KSPACING: Difference between revisions
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{{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. | {{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) | 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> | ||
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>\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>. | ||
The generated grid is either centred at the <math>\Gamma</math> point, i.e., includes the <math>\Gamma</math> point when | 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. is set. The default is to include the <math>\Gamma</math> point. | ||
{{NB|warning|This implementation is not entirely consistent with the automatic k-point generation (Mode{{=}}A) used in the {{FILE|KPOINTS}} file.}} | {{NB|warning|This implementation is not entirely consistent with the automatic k-point generation (Mode{{=}}A) 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 | ||
Revision as of 18:36, 1 September 2022
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, \lceil | \mathbf{b}_i| / \mathrm{KSPACING} \rceil) }[/math] with [math]\displaystyle{ \lceil x \rceil }[/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 = 2 \pi \delta_{ij} }[/math]. The generated grid is either centred at the [math]\displaystyle{ \Gamma }[/math] point, i.e., includes the [math]\displaystyle{ \Gamma }[/math] point when KGAMMA=.TRUE., or is shifted away from the [math]\displaystyle{ \Gamma }[/math] point, as done for Monkhorst-Pack grids when KGAMMA=.FALSE. is set. The default is to include the [math]\displaystyle{ \Gamma }[/math] point.
| Warning: This implementation is not entirely consistent with the automatic k-point generation (Mode=A) 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=1/\mathrm{KSPACING} }[/math] and rounding is to the nearest integer. We recommend using the KSPACING tag in the INCAR file and avoiding the automatic mode via the KPOINTS file.