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### kspace_style command

Syntax:

    kspace_style style value

- style = none or ewald or ewald/disp or ewald/omp or pppm or pppm/cg or pppm/disp or pppm/tip4p or pppm/disp/tip4p or pppm/gpu or pppm/omp or pppm/cg/omp or pppm/tip4p/omp or msm

        none value = none
        ewald 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 value = accuracy (smallq)
          accuracy = desired relative error in forces
          smallq = cutoff for charges to be considered (optional) (charge units)
        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/omp value = accuracy
          accuracy = desired relative error in forces
        pppm/cg/omp value = accuracy
          accuracy = desired relative error in forces
        pppm/tip4p/omp value = accuracy
          accuracy = desired relative error in forces
        msm 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 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 non-orthogonal (triclinic symmetry) simulation boxes. It is currently the only long-range solver that has this capability.

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^(3/2) where N is the number of atoms in the system. The PPPM solver scales as Nlog(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. 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/tip4p style is identical to the pppm style except that it adds a charge at the massless 4th site in each TIP4P water molecule. It should be used with pair styles with a long/tip4p in their style name.

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, it is currently recommended that you set the dispersion mesh size and other parameters explicitly via the kspace_modify command, rather than let LAMMPS set them automatically. For example, a set of parameters that works well for surface systems when using real units is a LJ cutoff of 10 Angstrom, interpolation order = 5 (the default), grid spacing = 4.17 Angstroms, and Ewald parameter = 0.28. These parameters work well for the ik differentiation. For the ad setting, a smaller grid spacing is needed, e.g. 3 Angstroms. Further information on the influence of the parameters and how to choose them is described in (Isele-Holder).

IMPORTANT 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 lo-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 calulations, particularly in parallel or on GPUs. The use of the -DFFT_SINGLE flag is discussed in this section of the manual.

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 solves 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 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 coulomb cutoff (i.e. 15 angstroms instead of 10 angstroms) provides better MSM accuracy for both the real space and grid computed forces.

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.

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 following the procedure outlined in chapter 3 of (Hardy), with equation 3.197 of particular note.

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

Styles with a cuda, gpu, 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 in Section_accelerate of the manual. 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 lo-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.

These accelerated styles are part of the USER-CUDA, GPU, USER-OMP, and OPT packages respectively. They are only enabled if LAMMPS was built with those packages. See the Making LAMMPS section for more info.

See Section_accelerate of the manual for more instructions on how to use the accelerated styles effectively.

Restrictions:

All of the kspace styles are part of the KSPACE package. They are only enabled if LAMMPS was built with that package. See the Making LAMMPS section for more info. Note that the KSPACE package is installed by default.

A simulation must be 3d and periodic in all dimensions to use an Ewald or PPPM solver. 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 msm style is fairly new, and still lacks some important features and optimizations. The upper MSM levels (above the first level) are not parallelized, so this MSM implementation may not yet scale very well on large core counts.

Related commands:

kspace_modify, pair_style lj/cut/coul/long, pair_style lj/charmm/coul/long, pair_style lj/coul, 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 Simualtion, 9, 351 (1992).

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

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

(Veld) In 't Veld, Ismail, Grest, J Chem Phys, in press (2007).

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

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

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