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 $\AA^{-1}$ . 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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