KSPACING: Difference between revisions
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<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 | 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} | 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 | These values are rounded to the next integer greater than or equal to <math> N </math>. In this equation | ||
<math> \vec{b} | <math> \vec{b}_i </math> | ||
are the reciprocal lattice vectors <math> \vec{b} | 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 | 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.''). | 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 | |||
(Mode=A) used in the KPOINTS file. If the k-points are generated using the automatic mode | |||
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 == | == Related Tags and Sections == | ||
Revision as of 09:30, 7 July 2017
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= \mathrm{max}(1, | \vec{b}_i| / \mathrm{KSPACING} ). }[/math] These values are rounded to the next integer greater than or equal to [math]\displaystyle{ N }[/math]. In this equation [math]\displaystyle{ \vec{b}_i }[/math] are the reciprocal lattice vectors [math]\displaystyle{ \vec{b}_i \vec{a}_j = 2 \pi \delta_{ij} }[/math]. The generated grid is either centred at the [math]\displaystyle{ \Gamma }[/math] point (e.g. includes the [math]\displaystyle{ \Gamma }[/math] point) (KGAMMA=.TRUE.) or is shifted away from the [math]\displaystyle{ \Gamma }[/math] point, as usually done for Monkhorst Pack grids (KGAMMA=.FALSE.). The default is to include the [math]\displaystyle{ \Gamma }[/math] point.
Note: 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 }[/math] is calculated as [math]\displaystyle{ 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.