KSPACING: Difference between revisions

Latest revision as of 07:13, 3 October 2023

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 $N_{i}=\mathrm {max} (1,\mathrm {ceiling} (|\mathbf {b} _{i}|2\pi /\mathrm {KSPACING} ))$ with $\mathrm {ceiling} (x)$ 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 $\mathbf {b} _{i}\mathbf {a} _{j}=\delta _{ij}$ . The generated grid is centered at the $\Gamma$ point if KGAMMA=True (default), i.e., includes the $\Gamma$ point. For KGAMMA=False, the grid is shifted away from the $\Gamma$ 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, $N_{i}$ is calculated as $N_{i}=\mathrm {int} (\mathrm {max} (1,R_{k}|\mathbf {b} _{i}|+0.5))$ with $R_{k}=2\pi /\mathrm {KSPACING}$ 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.

@@ 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_i= \mathrm{max}(1, \lceil | \mathbf{b}_i| / \mathrm{KSPACING} \rceil). </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, \mathrm{ceiling}( | \mathbf{b}_i| 2\pi / \mathrm{KSPACING} ))</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>.
+with <math>\mathrm{ceiling}( x )</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 = \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.
+The generated grid is centered at the <math>\Gamma</math> point if {{TAG|KGAMMA}}=True (default), i.e., includes the <math>\Gamma</math> point. For {{TAG|KGAMMA}}=False, the grid is shifted away from the <math>\Gamma</math> point as done for Monkhorst-Pack grids.
-{{NB|warning|This implementation is not entirely consistent with the automatic k-point generation (Mode{{=}}A) used in the {{FILE|KPOINTS}} file.}}
+{{NB|mind|This implementation is not entirely identical with the deprecated [[KPOINTS#Automatic_k-point_mesh|automatic k-point generation]] used in the {{FILE|KPOINTS}} file.}}
 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_i= \mathrm{int}(\mathrm{max}(1, R_k| \mathbf{b}_i| + 0.5)) </math> with <math>R_k=1/\mathrm{KSPACING}</math>
+<math> N_i= \mathrm{int}(\mathrm{max}(1, R_k| \mathbf{b}_i| + 0.5)) </math> with <math>R_k=2\pi/\mathrm{KSPACING}</math>
-and rounding is to the nearest integer.  We recommend using the {{TAG|KSPACING}} tag in the {{FILE|INCAR}} file
+and rounding it 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.

Latest revision as of 07:13, 3 October 2023

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