KSPACING: Difference between revisions

Latest revision as of 15:05, 20 March 2026

KSPACING = [real]
Default: KSPACING = 0.5

Description: Spacing between k points in automatically generated mesh 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], where [math]\displaystyle{ \mathrm{ceiling}( x ) }[/math] returns the least integer that is equal or larger than [math]\displaystyle{ x }[/math]. Here, [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 = T (default), i.e., includes the [math]\displaystyle{ \Gamma }[/math] point. For KGAMMA = F, the grid is shifted away from the [math]\displaystyle{ \Gamma }[/math] point as done for Monkhorst-Pack grids.

Mind: The definition of [math]\displaystyle{ N_i }[/math] is not entirely identical with the deprecated automatic k-point generation used in the KPOINTS file. We recommend using the KSPACING tag and avoiding the automatic mode via the KPOINTS file.

@@ Line 1: / Line 1: @@
 {{TAGDEF|KSPACING|[real]|0.5}}
-Description: The tag  {{TAG|KSPACING}} determines the number of k-points if the {{TAG|KPOINTS}} file
+Description: Spacing between '''k''' points in automatically generated mesh if the {{FILE|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-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>
-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>.
-The generated grid is either centred at the <math>\Gamma</math> point (e.g. includes the <math>\Gamma</math> point) ({{TAG|KGAMMA}}=''.TRUE.'') or is shifted away
-from the <math>\Gamma</math> point, as usually done for Monkhorst Pack grids ({{TAG|KGAMMA}}=''.FALSE.'').
-The default is to include the <math>\Gamma</math> point.
-Note: This implementation is not entirely consistent with the automatic k-point generation
+The number of '''k''' points in the direction of the first, second and third reciprocal lattice
-(Mode=A) used in the KPOINTS file. If the k-points are generated using the automatic mode
+vector is determined by <math> N_i= \mathrm{max}(1, \mathrm{ceiling}( | \mathbf{b}_i| 2\pi / \mathrm{KSPACING} ))</math>,
-in the KPOINTS file, <math> N</math>  is calculated as
+where <math>\mathrm{ceiling}( x )</math> returns the least integer that is equal or
-<math> N= \mathrm{max}(1, | \vec{b}_i| / (2 \pi \times \mathrm{KSPACING}) ) </math>
+larger than <math>x</math>. Here, <math> \mathbf{b}_i  </math> are the reciprocal lattice vectors <math> \mathbf{b}_i \mathbf{a}_j = \delta_{ij} </math>.
-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.
-== Related Tags and Sections ==
+The generated grid is centered at the <math>\Gamma</math> point if {{TAG|KGAMMA|T}} (default), i.e., includes the <math>\Gamma</math> point. For {{TAG|KGAMMA|F}}, the grid is shifted away from the <math>\Gamma</math> point as done for Monkhorst-Pack grids.
-{{TAG|KGAMMA}}
+{{NB|mind|The definition of <math> N_i</math> is not entirely identical with the deprecated [[KPOINTS#Automatic_k-point_mesh|automatic k-point generation]] used in the {{FILE|KPOINTS}} file. We recommend using the {{TAG|KSPACING}} tag and avoiding the automatic mode via the {{FILE|KPOINTS}} file.}}
-{{sc|KSPACING|Examples|Examples that use this tag}}
+== Related tags and articles ==
-----
+Tags: {{TAG|KGAMMA}}, {{TAG|KSPACING_OPT}}
-[[The_VASP_Manual|Contents]]
+Files: {{FILE|KPOINTS}}, {{FILE|KPOINTS_OPT}}
+{{sc|KSPACING|HowTo|Workflows that use this tag}}
-[[Category:INCAR]][[Category:Electronic Minimization]][[Category:Electronic Minimization Methods]]
+[[Category:INCAR tag]][[Category:Crystal momentum]]