KSPACING: Difference between revisions
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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 reciprocal lattice vector is determined by <math> N_i= \mathrm{max}(1, \mathrm{ceiling}( | \mathbf{b}_i| 2\pi / \mathrm{KSPACING} ))</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>. | 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 | 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| | {{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 | 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=2\pi/\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> | ||
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 . 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 with being the ceiling function which returns the least integer that is equal or larger than . In this equation, are the reciprocal lattice vectors . The generated grid is centered at the point if KGAMMA=True (default), i.e., includes the point. For KGAMMA=False, the grid is shifted away from the 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, is calculated as with 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.