\(\renewcommand{\AA}{\text{Å}}\)

# pair_style coul/cut command

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

# pair_style coul/cut/global command

Accelerator Variants: coul/cut/omp

# pair_style coul/ctip command

# pair_style coul/debye command

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

# pair_style coul/dsf command

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

# pair_style coul/exclude command

# pair_style coul/long command

Accelerator Variants: coul/long/omp, coul/long/kk, coul/long/gpu

# pair_style coul/msm command

Accelerator Variants: coul/msm/omp

# pair_style coul/streitz command

# pair_style coul/wolf command

Accelerator Variants: coul/wolf/kk, coul/wolf/omp

# pair_style tip4p/cut command

Accelerator Variants: tip4p/cut/omp

# pair_style tip4p/long command

Accelerator Variants: tip4p/long/omp

## Syntax

    pair_style coul/cut cutoff
    pair_style coul/cut/global cutoff
    pair_style coul/ctip alpha cutoff
    pair_style coul/debye kappa cutoff
    pair_style coul/dsf alpha cutoff
    pair_style coul/exclude cutoff
    pair_style coul/long cutoff
    pair_style coul/wolf alpha cutoff
    pair_style coul/streitz cutoff keyword alpha

    * cutoff = global cutoff for Coulombic interactions
    * kappa = Debye length (inverse distance units)
    * alpha = damping parameter (inverse distance units)

    pair_style tip4p/cut otype htype btype atype qdist cutoff
    pair_style tip4p/long otype htype btype atype qdist cutoff

    * otype,htype = atom types (numeric or type label) for TIP4P O and H
    * btype,atype = bond and angle types (numeric or type label) for TIP4P waters
    * qdist = distance from O atom to massless charge (distance units)

## Examples

    pair_style coul/cut 2.5
    pair_coeff * *
    pair_coeff 2 2 3.5

    pair_style coul/ctip 0.30 12.0
    pair_coeff * * NiO.ctip Ni O

    pair_style coul/debye 1.4 3.0
    pair_coeff * *
    pair_coeff 2 2 3.5

    pair_style coul/dsf 0.05 10.0
    pair_coeff * *

    pair_style hybrid/overlay coul/exclude 10.0 ...
    pair_coeff * * coul/exclude

    pair_style coul/long 10.0
    pair_coeff * *

    pair_style coul/msm 10.0
    pair_coeff * *

    pair_style coul/wolf 0.2 9.0
    pair_coeff * *

    pair_style coul/streitz 12.0 ewald
    pair_style coul/streitz 12.0 wolf 0.30
    pair_coeff * * AlO.streitz Al O

    pair_style coul/streitz 12.0 wolf 0.3         # default taper width is zero
    pair_style coul/streitz 12.0 wolf 0.3 2.0
    pair_style coul/streitz 12.0 dsf 0.3          # default taper width is zero
    pair_style coul/streitz 12.0 dsf 0.3 2.0
    pair_coeff * * GaN.streitz Ga N

    pair_style tip4p/cut 1 2 7 8 0.15 12.0
    pair_coeff * *

    pair_style tip4p/long 1 2 7 8 0.15 10.0
    pair_coeff * *

    pair_style tip4p/cut OW HW HW-OW HW-OW-HW 0.15 12.0
    labelmap atom 1 OW 2 HW
    labelmap bond 1 HW-OW
    labelmap angle 1 HW-OW-HW
    pair_coeff * *

## Description

The coul/cut style computes the standard Coulombic interaction potential given by

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

where C is an energy-conversion constant, Qi and Qj are the charges on the two atoms, and \(\epsilon\) is the dielectric constant which can be set by the dielectric command. The cutoff \(r_c\) truncates the interaction distance.

Pair style coul/cut/global computes the same Coulombic interactions as style coul/cut except that it allows only a single global cutoff and thus makes it compatible for use in combination with long-range coulomb styles in hybrid pair styles.

Added in version 19Nov2024.

Style coul/ctip computes the Coulomb interactions as described in Plummer. It uses the the damped shifted model as in style coul/dsf but is further extended to the second derivative of the potential and incorporates empirical charge shielding meant to approximate the more expensive Coulomb integrals used in style coul/streitz. More details can be found in the referenced paper. Like the style coul/streitz, style coul/ctip is a variable charge potential and must be hybridized with a short-range potential via the pair_style hybrid/overlay command. Charge equilibration must be performed with the fix qeq/ctip command. For example:

    pair_style hybrid/overlay eam/fs coul/ctip 0.30 12.0
    pair_coeff * * eam/fs NiO.eam.fs Ni O
    pair_coeff * * coul/ctip NiO.ctip Ni O
    fix 1 all qeq/ctip 1 12.0 1.0e-8 100 coul/ctip cdamp 0.30 maxrepeat 10

See the examples/ctip directory for an example input script using the CTIP potential. An Ni-O CTIP and EAM/FS parameterization are included for use with the example.

Style 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 Debye length. This potential is another way to mimic the screening effect of a polar solvent.

Style coul/dsf computes Coulombic interactions 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. The potential corrects issues in the Wolf model (described below) to provide consistent forces and energies (the Wolf potential is not differentiable at the cutoff) and smooth decay to zero.

Style coul/wolf computes Coulombic interactions 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 erf() and erfc() are error-function and 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.

Style coul/streitz is the Coulomb pair interaction defined as part of the Streitz-Mintmire potential, as described in this paper, in which charge distribution about an atom is modeled as a Slater 1s orbital. More details can be found in the referenced paper. To fully reproduce the published Streitz-Mintmire potential, which is a variable charge potential, style coul/streitz must be used with pair_style eam/alloy (or some other short-range potential that has been parameterized appropriately) via the pair_style hybrid/overlay command. Likewise, charge equilibration must be performed via the fix qeq/slater command. For example:

    pair_style hybrid/overlay coul/streitz 12.0 wolf 0.31 eam/alloy
    pair_coeff * * coul/streitz AlO.streitz Al O
    pair_coeff * * eam/alloy AlO.eam.alloy Al O
    fix 1 all qeq/slater 1 12.0 1.0e-6 100 coul/streitz

The keyword wolf in the coul/streitz command denotes computing Coulombic interactions via Wolf summation. An additional damping parameter is required for the Wolf summation, as described for the coul/wolf potential above. Alternatively, Coulombic interactions can be computed via an Ewald summation. For example:

    pair_style hybrid/overlay coul/streitz 12.0 ewald eam/alloy
    kspace_style ewald 1e-6

Keyword ewald does not need a damping parameter, but a kspace_style must be defined, which can be style ewald or pppm. The Ewald method was used in Streitz and Mintmire’s original paper, but a Wolf summation offers a speed-up in some cases.

For the fix qeq/slater command, the qfile can be a filename that contains QEq parameters as discussed on the fix qeq command doc page. Alternatively qfile can be replaced by “coul/streitz”, in which case the fix will extract QEq parameters from the coul/streitz pair style itself.

See the `examples/streitz` directory for an example input script that uses the Streitz-Mintmire potential. The potentials directory has the `AlO.eam.alloy` and `AlO.streitz` potential files used by the example.

Note that the Streitz-Mintmire potential is generally used for oxides, but there is no conceptual problem with extending it to nitrides and carbides (such as SiC, TiN). Pair coul/streitz used by itself or with any other pair style such as EAM, MEAM, Tersoff, or LJ in hybrid/overlay mode. To do this, you would need to provide a Streitz-Mintmire parameterization for the material being modeled.

Changed in version 11Feb2026.

In previous versions of LAMMPS, the real-space summations of Coulomb interactions were done by replacing 1/r using a damped potential erfc(alpha*r)/r with the parameter alpha controlling the rate of decay. However, any finite value of alpha leads to a jump at the cutoff, which interferes with equilibration if atoms move across the cutoff. The charge-neutralized potential of (Wolf et al.) (wolf) and its extension by (Fennell and Gezelter) (dsf) solve this problem. An extension was implemented to specify the width of taper (see (Mei et al.)) to smoothly terminate the Coulomb integrals at the cutoff. This is done by specifying the optional arguments wolf and dsf with the value representing the width of taper that smoothly terminates the Coulomb integrals. For example, if the cutoff is 8 A and the taper width is 2 A, the Coulomb integrals are smoothly rescaled from their actual value at r=6 A to zero at r=8 A. For backward compatibility, the default taper width is zero.

An implementation of the Streitz-Mintmire potential for GaN due to (Groger and Fikar) can be found in the examples/streitz directory. The electrostatic parameters of Ga and N are stored in file GaN.streitz and the short-range tersoff/mod potential in the file GaN.streitz+tersoff.mod. The total potential must be specified as:

    pair_style hybrid/overlay tersoff/mod coul/streitz 12.0 dsf 0.3 2.0
    pair_coeff * * tersoff/mod GaN.streitz+tersoff.mod Ga N
    pair_coeff * * coul/streitz GaN.streitz Ga N

where the last three parameters specify the method of calculation of Coulomb interactions (ewald, wolf or dsf), the value of alpha, and the width of taper to smoothly terminate the Coulomb integrals.

Pair style coul/exclude computes Coulombic interactions like coul/cut but only applies them to excluded pairs using a scaling factor of \(\gamma - 1.0\) with \(\gamma\) being the factor assigned to that excluded pair via the special_bonds coul setting. With this it is possible to treat Coulomb interactions for molecular systems with kspace style scafacos, which always computes the full Coulomb interactions without exclusions. Pair style coul/exclude will then subtract the excluded interactions accordingly. So to achieve the same forces as with `pair_style lj/cut/coul/long 12.0` with `kspace_style pppm 1.0e-6`, one would use `pair_style hybrid/overlay lj/cut 12.0 coul/exclude 12.0` with `kspace_style scafacos p3m 1.0e-6`.

Styles coul/long and coul/msm compute the same Coulombic interactions as style coul/cut except that an additional damping factor is applied 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.

Styles tip4p/cut and tip4p/long implement the Coulomb part of the TIP4P water model of (Jorgensen), which introduces a massless site located a short distance away from the oxygen atom along the bisector of the HOH angle. The atomic types of the oxygen and hydrogen atoms, the bond and angle types for OH and HOH interactions, and the distance to the massless charge site are specified as pair_style arguments. Style tip4p/cut uses a global cutoff for Coulomb interactions; style tip4p/long is for use with a long-range Coulombic solver (Ewald or PPPM).

Note

For each TIP4P water molecule in your system, the atom IDs for the O and 2 H atoms must be consecutive, with the O atom first. This is to enable LAMMPS to “find” the 2 H atoms associated with each O atom. For example, if the atom ID of an O atom in a TIP4P water molecule is 500, then its 2 H atoms must have IDs 501 and 502.

Note

If using type labels, the type labels must be defined before calling the pair_coeff command.

See the Howto tip4p page for more information on how to use the TIP4P pair styles and lists of parameters to set. Note that the neighbor list cutoff for Coulomb interactions is effectively extended by a distance 2*qdist when using the TIP4P pair style, to account for the offset distance of the fictitious charges on O atoms in water molecules. Thus it is typically best in an efficiency sense to use a LJ cutoff >= Coulombic cutoff + 2*qdist, to shrink the size of the neighbor list. This leads to slightly larger cost for the long-range calculation, so you can test the trade-off for your model.

Note that these potentials are designed to be combined with other pair potentials via the pair_style hybrid/overlay command. This is because they have no repulsive core. Hence if they are used by themselves, there will be no repulsion to keep two oppositely charged particles from moving arbitrarily close to each other.

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 or restart files read by the read_data or read_restart commands, or by mixing as described below:

- cutoff (distance units)

For coul/cut and coul/debye the cutoff coefficient is optional. If it is not used (as in some of the examples above), the default global value specified in the pair_style command is used.

For coul/cut/global, coul/long and coul/msm no cutoff can be specified for an individual I,J type pair via the pair_coeff command. All type pairs use the same global Coulomb cutoff specified in the pair_style command.

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 cutoff distance for the coul/cut style can be mixed. The default mix value is geometric. See the “pair_modify” command for details.

The pair_modify shift option is not relevant for these pair styles.

The coul/long style supports the pair_modify table option for tabulation of the short-range portion of the long-range Coulombic interaction.

These pair styles do not support the pair_modify tail option for adding long-range tail corrections to energy and pressure.

These 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.

These pair styles can only be used via the pair keyword of the run_style respa command. They do not support the inner, middle, outer keywords.

## Restrictions

The coul/long, coul/msm, coul/streitz, and tip4p/long styles are part of the KSPACE package. The coul/cut/global, coul/exclude, and coul/ctip styles are part of the EXTRA-PAIR package. The tip4p/cut style is part of the MOLECULE package. A pair style is only enabled if LAMMPS was built with its corresponding package. See the Build package page for more info.

## Related commands

pair_coeff, pair_style hybrid/overlay, kspace_style

## 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).

(Streitz) F. H. Streitz, J. W. Mintmire, Phys Rev B, 50, 11996-12003 (1994).

(Plummer) G. Plummer, J. P. Tavenner, M. I. Mendelev, Z. Wu, J. W. Lawson, J Chemical Physics, 162, 054709 (2025).

(Jorgensen) Jorgensen, Chandrasekhar, Madura, Impey, Klein, J Chem Phys, 79, 926 (1983).

(Mei) J. Mei, J. W. Davenport, G. W. Fernando, Phys. Rev. B 43, 4653 (1991).

(Groger) R. Groger, J. Fikar, Acta Mater. (2026) in review.