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 $\mathrm {\AA} ^{-1}$ . 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 $N_{i}=\mathrm {max} (1,\lceil |\mathbf {b} _{i}|/\mathrm {KSPACING} \rceil )$ with $\lceil x\rceil$ being the ceiling function which returns the least integer that is equal or larger than $x$ . In this equation, $\mathbf {b} _{i}$ are the reciprocal lattice vectors $\mathbf {b} _{i}\mathbf {a} _{j}=2\pi \delta _{ij}$ . The generated grid is either centred at the $\Gamma$ point, i.e., includes the $\Gamma$ point when KGAMMA=.TRUE., or is shifted away from the $\Gamma$ point, as done for Monkhorst-Pack grids when KGAMMA=.FALSE. is set. The default is to include the $\Gamma$ point.

Warning: This implementation is not entirely consistent with the automatic k-point generation (Mode=A) used in the KPOINTS file.

If the k points are generated using the automatic mode in the KPOINTS file, $N_{i}$ is calculated as $N_{i}=\mathrm {int} (\mathrm {max} (1,R_{k}|\mathbf {b} _{i}|+0.5))$ with $R_{k}=1/\mathrm {KSPACING}$ and rounding is to the nearest integer. We recommend using the KSPACING tag in the INCAR file and avoiding the automatic mode via the KPOINTS file.

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