# kspace_style command¶

## Syntax¶

```
kspace_style style value
```

style =

*none*or*ewald*or*ewald/dipole*or*ewald/dipole/spin*or*ewald/disp*or*ewald/omp*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*msm*or*msm/cg*or*msm/omp*or*msm/cg/omp*or*scafacos**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/omp*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*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)*scafacos*values = method accuracy method = fmm or p2nfft or p3m or ewald or direct 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
```

## 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 |

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* 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 *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 (Who)
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://scafacos.de” or can be cloned from the git-repository “git://github.com/scafacos/scafacos.git”.

In order to use this KSpace style, you must download and build the ScaFaCoS library, then build LAMMPS with the USER-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.

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 Speed packages doc
page. The accelerated styles take the same arguments and should
produce the same results, except for round-off and precision issues.

More specifically, 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.

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.

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

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

## 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.

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

For MSM, a simulation must be 3d and one can use any combination of periodic, non-periodic, or 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 USER-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.

## 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)

**(Who)** Who, Author2, Author3, J of Long Range Solvers, 35, 164-177
(2012).