KSPACING - Revision history

Huebsch at 11:34, 21 October 2024

2024-10-21T11:34:14Z

← Older revision		Revision as of 11:34, 21 October 2024
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	----		----

	[[Category:INCAR tag]][[Category:~~Electronic minimization~~]]		[[Category:INCAR tag]][[Category:Crystal momentum]]

Huebsch at 07:13, 3 October 2023

2023-10-03T07:13:31Z

← Older revision		Revision as of 07:13, 3 October 2023
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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 ~~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~~.		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\|~~warning~~\|This implementation is not entirely ~~consistent~~ with the automatic k-point generation ~~(Mode{{=}}A)~~ used in the {{FILE\|KPOINTS}} file.}}		{{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>

Miranda.henrique at 18:45, 1 September 2022

2022-09-01T18:45:38Z

← Older revision		Revision as of 18:45, 1 September 2022
Line 7:		Line 7:

	{{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~~)</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>\~~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>\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 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.		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.}}

Miranda.henrique at 18:40, 1 September 2022

2022-09-01T18:40:32Z

← Older revision		Revision as of 18:40, 1 September 2022
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	{{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
	<math> N_i= \mathrm{int}(\mathrm{max}(1, R_k\| \mathbf{b}_i\| + 0.5)) </math> with <math>R_k=1/\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>
	and rounding it to the nearest integer. We recommend using the {{TAG\|KSPACING}} tag in the {{FILE\|INCAR}} file		and rounding it to the nearest integer. We recommend using the {{TAG\|KSPACING}} tag in the {{FILE\|INCAR}} file
	and avoiding the automatic mode via the {{FILE\|KPOINTS}} file.		and avoiding the automatic mode via the {{FILE\|KPOINTS}} file.

Miranda.henrique at 18:38, 1 September 2022

2022-09-01T18:38:03Z

← Older revision		Revision as of 18:38, 1 September 2022
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	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=1/\mathrm{KSPACING}</math>		<math> N_i= \mathrm{int}(\mathrm{max}(1, R_k\| \mathbf{b}_i\| + 0.5)) </math> with <math>R_k=1/\mathrm{KSPACING}</math>
	and rounding is to the nearest integer. We recommend using the {{TAG\|KSPACING}} tag in the {{FILE\|INCAR}} file		and rounding it to the nearest integer. We recommend using the {{TAG\|KSPACING}} tag in the {{FILE\|INCAR}} file
	and avoiding the automatic mode via the {{FILE\|KPOINTS}} file.		and avoiding the automatic mode via the {{FILE\|KPOINTS}} file.

Miranda.henrique at 18:36, 1 September 2022

2022-09-01T18:36:44Z

← Older revision		Revision as of 18:36, 1 September 2022
Line 7:		Line 7:

	{{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). </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, \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 ({{TAG\|KGAMMA}}=.TRUE., or is shifted away from the <math>\Gamma</math> point, as done for Monkhorst-Pack grids when ({{TAG\|KGAMMA}}=.FALSE.. The default is to include the <math>\Gamma</math> point.		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

Miranda.henrique at 18:33, 1 September 2022

2022-09-01T18:33:38Z

← Older revision		Revision as of 18:33, 1 September 2022
Line 7:		Line 7:

	{{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= \mathrm{max}(1, \| \~~vec~~{b}_i\| / \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, \lceil \| \mathbf{b}_i\| / \mathrm{KSPACING} \rceil). </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>.		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 ({{TAG\|KGAMMA}}=.TRUE., or is shifted away from the <math>\Gamma</math> point, as done for Monkhorst-Pack grids when ({{TAG\|KGAMMA}}=.FALSE.. The default is to include the <math>\Gamma</math> point.		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.. 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 automatic mode in the {{FILE\|KPOINTS}} file, <math> N</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= \mathrm{max}(1, \| \~~vec~~{b}_i\| / ~~(2 \pi \times~~ \mathrm{KSPACING}~~) )~~ </math>		<math> N_i= \mathrm{int}(\mathrm{max}(1, R_k\| \mathbf{b}_i\| + 0.5)) </math> with <math>R_k=1/\mathrm{KSPACING}</math>
	and rounding is to the nearest integer. We recommend using the {{TAG\|KSPACING}} tag in the {{FILE\|INCAR}} file		and rounding is to the nearest integer. We recommend using the {{TAG\|KSPACING}} tag in the {{FILE\|INCAR}} file
	and avoiding the automatic mode via the {{FILE\|KPOINTS}} file.		and avoiding the automatic mode via the {{FILE\|KPOINTS}} file.

Karsai at 14:25, 8 April 2022

2022-04-08T14:25:41Z

← Older revision		Revision as of 14:25, 8 April 2022
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	----		----

	[[Category:INCAR]][[Category:Electronic minimization]]		[[Category:INCAR tag]][[Category:Electronic minimization]]

Karsai at 14:25, 8 April 2022

2022-04-08T14:25:18Z

← Older revision		Revision as of 14:25, 8 April 2022
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	{{sc\|KSPACING\|Examples\|Examples that use this tag}}		{{sc\|KSPACING\|Examples\|Examples that use this tag}}
	----		----
	~~[[The_VASP_Manual\|Contents]]~~

	[[Category:INCAR]][[Category:Electronic minimization]]		[[Category:INCAR]][[Category:Electronic minimization]]

Huebsch at 12:53, 6 April 2022

2022-04-06T12:53:44Z

← Older revision		Revision as of 12:53, 6 April 2022
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	{{TAGDEF\|KSPACING\|[real]\|0.5}}		{{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.		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>
	The number of k-points in the direction of the first, second and third		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>.
	reciprocal lattice vector is determined by <math> N= \mathrm{max}(1, \| \vec{b}_i\| / \mathrm{KSPACING} ). </math>		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.. The default is to include the <math>\Gamma</math> point.
	These values are rounded to the next integer greater than or equal to <math> N </math>. In this equation		{{NB\|warning\|This implementation is not entirely consistent with the automatic k-point generation (Mode{{=}}A) used in the {{FILE\|KPOINTS}} file.}}
	<math> \vec{b}_i </math>		If the k points are generated using the automatic mode in the {{FILE\|KPOINTS}} file, <math> N</math> is calculated as
	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
	(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>		<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 rounding is to the nearest integer. We recommend using the {{TAG\|KSPACING}} tag in the {{FILE\|INCAR}} file
	and ~~to avoid using~~ the automatic mode via the KPOINTS file.		and avoiding the automatic mode via the {{FILE\|KPOINTS}} file.

	== Related ~~Tags~~ and ~~Sections~~ ==		== Related tags and articles ==
	{{TAG\|KGAMMA}}		{{TAG\|KGAMMA}}, {{FILE\|KPOINTS}}

	{{sc\|KSPACING\|Examples\|Examples that use this tag}}		{{sc\|KSPACING\|Examples\|Examples that use this tag}}
Line 31:		Line 23:
	[[The_VASP_Manual\|Contents]]		[[The_VASP_Manual\|Contents]]

	[[Category:INCAR]][[Category:Electronic ~~Minimization]][[Category:Electronic Minimization Methods~~]]		[[Category:INCAR]][[Category:Electronic minimization]]

← Older revision		Revision as of 07:13, 3 October 2023
Line 9:		Line 9:
	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 ~~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~~.		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\|~~warning~~\|This implementation is not entirely ~~consistent~~ with the automatic k-point generation ~~(Mode{{=}}A)~~ used in the {{FILE\|KPOINTS}} file.}}		{{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>

← Older revision		Revision as of 18:45, 1 September 2022
Line 7:		Line 7:

	{{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~~)</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>\~~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>\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 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.		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.}}

← Older revision		Revision as of 18:40, 1 September 2022
Line 12:		Line 12:
	{{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
	<math> N_i= \mathrm{int}(\mathrm{max}(1, R_k\| \mathbf{b}_i\| + 0.5)) </math> with <math>R_k=1/\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>
	and rounding it to the nearest integer. We recommend using the {{TAG\|KSPACING}} tag in the {{FILE\|INCAR}} file		and rounding it to the nearest integer. We recommend using the {{TAG\|KSPACING}} tag in the {{FILE\|INCAR}} file
	and avoiding the automatic mode via the {{FILE\|KPOINTS}} file.		and avoiding the automatic mode via the {{FILE\|KPOINTS}} file.

← Older revision		Revision as of 18:38, 1 September 2022
Line 13:		Line 13:
	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=1/\mathrm{KSPACING}</math>		<math> N_i= \mathrm{int}(\mathrm{max}(1, R_k\| \mathbf{b}_i\| + 0.5)) </math> with <math>R_k=1/\mathrm{KSPACING}</math>
	and rounding is to the nearest integer. We recommend using the {{TAG\|KSPACING}} tag in the {{FILE\|INCAR}} file		and rounding it to the nearest integer. We recommend using the {{TAG\|KSPACING}} tag in the {{FILE\|INCAR}} file
	and avoiding the automatic mode via the {{FILE\|KPOINTS}} file.		and avoiding the automatic mode via the {{FILE\|KPOINTS}} file.

← Older revision		Revision as of 18:36, 1 September 2022
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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). </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, \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 ({{TAG\|KGAMMA}}=.TRUE., or is shifted away from the <math>\Gamma</math> point, as done for Monkhorst-Pack grids when ({{TAG\|KGAMMA}}=.FALSE.. The default is to include the <math>\Gamma</math> point.		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