KSPACING
KSPACING = [real]
Default: KSPACING = 0.5
Description: The tag KSPACING determines the number of k points if the KPOINTS file is not present.
KSPACING is the smallest allowed spacing between k points in units of [math]\displaystyle{ \AA^{-1} }[/math]. The number of k points increases when the spacing is decreased. The number of k points in the direction of the first, second and third reciprocal lattice vector is determined by [math]\displaystyle{ N_i= \mathrm{max}(1, \mathrm{ceiling}( | \mathbf{b}_i| 2\pi / \mathrm{KSPACING} )) }[/math] with [math]\displaystyle{ \mathrm{ceiling}( x ) }[/math] being the ceiling function which returns the least integer that is equal or larger than [math]\displaystyle{ x }[/math]. In this equation, [math]\displaystyle{ \mathbf{b}_i }[/math] are the reciprocal lattice vectors [math]\displaystyle{ \mathbf{b}_i \mathbf{a}_j = \delta_{ij} }[/math]. The generated grid is centered at the [math]\displaystyle{ \Gamma }[/math] point if KGAMMA=True (default), i.e., includes the [math]\displaystyle{ \Gamma }[/math] point. For KGAMMA=False, the grid is shifted away from the [math]\displaystyle{ \Gamma }[/math] point as done for Monkhorst-Pack grids.
| Mind: This implementation is not entirely identical with the deprecated automatic k-point generation used in the KPOINTS file. |
If the k points are generated using the automatic mode in the KPOINTS file, [math]\displaystyle{ N_i }[/math] is calculated as [math]\displaystyle{ N_i= \mathrm{int}(\mathrm{max}(1, R_k| \mathbf{b}_i| + 0.5)) }[/math] with [math]\displaystyle{ R_k=2\pi/\mathrm{KSPACING} }[/math] and rounding it to the nearest integer. We recommend using the KSPACING tag in the INCAR file and avoiding the automatic mode via the KPOINTS file.