jones portion of the pair interaction.

The lj/cut/sphere pair style does not support the pair_modify tail option for adding a long-range tail corrections to the energy and pressure.

The lj/cut/sphere pair style writes its information to binary restart files, so pair_style and pair_coeff commands do not need to be specified in an input script that reads a restart file.

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

The lj/cut/sphere pair style is only enabled if LAMMPS was built with the EXTRA-PAIR package. See the Build package page for more info.

The lj/cut/sphere pair style does not support the sixthpower mixing rule.

## Related commands

- pair_coeff

- pair_style lj/cut

- pair_style lj/expnd/sphere

## Default

none