What is k-point sampling and why does it matter?

K-point sampling refers to the discrete grid of points in reciprocal space (the Brillouin zone) used to compute integrals over electronic states. The density of this grid directly affects the accuracy and cost of DFT calculations.

Why K-Points Matter

In a periodic crystal, electronic properties must be averaged over all allowed wavevectors (k-points) in the Brillouin zone. Since there are infinitely many k-points, we approximate by sampling a finite grid:

• Too few k-points: Inaccurate total energies, forces, and electronic properties
• Too many k-points: Unnecessarily expensive calculations
• Just right: Converged results at minimal cost

Typical Grids

• Metals: Need dense grids (8x8x8 or higher for small cells) because of sharp features at the Fermi surface
• Semiconductors: Moderate grids (4x4x4 to 6x6x6) usually suffice
• Large supercells: Can use sparser grids because the Brillouin zone is smaller

Band Structure Calculations

Band structure plots use a special k-point path along high-symmetry directions rather than a uniform grid. The path depends on the crystal system.

Database Consistency

All three databases (MP, AFLOW, JARVIS) use converged k-point grids, but their convergence criteria differ slightly. This can lead to small numerical differences for the same material across databases.