# WIEN2k-FAQ: KGEN: Add inversion ? Shift k-mesh ?

©2001 by P. Blaha, K. Schwarz and J. Luitz

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The program KGEN generates a k-mesh in the irreducible part of the BZ by using the symmetry operations defined in case.struct.
• How many points should I use ?
• This is difficult to answer in general, only general recommendations can be given. Note: a k-mesh MUST always be checked by first doing a calculation with a crude mesh, save the results and continue with a fine mesh. Compare your results, eventually switch back to the crude mesh or continue with an even finer mesh until convergence is reached.
• Metallic systems need a fine mesh, insulators are often ok with very few k-points.
• Small unit cells need a fine mesh, large unit cells most likely not.
• Thus: insulators with many atoms/cell (say 40-60) may need only ONE (shifted) k-point. On the other hand fcc Al may need several 10000 k-points for a good DOS.
• Supercells for single atoms or molecules should be done just with Gamma.
• Supercells for surfaces (slabs) need only 1 k-point along the z-direction (perpendicular to the surface). Eventually you can even increase the c lattice-parameter before running KGEN, so that even for fine meshes only 1 point along z is generated (don't forget to change "c" back afterwards).
• "add inversion" ? This is asked only when inversion is NOT present.
• Say "YES" in all cases except when you do spin-polarized (magnetic) calculations WITH spin-orbit coupling (this breaks time-inversion symmetry and thus one MUST NOT add inversion symmetry (eigenvalues at +k and -k may be different).
• "shift"the k-mesh ? (only for some lattice types)
• "Shifting" of k-mesh means that it will add (x,x,x) to all generated k-points, thus shifting them from high symmetry points (lines) to more "general" points with a higher weight. By this procedure (known also as "special k-point methods") one generates an equally "dense" mesh, but with less basis points.
• Usually a shift is recommended . Only one word of warning: When you are interested in "gaps" of semiconductors, they are often located at Gamma or X (or at some other BZ-border point). With shifted meshes you will NOT have those high-symmetry points in your mesh, thus the gap may seem to be smaller/larger than expected.
• Solution to this problem: Do the scf cycle with the shifted mesh, but for a DOS change to a fine unshifted mesh.

Peter Blaha,