\(\renewcommand{\AA}{\text{Å}}\)

# kspace_style command

## Syntax

    kspace_style style value

- style = none or ewald or ewald/dipole or ewald/dipole/spin or ewald/disp or ewald/disp/dipole or ewald/omp or ewald/electrode or pppm or pppm/cg or pppm/disp or pppm/tip4p or pppm/stagger or pppm/disp/tip4p or pppm/gpu or pppm/intel or pppm/disp/intel or pppm/kk or pppm/omp or pppm/cg/omp or pppm/disp/tip4p/omp or pppm/tip4p/omp or pppm/dielectic or pppm/disp/dielectric or pppm/electrode or pppm/electrode/intel or msm or msm/cg or msm/omp or msm/cg/omp or msm/dielectric or scafacos or zero

      none value = none
      ewald value = accuracy
        accuracy = desired relative error in forces
      ewald/dipole value = accuracy
        accuracy = desired relative error in forces
      ewald/dipole/spin value = accuracy
        accuracy = desired relative error in forces
      ewald/disp value = accuracy
        accuracy = desired relative error in forces
      ewald/disp/dipole value = accuracy
        accuracy = desired relative error in forces
      ewald/omp value = accuracy
        accuracy = desired relative error in forces
      ewald/electrode value = accuracy
        accuracy = desired relative error in forces
      pppm value = accuracy
        accuracy = desired relative error in forces
      pppm/cg values = accuracy (smallq)
        accuracy = desired relative error in forces
        smallq = cutoff for charges to be considered (optional) (charge units)
      pppm/dipole value = accuracy
        accuracy = desired relative error in forces
      pppm/dipole/spin value = accuracy
        accuracy = desired relative error in forces
      pppm/disp value = accuracy
        accuracy = desired relative error in forces
      pppm/tip4p value = accuracy
        accuracy = desired relative error in forces
      pppm/disp/tip4p value = accuracy
        accuracy = desired relative error in forces
      pppm/gpu value = accuracy
        accuracy = desired relative error in forces
      pppm/intel value = accuracy
        accuracy = desired relative error in forces
      pppm/disp/intel value = accuracy
        accuracy = desired relative error in forces
      pppm/kk value = accuracy
        accuracy = desired relative error in forces
      pppm/omp value = accuracy
        accuracy = desired relative error in forces
      pppm/cg/omp values = accuracy (smallq)
        accuracy = desired relative error in forces
        smallq = cutoff for charges to be considered (optional) (charge units)
      pppm/disp/omp value = accuracy
        accuracy = desired relative error in forces
      pppm/tip4p/omp value = accuracy
        accuracy = desired relative error in forces
      pppm/disp/tip4p/omp value = accuracy
        accuracy = desired relative error in forces
      pppm/stagger value = accuracy
        accuracy = desired relative error in forces
      pppm/dielectric value = accuracy
        accuracy = desired relative error in forces
      pppm/disp/dielectric value = accuracy
        accuracy = desired relative error in forces
      pppm/electrode value = accuracy
        accuracy = desired relative error in forces
      pppm/electrode/intel value = accuracy
        accuracy = desired relative error in forces
      msm value = accuracy
        accuracy = desired relative error in forces
      msm/cg value = accuracy (smallq)
        accuracy = desired relative error in forces
        smallq = cutoff for charges to be considered (optional) (charge units)
      msm/omp value = accuracy
        accuracy = desired relative error in forces
      msm/cg/omp value = accuracy (smallq)
        accuracy = desired relative error in forces
        smallq = cutoff for charges to be considered (optional) (charge units)
      msm/dielectric value = accuracy
        accuracy = desired relative error in forces
      scafacos values = method accuracy
        method = fmm or p2nfft or p3m or ewald or direct
        accuracy = desired relative error in forces
      zero value = accuracy
        accuracy = desired relative error in forces

## Examples

    kspace_style pppm 1.0e-4
    kspace_style pppm/cg 1.0e-5 1.0e-6
    kspace_style msm 1.0e-4
    kspace_style scafacos fmm 1.0e-4
    kspace_style none
    kspace_style zero 1.0e-6

Used in input scripts:

>     examples/peptide/in.peptide

## Description

Define a long-range solver for LAMMPS to use each timestep to compute long-range Coulombic interactions or long-range \(1/r^6\) interactions. Most of the long-range solvers perform their computation in K-space, hence the name of this command.

When such a solver is used in conjunction with an appropriate pair style, the cutoff for Coulombic or \(1/r^N\) interactions is effectively infinite. If the Coulombic case, this means each charge in the system interacts with charges in an infinite array of periodic images of the simulation domain.

Note that using a long-range solver requires use of a matching pair style to perform consistent short-range pairwise calculations. This means that the name of the pair style contains a matching keyword to the name of the KSpace style, as in this table:

Pair style | KSpace style
coul/long | ewald or pppm
coul/msm | msm
lj/long or buck/long | disp (for dispersion)
tip4p/long | tip4p
dipole/long | dipole

The ewald style performs a standard Ewald summation as described in any solid-state physics text.

The ewald/disp style adds a long-range dispersion sum option for \(1/r^6\) potentials and is useful for simulation of interfaces (Veld). It also performs standard Coulombic Ewald summations, but in a more efficient manner than the ewald style. The \(1/r^6\) capability means that Lennard-Jones or Buckingham potentials can be used without a cutoff, i.e. they become full long-range potentials.

The ewald/disp/dipole style can also be used with point-dipoles, see (Toukmaji).

The ewald/dipole style adds long-range standard Ewald summations for dipole-dipole interactions, see (Toukmaji).

The ewald/dipole/spin style adds long-range standard Ewald summations for magnetic dipole-dipole interactions between magnetic spins.

The pppm style invokes a particle-particle particle-mesh solver (Hockney) which maps atom charge to a 3d mesh, uses 3d FFTs to solve Poisson’s equation on the mesh, then interpolates electric fields on the mesh points back to the atoms. It is closely related to the particle-mesh Ewald technique (PME) (Darden) used in AMBER and CHARMM. The cost of traditional Ewald summation scales as \(N^{\frac{3}{2}}\) where \(N\) is the number of atoms in the system. The PPPM solver scales as \(N \log{N}\) due to the FFTs, so it is almost always a faster choice (Pollock).

The pppm/cg style is identical to the pppm style except that it has an optimization for systems where most particles are uncharged. Similarly the msm/cg style implements the same optimization for msm. The optional smallq argument defines the cutoff for the absolute charge value which determines whether a particle is considered charged or not. Its default value is 1.0e-5.

The pppm/dipole style invokes a particle-particle particle-mesh solver for dipole-dipole interactions, following the method of (Cerda).

The pppm/dipole/spin style invokes a particle-particle particle-mesh solver for magnetic dipole-dipole interactions between magnetic spins.

The pppm/tip4p style is identical to the pppm style except that it adds a charge at the massless fourth site in each TIP4P water molecule. It should be used with pair styles with a tip4p/long in their style name.

The pppm/stagger style performs calculations using two different meshes, one shifted slightly with respect to the other. This can reduce force aliasing errors and increase the accuracy of the method for a given mesh size. Or a coarser mesh can be used for the same target accuracy, which saves CPU time. However, there is a trade-off since FFTs on two meshes are now performed which increases the computation required. See (Cerutti), (Neelov), and (Hockney) for details of the method.

For high relative accuracy, using staggered PPPM allows the mesh size to be reduced by a factor of 2 in each dimension as compared to regular PPPM (for the same target accuracy). This can give up to a 4x speedup in the KSpace time (8x less mesh points, 2x more expensive). However, for low relative accuracy, the staggered PPPM mesh size may be essentially the same as for regular PPPM, which means the method will be up to 2x slower in the KSpace time (simply 2x more expensive). For more details and timings, see the Speed tips doc page.

Note

Using pppm/stagger may not give the same increase in the accuracy of energy and pressure as it does in forces, so some caution must be used if energy and/or pressure are quantities of interest, such as when using a barostat.

The pppm/disp and pppm/disp/tip4p styles add a mesh-based long-range dispersion sum option for 1/r^6 potentials (Isele-Holder), similar to the ewald/disp style. The 1/r^6 capability means that Lennard-Jones or Buckingham potentials can be used without a cutoff, i.e. they become full long-range potentials.

For these styles, you will possibly want to adjust the default choice of parameters by using the kspace_modify command. This can be done by either choosing the Ewald and grid parameters, or by specifying separate accuracies for the real and kspace calculations. When not making any settings, the simulation will stop with an error message. Further information on the influence of the parameters and how to choose them is described in (Isele-Holder), (Isele-Holder2) and the Howto dispersion doc page.

Note

All of the PPPM styles can be used with single-precision FFTs by using the compiler switch -DFFT_SINGLE for the FFT_INC setting in your low-level Makefile. This setting also changes some of the PPPM operations (e.g. mapping charge to mesh and interpolating electric fields to particles) to be performed in single precision. This option can speed-up long-range calculations, particularly in parallel or on GPUs. The use of the -DFFT_SINGLE flag is discussed on the Build settings doc page. MSM does not currently support the -DFFT_SINGLE compiler switch.

The electrode styles add methods that are required for the constant potential method implemented in fix electrode/*. The styles ewald/electrode, pppm/electrode and pppm/electrode/intel are available. These styles do not support the kspace_modify slab nozforce command.

The msm style invokes a multi-level summation method MSM solver, (Hardy) or (Hardy2), which maps atom charge to a 3d mesh, and uses a multi-level hierarchy of coarser and coarser meshes on which direct Coulomb solvers are done. This method does not use FFTs and scales as \(N\). It may therefore be faster than the other K-space solvers for relatively large problems when running on large core counts. MSM can also be used for non-periodic boundary conditions and for mixed periodic and non-periodic boundaries.

MSM is most competitive versus Ewald and PPPM when only relatively low accuracy forces, about 1e-4 relative error or less accurate, are needed. Note that use of a larger Coulombic cutoff (i.e. 15 Angstroms instead of 10 Angstroms) provides better MSM accuracy for both the real space and grid computed forces.

Currently calculation of the full pressure tensor in MSM is expensive. Using the kspace_modify pressure/scalar yes command provides a less expensive way to compute the scalar pressure (Pxx + Pyy + Pzz)/3.0. The scalar pressure can be used, for example, to run an isotropic barostat. If the full pressure tensor is needed, then calculating the pressure at every timestep or using a fixed pressure simulation with MSM will cause the code to run slower.

The scafacos style is a wrapper on the ScaFaCoS Coulomb solver library which provides a variety of solver methods which can be used with LAMMPS. The paper by (Sutman) gives an overview of ScaFaCoS.

ScaFaCoS was developed by a consortium of German research facilities with a BMBF (German Ministry of Science and Education) funded project in 2009-2012. Participants of the consortium were the Universities of Bonn, Chemnitz, Stuttgart, and Wuppertal as well as the Forschungszentrum Juelich.

The library is available for download at “http://www.scafacos.de/” or can be cloned from the git-repository “https://github.com/scafacos/scafacos”.

In order to use this KSpace style, you must download and build the ScaFaCoS library, then build LAMMPS with the SCAFACOS package installed package which links LAMMPS to the ScaFaCoS library. See details on this page.

Note

Unlike other KSpace solvers in LAMMPS, ScaFaCoS computes all Coulombic interactions, both short- and long-range. Thus you should NOT use a Coulombic pair style when using kspace_style scafacos. This also means the total Coulombic energy (short- and long-range) will be tallied for thermodynamic output command as part of the elong keyword; the ecoul keyword will be zero.

Note

See the current restriction below about use of ScaFaCoS in LAMMPS with molecular charged systems or the TIP4P water model.

The specified method determines which ScaFaCoS algorithm is used. These are the ScaFaCoS methods currently available from LAMMPS:

- fmm = Fast Multi-Pole method

- p2nfft = FFT-based Coulomb solver

- ewald = Ewald summation

- direct = direct O(N^2) summation

- p3m = PPPM

We plan to support additional ScaFaCoS solvers from LAMMPS in the future. For an overview of the included solvers, refer to (Sutmann)

The specified accuracy is similar to the accuracy setting for other LAMMPS KSpace styles, but is passed to ScaFaCoS, which can interpret it in different ways for different methods it supports. Within the ScaFaCoS library the accuracy is treated as a tolerance level (either absolute or relative) for the chosen quantity, where the quantity can be either the Columic field values, the per-atom Columic energy or the total Columic energy. To select from these options, see the kspace_modify scafacos accuracy doc page.

The kspace_modify scafacos command also explains other ScaFaCoS options currently exposed to LAMMPS.

Added in version 12Jun2025.

The zero style does not do any calculations, but is compatible with all pair styles that require some version of a kspace style. The accuracy argument is required for some internal calculations but has no impact of forces or energy, since those will always be zero.

The specified accuracy determines the relative RMS error in per-atom forces calculated by the long-range solver. It is set as a dimensionless number, relative to the force that two unit point charges (e.g. 2 monovalent ions) exert on each other at a distance of 1 Angstrom. This reference value was chosen as representative of the magnitude of electrostatic forces in atomic systems. Thus an accuracy value of 1.0e-4 means that the RMS error will be a factor of 10000 smaller than the reference force.

The accuracy setting is used in conjunction with the pairwise cutoff to determine the number of K-space vectors for style ewald or the grid size for style pppm or msm.

Note that style pppm only computes the grid size at the beginning of a simulation, so if the length or triclinic tilt of the simulation cell increases dramatically during the course of the simulation, the accuracy of the simulation may degrade. Likewise, if the kspace_modify slab option is used with shrink-wrap boundaries in the z-dimension, and the box size changes dramatically in z. For example, for a triclinic system with all three tilt factors set to the maximum limit, the PPPM grid should be increased roughly by a factor of 1.5 in the y direction and 2.0 in the z direction as compared to the same system using a cubic orthogonal simulation cell. One way to handle this issue if you have a long simulation where the box size changes dramatically, is to break it into shorter simulations (multiple run commands). This works because the grid size is re-computed at the beginning of each run. Another way to ensure the described accuracy requirement is met is to run a short simulation at the maximum expected tilt or length, note the required grid size, and then use the kspace_modify mesh command to manually set the PPPM grid size to this value for the long run. The simulation then will be “too accurate” for some portion of the run.

RMS force errors in real space for ewald and pppm are estimated using equation 18 of (Kolafa), which is also referenced as equation 9 of (Petersen). RMS force errors in K-space for ewald are estimated using equation 11 of (Petersen), which is similar to equation 32 of (Kolafa). RMS force errors in K-space for pppm are estimated using equation 38 of (Deserno). RMS force errors for msm are estimated using ideas from chapter 3 of (Hardy), with equation 3.197 of particular note. When using msm with non-periodic boundary conditions, it is expected that the error estimation will be too pessimistic. RMS force errors for dipoles when using ewald/disp or ewald/dipole are estimated using equations 33 and 46 of (Wang). The RMS force errors for pppm/dipole are estimated using the equations in (Cerda).

See the kspace_modify command for additional options of the K-space solvers that can be set, including a force option for setting an absolute RMS error in forces, as opposed to a relative RMS error.

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.

Note

For the GPU package, the pppm/gpu style performs charge assignment and force interpolation calculations on the GPU. These processes are performed either in single or double precision, depending on whether the -DFFT_SINGLE setting was specified in your low-level Makefile, as discussed above. The FFTs themselves are still calculated on the CPU. If pppm/gpu is used with a GPU-enabled pair style, part of the PPPM calculation can be performed concurrently on the GPU while other calculations for non-bonded and bonded force calculation are performed on the CPU.

Note

For the KOKKOS package, the pppm/kk style performs charge assignment and force interpolation calculations, along with the FFTs themselves, on the GPU or (optionally) threaded on the CPU when using OpenMP and FFTW3. The specific FFT library is selected using the FFT_KOKKOS CMake parameter. See the Build settings doc page for how to select a 3rd-party FFT library.

## Restrictions

Note that the long-range electrostatic solvers in LAMMPS assume conducting metal (tinfoil) boundary conditions for both charge and dipole interactions. Vacuum boundary conditions are not currently supported.

The ewald/disp, ewald, pppm, and msm styles support non-orthogonal (triclinic symmetry) simulation boxes. However, triclinic simulation cells may not yet be supported by all suffix versions of these styles.

Most of the base kspace styles are part of the KSPACE package. They are only enabled if LAMMPS was built with that package. See the Build package page for more info.

The msm/dielectric and pppm/dielectric kspace styles are part of the DIELECTRIC package. They are only enabled if LAMMPS was built with that package and the KSPACE package. See the Build package page for more info.

For MSM, a simulation must be 3d and one can use any combination of periodic, non-periodic, but not shrink-wrapped boundaries (specified using the boundary command).

For Ewald and PPPM, a simulation must be 3d and periodic in all dimensions. The only exception is if the slab option is set with kspace_modify, in which case the xy dimensions must be periodic and the z dimension must be non-periodic.

The scafacos KSpace style will only be enabled if LAMMPS is built with the SCAFACOS package. See the Build package doc page for more info.

The use of ScaFaCos in LAMMPS does not yet support molecular charged systems where the short-range Coulombic interactions between atoms in the same bond/angle/dihedral are weighted by the special_bonds command. Likewise it does not support the “TIP4P water style” where a fictitious charge site is introduced in each water molecule. Finally, the methods p3m and ewald do not support computing the virial, so this contribution is not included.

## Related commands

kspace_modify, pair_style lj/cut/coul/long, pair_style lj/charmm/coul/long, pair_style lj/long/coul/long, pair_style buck/coul/long

## Default

    kspace_style none

(Darden) Darden, York, Pedersen, J Chem Phys, 98, 10089 (1993).

(Deserno) Deserno and Holm, J Chem Phys, 109, 7694 (1998).

(Hockney) Hockney and Eastwood, Computer Simulation Using Particles, Adam Hilger, NY (1989).

(Kolafa) Kolafa and Perram, Molecular Simulation, 9, 351 (1992).

(Petersen) Petersen, J Chem Phys, 103, 3668 (1995).

(Wang) Wang and Holm, J Chem Phys, 115, 6277 (2001).

(Pollock) Pollock and Glosli, Comp Phys Comm, 95, 93 (1996).

(Cerutti) Cerutti, Duke, Darden, Lybrand, Journal of Chemical Theory and Computation 5, 2322 (2009)

(Neelov) Neelov, Holm, J Chem Phys 132, 234103 (2010)

(Veld) In ‘t Veld, Ismail, Grest, J Chem Phys, 127, 144711 (2007).

(Toukmaji) Toukmaji, Sagui, Board, and Darden, J Chem Phys, 113, 10913 (2000).

(Isele-Holder) Isele-Holder, Mitchell, Ismail, J Chem Phys, 137, 174107 (2012).

(Isele-Holder2) Isele-Holder, Mitchell, Hammond, Kohlmeyer, Ismail, J Chem Theory Comput 9, 5412 (2013).

(Hardy) David Hardy thesis: Multilevel Summation for the Fast Evaluation of Forces for the Simulation of Biomolecules, University of Illinois at Urbana-Champaign, (2006).

(Hardy2) Hardy, Stone, Schulten, Parallel Computing, 35, 164-177 (2009).

(Sutmann) Sutmann, Arnold, Fahrenberger, et. al., Physical review / E 88(6), 063308 (2013)

(Cerda) Cerda, Ballenegger, Lenz, Holm, J Chem Phys 129, 234104 (2008)

(Sutmann) G. Sutmann. ScaFaCoS - a Scalable library of Fast Coulomb Solvers for particle Systems.

  In Bajaj, Zavattieri, Koslowski, Siegmund, Proceedings of the Society of Engineering Science 51st Annual Technical Meeting. 2014.