\(\renewcommand{\AA}{\text{Å}}\)

# pair_style lj/cut/coul/cut command

Accelerator Variants: lj/cut/coul/cut/gpu, lj/cut/coul/cut/kk, lj/cut/coul/cut/omp

# pair_style lj/cut/coul/debye command

Accelerator Variants: lj/cut/coul/debye/gpu, lj/cut/coul/debye/kk, lj/cut/coul/debye/omp

# pair_style lj/cut/coul/dsf command

Accelerator Variants: lj/cut/coul/dsf/gpu, lj/cut/coul/dsf/kk, lj/cut/coul/dsf/omp

# pair_style lj/cut/coul/long command

Accelerator Variants: lj/cut/coul/long/gpu, lj/cut/coul/long/kk, lj/cut/coul/long/intel, lj/cut/coul/long/opt, lj/cut/coul/long/omp

# pair_style lj/cut/coul/msm command

Accelerator Variants: lj/cut/coul/msm/gpu, lj/cut/coul/msm/omp

# pair_style lj/cut/coul/wolf command

Accelerator Variants: lj/cut/coul/wolf/omp

## Syntax

    pair_style style args

- style = lj/cut/coul/cut or lj/cut/coul/debye or lj/cut/coul/dsf or lj/cut/coul/long lj/cut/coul/msm or lj/cut/coul/wolf

- args = list of arguments for a particular style

    lj/cut/coul/cut args = cutoff (cutoff2)
      cutoff = global cutoff for LJ (and Coulombic if only 1 arg) (distance units)
      cutoff2 = global cutoff for Coulombic (optional) (distance units)
    lj/cut/coul/debye args = kappa cutoff (cutoff2)
      kappa = inverse of the Debye length (inverse distance units)
      cutoff = global cutoff for LJ (and Coulombic if only 1 arg) (distance units)
      cutoff2 = global cutoff for Coulombic (optional) (distance units)
    lj/cut/coul/dsf args = alpha cutoff (cutoff2)
      alpha = damping parameter (inverse distance units)
      cutoff = global cutoff for LJ (and Coulombic if only 1 arg) (distance units)
      cutoff2 = global cutoff for Coulombic (distance units)
    lj/cut/coul/long args = cutoff (cutoff2)
      cutoff = global cutoff for LJ (and Coulombic if only 1 arg) (distance units)
      cutoff2 = global cutoff for Coulombic (optional) (distance units)
    lj/cut/coul/msm args = cutoff (cutoff2)
      cutoff = global cutoff for LJ (and Coulombic if only 1 arg) (distance units)
      cutoff2 = global cutoff for Coulombic (optional) (distance units)
    lj/cut/coul/wolf args = alpha cutoff (cutoff2)
      alpha = damping parameter (inverse distance units)
      cutoff = global cutoff for LJ (and Coulombic if only 2 arg) (distance units)
      cutoff2 = global cutoff for Coulombic (optional) (distance units)

## Examples

    pair_style lj/cut/coul/cut 10.0
    pair_style lj/cut/coul/cut 10.0 8.0
    pair_coeff * * 100.0 3.0
    pair_coeff 1 1 100.0 3.5 9.0
    pair_coeff 1 1 100.0 3.5 9.0 9.0

    pair_style lj/cut/coul/debye 1.5 3.0
    pair_style lj/cut/coul/debye 1.5 2.5 5.0
    pair_coeff * * 1.0 1.0
    pair_coeff 1 1 1.0 1.5 2.5
    pair_coeff 1 1 1.0 1.5 2.5 5.0

    pair_style lj/cut/coul/dsf 0.05 2.5 10.0
    pair_coeff * * 1.0 1.0
    pair_coeff 1 1 1.0 1.0 2.5

    pair_style lj/cut/coul/long 10.0
    pair_style lj/cut/coul/long 10.0 8.0
    pair_coeff * * 100.0 3.0
    pair_coeff 1 1 100.0 3.5 9.0

    pair_style lj/cut/coul/msm 10.0
    pair_style lj/cut/coul/msm 10.0 8.0
    pair_coeff * * 100.0 3.0
    pair_coeff 1 1 100.0 3.5 9.0

    pair_style lj/cut/coul/wolf 0.2 5. 10.0
    pair_coeff * * 1.0 1.0
    pair_coeff 1 1 1.0 1.0 2.5

## Description

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

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

\(r_c\) is the cutoff.

Style lj/cut/coul/cut adds a Coulombic pairwise interaction given by

\[E = \frac{C q_i q_j}{\epsilon r} \qquad r < r_c\]

where \(C\) is an energy-conversion constant, \(q_i\) and \(q_j\) are the charges on the two atoms, and \(\epsilon\) is the dielectric constant which can be set by the dielectric command. If one cutoff is specified in the pair_style command, it is used for both the LJ and Coulombic terms. If two cutoffs are specified, they are used as cutoffs for the LJ and Coulombic terms respectively.

Style lj/cut/coul/debye adds an additional exp() damping factor to the Coulombic term, given by

\[E = \frac{C q_i q_j}{\epsilon r} \exp(- \kappa r) \qquad r < r_c\]

where \(\kappa\) is the inverse of the Debye length. This potential is another way to mimic the screening effect of a polar solvent.

Style lj/cut/coul/dsf computes the Coulombic term via the damped shifted force model described in Fennell, given by:

\[E = q_iq_j \left[ \frac{\mbox{erfc} (\alpha r)}{r} - \frac{\mbox{erfc} (\alpha r_c)}{r_c} + \left( \frac{\mbox{erfc} (\alpha r_c)}{r_c^2} + \frac{2\alpha}{\sqrt{\pi}}\frac{\exp (-\alpha^2 r^2_c)}{r_c} \right)(r-r_c) \right] \qquad r < r_c\]

where \(\alpha\) is the damping parameter and erfc() is the complementary error-function. This potential is essentially a short-range, spherically-truncated, charge-neutralized, shifted, pairwise 1/r summation. The potential is based on Wolf summation, proposed as an alternative to Ewald summation for condensed phase systems where charge screening causes electrostatic interactions to become effectively short-ranged. In order for the electrostatic sum to be absolutely convergent, charge neutralization within the cutoff radius is enforced by shifting the potential through placement of image charges on the cutoff sphere. Convergence can often be improved by setting \(\alpha\) to a small non-zero value.

Styles lj/cut/coul/long and lj/cut/coul/msm compute the same Coulombic interactions as style lj/cut/coul/cut except that an additional damping factor is applied to the Coulombic term so it can be used in conjunction with the kspace_style command and its ewald or pppm option. The Coulombic cutoff specified for this style means that pairwise interactions within this distance are computed directly; interactions outside that distance are computed in reciprocal space.

Style lj/cut/coul/wolf adds a Coulombic pairwise interaction via the Wolf summation method, described in Wolf, given by:

\[E_i = \frac{1}{2} \sum_{j \neq i} \frac{q_i q_j \mathrm{erfc}(\alpha r_{ij})}{r_{ij}} + \frac{1}{2} \sum_{j \neq i} \frac{q_i q_j \mathrm{erf}(\alpha r_{ij})}{r_{ij}} \qquad r < r_c\]

where \(\alpha\) is the damping parameter, and erfc() is the complementary error-function terms. This potential is essentially a short-range, spherically-truncated, charge-neutralized, shifted, pairwise 1/r summation. With a manipulation of adding and subtracting a self term (for i = j) to the first and second term on the right-hand-side, respectively, and a small enough \(\alpha\) damping parameter, the second term shrinks and the potential becomes a rapidly-converging real-space summation. With a long enough cutoff and small enough \(\alpha\) parameter, the energy and forces calculated by the Wolf summation method approach those of the Ewald sum. So it is a means of getting effective long-range interactions with a short-range potential.

## Coefficients

For all of the lj/cut/coul pair styles, 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)

- \(\sigma\) (distance units)

- cutoff1 (distance units)

- cutoff2 (distance units)

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

The latter 2 coefficients are optional. If not specified, the global LJ and Coulombic cutoffs specified in the pair_style command are used. If only one cutoff is specified, it is used as the cutoff for both LJ and Coulombic interactions for this type pair. If both coefficients are specified, they are used as the LJ and Coulombic cutoffs for this type pair.

For lj/cut/coul/long and lj/cut/coul/msm only the LJ cutoff can be specified since a Coulombic cutoff cannot be specified for an individual I,J type pair. All type pairs use the same global Coulombic cutoff specified in the pair_style command.

A version of these styles with a soft core, lj/cut/coul/softand lj/cut/coul/long/soft, suitable for use in free energy calculations, is part of the FEP package and is documented with the pair_style */soft styles.

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 and sigma coefficients and cutoff distance for all of the lj/cut pair styles can be mixed. The default mix value is geometric. See the “pair_modify” command for details.

All of the lj/cut pair styles support the pair_modify shift option for the energy of the Lennard-Jones portion of the pair interaction.

The lj/cut/coul/long pair styles support the pair_modify table option since they can tabulate the short-range portion of the long-range Coulombic interaction.

All of the lj/cut pair styles support the pair_modify tail option for adding a long-range tail correction to the energy and pressure for the Lennard-Jones portion of the pair interaction.

All of the lj/cut pair styles write their 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.

The lj/cut/coul/long pair styles support the use of the inner, middle, and outer keywords of the run_style respa command, meaning the pairwise forces can be partitioned by distance at different levels of the rRESPA hierarchy. The other styles only support the pair keyword of run_style respa. See the run_style command for details.

## Restrictions

The lj/cut/coul/long and lj/cut/coul/msm styles are part of the KSPACE package.

The lj/cut/coul/debye, lj/cut/coul/dsf, and lj/cut/coul/wolf styles are part of the EXTRA-PAIR package.

These styles are only enabled if LAMMPS was built with those respective packages. See the Build package page for more info.

## Related commands

pair_coeff

## Default

none

(Wolf) D. Wolf, P. Keblinski, S. R. Phillpot, J. Eggebrecht, J Chem Phys, 110, 8254 (1999).

(Fennell) C. J. Fennell, J. D. Gezelter, J Chem Phys, 124, 234104 (2006).