KSPACING: Difference between revisions

Revision as of 18:33, 1 September 2022

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.. 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.

@@ Line 7: / Line 7: @@
 {{TAG|KSPACING}} is the smallest allowed spacing between k points in units of <math>\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> N= \mathrm{max}(1, | \vec{b}_i| / \mathrm{KSPACING} ). </math>
+The number of k points in the direction of the first, second and third reciprocal lattice vector is determined by <math> N_i= \mathrm{max}(1, \lceil | \mathbf{b}_i| / \mathrm{KSPACING} \rceil). </math>
-These values are rounded to the next integer greater than or equal to <math> N </math>. In this equation, <math> \vec{b}_i  </math> are the reciprocal lattice vectors <math> \vec{b}_i \vec{a}_j = 2 \pi \delta_{ij} </math>.
+with <math>\lceil x \rceil</math> being the ceiling function which returns the least integer that is equal or larger than <math>x</math>. In this equation, <math> \mathbf{b}_i  </math> are the reciprocal lattice vectors <math> \mathbf{b}_i \mathbf{a}_j = 2 \pi \delta_{ij} </math>.
 The generated grid is either centred at the <math>\Gamma</math> point, i.e., includes the <math>\Gamma</math> point when ({{TAG|KGAMMA}}=.TRUE., or is shifted away from the <math>\Gamma</math> point, as done for Monkhorst-Pack grids when ({{TAG|KGAMMA}}=.FALSE.. The default is to include the <math>\Gamma</math> point.
 {{NB|warning|This implementation is not entirely consistent with the automatic k-point generation (Mode{{=}}A) used in the {{FILE|KPOINTS}} file.}}
-If the k points are generated using the automatic mode in the {{FILE|KPOINTS}} file, <math> N</math>  is calculated as
+If the k points are generated using the [[KPOINTS#Automatic_k-point_mesh|automatic mode]] in the {{FILE|KPOINTS}} file, <math> N_i</math>  is calculated as
-<math> N= \mathrm{max}(1, | \vec{b}_i| / (2 \pi \times \mathrm{KSPACING}) ) </math>
+<math> N_i= \mathrm{int}(\mathrm{max}(1, R_k| \mathbf{b}_i| + 0.5)) </math> with <math>R_k=1/\mathrm{KSPACING}</math>
 and rounding is to the nearest integer.  We recommend using the {{TAG|KSPACING}} tag in the {{FILE|INCAR}} file
 and avoiding the automatic mode via the {{FILE|KPOINTS}} file.

Revision as of 18:33, 1 September 2022

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