KSPACING: Difference between revisions

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 $\AA^{-1}$ . 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 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: The tag  {{TAG|KSPACING}} determines the number of k points if the {{TAG|KPOINTS}} file
 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_i= \mathrm{max}(1, \mathrm{ceiling}( | \mathbf{b}_i| 2\pi / \mathrm{KSPACING} ))</math>
-The number of k-points in the direction of the first, second and third
+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> N= \mathrm{max}(1, | \vec{b}_i| / \mathrm{KSPACING} ). </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.
-These values are rounded to the next integer greater than or equal to <math> N </math>. In this equation
+{{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> \vec{b}_i  </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> \vec{b}_i \vec{a}_j = 2 \pi \delta_{ij} </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 either centred at the <math>\Gamma</math> point (e.g. includes the <math>\Gamma</math> point) ({{TAG|KGAMMA}}=''.TRUE.'') or is shifted away
+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, as usually done for Monkhorst Pack grids ({{TAG|KGAMMA}}=''.FALSE.'').
+and avoiding the automatic mode via the {{FILE|KPOINTS}} file.
-The default is to include the <math>\Gamma</math> point.
-Note: This implementation is not entirely consistent with the automatic k-point generation
+== Related tags and articles ==
-(Mode=A) used in the KPOINTS file. If the k-points are generated using the automatic mode
+{{TAG|KGAMMA}}, {{FILE|KPOINTS}}
-in the KPOINTS file, <math> N</math>  is calculated as
-<math> N= \mathrm{max}(1, | \vec{b}_i| / (2 \pi \times \mathrm{KSPACING}) ) </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 ==
-{{TAG|KGAMMA}}
 {{sc|KSPACING|Examples|Examples that use this tag}}
 ----
-[[The_VASP_Manual|Contents]]
-[[Category:INCAR]][[Category:Electronic Minimization]][[Category:Electronic Minimization Methods]]
+[[Category:INCAR tag]][[Category:Crystal momentum]]