Pre-defined k-point sets for Crystalline calculations: simple cubic lattices

REGULAR                       SPECIAL
Order  1
Order  2
Order  4                      Order  4
Order  6                      Order  6
Order  8                      Order  8
Order 10                      Order 10
Order 12                      Order 12

The First Brillouin zone of a simple cubic lattice, with high symmetry k points marked.

The above k-point meshes were generated for simple cubic lattices, where the symmetry of the crystal is fully cubic, and the primitive lattice vectors are given by

• a₁ = ( a , 0 , 0 )
• a₂ = ( 0 , a , 0 )
• a₃ = ( 0 , 0 , a )

with reciprocal lattice vectors

• b₁ = ( 2 pi/a , 0 , 0 )
• b₂ = ( 0 , 2 pi/a , 0 )
• b₃ = ( 0 , 0 , 2 pi/a )

these lattices include the space groups

• Pm(-3)m (#221) (simple cubic lattices, CsCl, Perovskite, Cu₃Au)
• Pm(-3)n (#223) (A15 lattices)
• Pn(-3)m (#224) (Cuprite (Ag₂O) lattices)

Both "regular" and "special" k-point meshes are listed, in lattice-coordinate format. The order of the mesh is the number of k-points which lie on the line between the origin and the point X (2 pi/a, 0, 0) in reciprocal space, or at X. (For "special" k-points, this is the number of points on a line parallel to the origin-X line.) "Regular" and "Special" k-points on the same line have the same density of k-points in reciprocal space. Since the later meshes are "special", there are generally fewer symmetrized special k-points than regular k-points.

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