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### kspace_style command

Syntax:

    kspace_style style value

- style = none or ewald or pppm or pppm/cg or pppm/tip4p or ewald/n or pppm/gpu or ewald/omp or pppm/omp or pppm/cg/omp or pppm/tip4p/omp or pppm/proxy or pppm/tip4p/proxy

        none value = none
        ewald 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/tip4p value = accuracy
          accuracy = desired relative error in forces
        ewald/n value = accuracy
          accuracy = desired relative error in forces
        pppm/gpu value = accuracy
          accuracy = desired relative error in forces
        ewald/omp value = accuracy
          accuracy = desired relative error in forces
        pppm/omp value = accuracy
          accuracy = desired relative error in forces
        pppm/tip4p/omp value = accuracy
          accuracy = desired relative error in forces
        pppm/proxy value = accuracy
          accuracy = desired relative error in forces

        pppm/tip4p/proxy 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 none

Description:

Define a K-space solver for LAMMPS to use each timestep to compute long-range Coulombic interactions or long-range 1/r^N interactions. When such a solver is used in conjunction with an appropriate pair style, the cutoff for Coulombic or other 1/r^N interactions is effectively infinite; each charge in the system interacts with charges in an infinite array of periodic images of the simulation domain.

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

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 ewald/n style augments ewald by adding long-range dispersion sum capabilities for 1/r^N 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^N capability means that Lennard-Jones or Buckingham potentials can be used with ewald/n without a cutoff, i.e. they become full long-range potentials.

Currently, only the ewald/n style can be used with non-orthogonal (triclinic symmetry) simulation boxes.

The pppm/proxy style is a special variant for calculations in hybrid OpenMP/MPI parallel mode. It is functionally equivalent with pppm, but it its force computation is being executed as a single thread concurrently with a multi-threaded non-bonded calculation for a pair style with pppm/omp suffix. For calcuations across many multi-core nodes, this can have a performance benefit over performing the real and reciprocal space part separately, specifically when otherwise the time spent on the pair style would slightly less than in pppm without threading.

Note that 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.

When a kspace style is used, a pair style that includes the short-range correction to the pairwise Coulombic or other 1/r^N forces must also be selected. For Coulombic interactions, these styles are ones that have a coul/long in their style name. For 1/r^6 dispersion forces in a Lennard-Jones or Buckingham potential, see the pair_style lj/coul or pair_style buck/coul commands.

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 FFT grid size for style pppm.

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).

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:

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.

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.

The ewald/n style is part of the USER-EWALDN package. It is only enabled if LAMMPS was built with that package. See the Making LAMMPS section for more info.

When using a long-range pairwise TIP4P potential, you must use kspace style pppm/tip4p and vice versa.

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).