kpunten

Kpunten, or k-punten in Dutch, is a term used in physics and mathematics to denote points in k-space, the reciprocal space associated with a crystal lattice. The letter k typically represents the wavevector or crystal momentum, so a k-point specifies a particular position in reciprocal space. The concept is central whenever properties of periodic systems are calculated or discussed.

In solid-state physics and computational materials science, k-points are used to sample the Brillouin zone, the primitive cell of reciprocal space. Since integrals over the Brillouin zone in electronic structure calculations are often challenging to perform exactly, they are approximated by sums over a finite set of k-points. The density and distribution of these points define a k-point grid. Common grid schemes include Monkhorst-Pack grids and gamma-centered grids, which exploit crystal symmetry to reduce the number of independent points.

The choice of k-points affects calculated quantities such as total energy, electronic band structure, and density of states. Metals generally require finer k-point grids to resolve the sharp features near the Fermi surface, while insulators and wide-bandgap semiconductors may converge with coarser grids. Convergence tests are typically performed by increasing the k-point density until the results change insignificantly.

In practice, k-points are implemented in widely used electronic structure codes and visualization tools, such as VASP, Quantum ESPRESSO, ABINIT, and others. While k-points originate from the mathematics of Fourier transforms and reciprocal lattices, their practical use enables feasible and accurate modeling of the electronic properties of crystalline materials. See also Brillouin zone, reciprocal lattice, and k-point sampling.