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KSPACING

KSPACING is the smallest allowed spacing between k points in units of ${\displaystyle \mathrm {\AA} ^{-1}}$. 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 ${\displaystyle N={\mathrm {max}}(1,|{\vec {b}}_{i}|/{\mathrm {KSPACING}}).}$ These values are rounded to the next integer greater than or equal to ${\displaystyle N}$. In this equation ${\displaystyle {\vec {b}}_{i}}$ are the reciprocal lattice vectors ${\displaystyle {\vec {b}}_{i}{\vec {a}}_{j}=2\pi \delta _{{ij}}}$. The generated grid is either centred at the ${\displaystyle \Gamma }$ point (e.g. includes the ${\displaystyle \Gamma }$ point) (KGAMMA=.TRUE.) or is shifted away from the ${\displaystyle \Gamma }$ point, as usually done for Monkhorst Pack grids (KGAMMA=.FALSE.). The default is to include the ${\displaystyle \Gamma }$ point.
Note: 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, ${\displaystyle N}$ is calculated as ${\displaystyle N={\mathrm {max}}(1,|{\vec {b}}_{i}|/(2\pi \times {\mathrm {KSPACING}}))}$ and rounding is to the nearest integer. We recommend to use the KSPACING tag in the INCAR file and to avoid using the automatic mode via the KPOINTS file.