K-Points

Periodic Quickstep calculations can sample the Brillouin zone through the &DFT%KPOINTS section. The most common setup is a Monkhorst-Pack mesh:

&DFT
  &KPOINTS
    SCHEME MONKHORST-PACK 6 6 6
    WAVEFUNCTIONS COMPLEX
  &END KPOINTS
&END DFT

SCHEME GAMMA uses only the Gamma point. SCHEME MONKHORST-PACK and SCHEME MACDONALD generate regular meshes. SCHEME GENERAL uses explicitly listed k-points:

&KPOINTS
  SCHEME GENERAL
  KPOINT 0.0 0.0 0.0 1.0
  KPOINT 0.5 0.0 0.0 1.0
&END KPOINTS

K-points are given in reciprocal lattice-vector coordinates by default (UNITS B_VECTOR). Cartesian coordinates can be selected with UNITS CART_BOHR or UNITS CART_ANGSTROM.

Symmetry Reduction

Atomic symmetry can reduce the number of k-points that have to be solved explicitly:

&KPOINTS
  SCHEME MONKHORST-PACK 8 8 8
  SYMMETRY ON
  SYMMETRY_BACKEND SPGLIB
  WAVEFUNCTIONS COMPLEX
&END KPOINTS

SYMMETRY_BACKEND selects the backend that provides and applies atom and k-point symmetry operations:

  • K290: the established CP2K default.

  • SPGLIB: use the space-group operations returned by SPGLIB, including fractional translations.

SYMMETRY_REDUCTION_METHOD selects the method used to build the irreducible k-point set. If SYMMETRY_BACKEND is set explicitly and SYMMETRY_REDUCTION_METHOD is omitted, the reduction method follows the backend. SYMMETRY_REDUCTION_METHOD SPGLIB with SYMMETRY_BACKEND K290 can be used as a comparison mode: SPGLIB proposes the k-point orbits, while only mappings represented by the K290 backend are used for the actual transformations.

INVERSION_SYMMETRY_ONLY ON restricts the reduction to time-reversal/inversion symmetry. FULL_GRID ON disables symmetry reduction while still generating the regular mesh.

For general atomic k-point symmetry, use complex wavefunctions. Real wavefunctions are only valid for Gamma and special k-points with real Bloch phases.

Explicit K-Point Sets

SCHEME GENERAL can be used with symmetry reduction when the explicit k-point set is equally weighted and closed under the requested symmetry operations:

&KPOINTS
  SCHEME GENERAL
  SYMMETRY ON
  SYMMETRY_BACKEND SPGLIB
  KPOINT -0.25 -0.25 -0.25 1.0
  KPOINT -0.25 -0.25  0.25 1.0
  KPOINT -0.25  0.25 -0.25 1.0
  KPOINT -0.25  0.25  0.25 1.0
  KPOINT  0.25 -0.25 -0.25 1.0
  KPOINT  0.25 -0.25  0.25 1.0
  KPOINT  0.25  0.25 -0.25 1.0
  KPOINT  0.25  0.25  0.25 1.0
&END KPOINTS

The same closure requirement applies to K290, SPGLIB, and mixed SPGLIB-reduction/K290-backend setups. For band paths or other intentionally nonuniform explicit lists, keep SYMMETRY OFF, because the order and weights of the points are part of the requested property.

Cell Convention

CP2K’s k-point machinery assumes the standard CP2K cell convention: vector A lies along the Cartesian X axis and vector B lies in the XY plane. Using ABC together with ALPHA_BETA_GAMMA, or reading a CIF file, lets CP2K construct the cell in that convention from orientation-independent lattice parameters.

Moving Geometries

For moving geometries (GEO_OPT, CELL_OPT, MD, and related run types), atomic k-point symmetry is rebuilt from the current cell and coordinates instead of reusing operations from the initial geometry. This applies to regular Monkhorst-Pack/MacDonald meshes and to closed GENERAL k-point sets. If the current geometry no longer supports a symmetry operation, the reduced set changes accordingly or the explicit GENERAL set is rejected if it is no longer symmetry-closed.

KEEP_SPACE_GROUP T is the safest way to combine geometry optimization with full atomic k-point symmetry. KEEP_SYMMETRY T constrains the cell metric, but does not by itself keep atoms on space-group-related positions.

Wannier90

The Wannier90 interface can either keep its historical k-point path controlled by DFT%PRINT%WANNIER90%MP_GRID, or use the full SCF k-point mesh via DFT%PRINT%WANNIER90%KPOINTS_SOURCE SCF. The SCF source supports Gamma, Monkhorst-Pack, MacDonald, and explicit SCHEME GENERAL k-point meshes. If the SCF calculation used K290 or SPGLIB symmetry reduction, the corresponding unreduced mesh is regenerated or recovered for the Wannier90 export, because Wannier90 expects the full mesh and its nearest-neighbour connectivity. By default, DFT%PRINT%WANNIER90%REUSE_SCF_MOS T reuses already available SCF MO coefficients when the SCF mesh is already complete, including explicit SCHEME GENERAL meshes, and for simple time-reversal/inversion partners. Atom/AO symmetry reconstruction from an irreducible SCF mesh is available for single-band exports and for multi-band exports whose bands are non-degenerate over the reduced SCF mesh. Cases where the Wannier90 band window contains or cuts through a degenerate subspace are guarded until the gauge and degeneracy alignment is fully validated; guarded cases fall back to the historical full-mesh diagonalization for the Wannier90 files.