KSPACING: Difference between revisions
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{{TAGDEF|KSPACING|[real]|0.5}} | {{TAGDEF|KSPACING|[real]|0.5}} | ||
Description: The tag {{TAG|KSPACING}} determines the number of k | Description: The tag {{TAG|KSPACING}} determines the number of k points if the {{TAG|KPOINTS}} file | ||
is not present. | is not present. | ||
---- | ---- | ||
{{TAG|KSPACING}} is the smallest allowed spacing between k points in units of | {{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. | ||
<math>\AA^{-1}</math>. The number of k | 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> | ||
The number of k | 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>. | ||
reciprocal lattice vector is determined by <math> | 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|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.}} | |||
<math> \ | 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 | ||
are the reciprocal lattice vectors <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> | ||
The generated grid is | and rounding it to the nearest integer. We recommend using the {{TAG|KSPACING}} tag in the {{FILE|INCAR}} file | ||
from the <math>\Gamma</math> point | and avoiding the automatic mode via the {{FILE|KPOINTS}} file. | ||
== Related tags and articles == | |||
{{TAG|KGAMMA}}, {{FILE|KPOINTS}} | |||
== Related | |||
{{TAG|KGAMMA}} | |||
{{sc|KSPACING|Examples|Examples that use this tag}} | {{sc|KSPACING|Examples|Examples that use this tag}} | ||
---- | ---- | ||
[[Category:INCAR]][[Category: | [[Category:INCAR tag]][[Category:Crystal momentum]] | ||
Latest revision as of 11:34, 21 October 2024
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 [math]\displaystyle{ \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]\displaystyle{ N_i= \mathrm{max}(1, \mathrm{ceiling}( | \mathbf{b}_i| 2\pi / \mathrm{KSPACING} )) }[/math] with [math]\displaystyle{ \mathrm{ceiling}( x ) }[/math] being the ceiling function which returns the least integer that is equal or larger than [math]\displaystyle{ x }[/math]. In this equation, [math]\displaystyle{ \mathbf{b}_i }[/math] are the reciprocal lattice vectors [math]\displaystyle{ \mathbf{b}_i \mathbf{a}_j = \delta_{ij} }[/math]. The generated grid is centered at the [math]\displaystyle{ \Gamma }[/math] point if KGAMMA=True (default), i.e., includes the [math]\displaystyle{ \Gamma }[/math] point. For KGAMMA=False, the grid is shifted away from the [math]\displaystyle{ \Gamma }[/math] 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, [math]\displaystyle{ N_i }[/math] is calculated as [math]\displaystyle{ N_i= \mathrm{int}(\mathrm{max}(1, R_k| \mathbf{b}_i| + 0.5)) }[/math] with [math]\displaystyle{ R_k=2\pi/\mathrm{KSPACING} }[/math] 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.