Smearing technique - Revision history

Csheldon: Capitalize first letter of file/image link target (broken by wiki case-sensitivity change)

2026-07-22T14:50:48Z

Capitalize first letter of file/image link target (broken by wiki case-sensitivity change)

← Older revision		Revision as of 14:50, 22 July 2026
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	== Broadening techniques ==		== Broadening techniques ==

	[[File:~~smearing~~.png\|thumbnail\|400px\|Broading of different smearing techniques near the Fermi energy ϵ<sub>F</sub>.		[[File:Smearing.png\|thumbnail\|400px\|Broading of different smearing techniques near the Fermi energy ϵ<sub>F</sub>.
	The energy is measured in units of the smearing σ ({{TAG\|SIGMA}}).		The energy is measured in units of the smearing σ ({{TAG\|SIGMA}}).
	The Methfessel-Paxton method (cyan) is narrower than the Gaussian distribution (blue) but also has negative features.		The Methfessel-Paxton method (cyan) is narrower than the Gaussian distribution (blue) but also has negative features.
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	== Tetrahedron methods ==		== Tetrahedron methods ==

	[[File:~~dos~~-gauss-tetra.png\|thumbnail\|400px\|The density of states (DOS) obtained with Gaussian broadening (blue) has much more oscillations than the one obtained with tetrahedron interpolation (red).		[[File:Dos-gauss-tetra.png\|thumbnail\|400px\|The density of states (DOS) obtained with Gaussian broadening (blue) has much more oscillations than the one obtained with tetrahedron interpolation (red).
	These spikes correspond to eigenvalue of the bands at different '''k''' points.		These spikes correspond to eigenvalue of the bands at different '''k''' points.
	In the tetrahedron method the band is interpolated between the points flattening out the DOS.		In the tetrahedron method the band is interpolated between the points flattening out the DOS.

Schlipf: /* Related tags and articles */

2026-07-07T09:28:36Z

Schlipf: /* Tetrahedron methods */

2026-07-07T09:28:24Z

Tetrahedron methods

← Older revision		Revision as of 09:28, 7 July 2026
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	Another artifact of the broadening is that the DOS extends into the band gap.]]		Another artifact of the broadening is that the DOS extends into the band gap.]]

	In bulk materials, we recommend the tetrahedron method with Blöchl corrections ({{TAG\|ISMEAR}}=-5) for the calculation of very precise ''total energies'' or the electronic [[:Category:Density of states\|density of states]] (DOS).		In bulk materials, we recommend the tetrahedron method with Blöchl corrections{{cite\|bloechl:prb:1994}} ({{TAG\|ISMEAR}}=-5) for the calculation of very precise ''total energies'' or the electronic [[:Category:Density of states\|density of states]] (DOS).
	In contrast to broadening methods, the tetrahedron method interpolates between '''k''' points of a band.		In contrast to broadening methods, the tetrahedron method interpolates between '''k''' points of a band.
	As a consequence, if a band spans a certain energy range, the tetrahedron method will yield no contribution outside of this energy range.		As a consequence, if a band spans a certain energy range, the tetrahedron method will yield no contribution outside of this energy range.

Singraber at 08:10, 24 October 2025

2025-10-24T08:10:30Z

Huebsch: /* Tetrahedron methods */

2025-10-15T12:37:25Z

Tetrahedron methods

← Older revision		Revision as of 12:37, 15 October 2025
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	Partial occupancies arise from the fact that a tetrahedron crosses the Fermi energy.		Partial occupancies arise from the fact that a tetrahedron crosses the Fermi energy.
	We provide also the option to add temperature on top of the tetrahedron method with {{TAGO\|ISMEAR\|-14}} and {{TAGO\|ISMEAR\|-15}}.		We provide also the option to add temperature on top of the tetrahedron method with {{TAGO\|ISMEAR\|-14}} and {{TAGO\|ISMEAR\|-15}}.
	This is particularly relevant if accurate occupancies are required e.g. in the context of transport calculations.		This is particularly relevant if accurate occupancies are required e.g. in the context of [[Transport coefficients including electron-phonon scattering\|transport calculations]].

	== Calculation of the Fermi energy ==		== Calculation of the Fermi energy ==

Huebsch: /* How to set ISMEAR */

2025-03-11T09:33:09Z

How to set ISMEAR

← Older revision		Revision as of 09:33, 11 March 2025
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	For the calculation of the ''total energy'' in bulk materials, we recommend the tetrahedron method with Blöchl corrections ({{TAG\|ISMEAR}}=-5). This method also gives a good account of the electronic [[:Category:Density of states\|density]]. In VASP, it is a good idea to always set a smearing method in the {{FILE\|INCAR}} file because the default choice may lead to incorrect results for some materials.		For the calculation of the ''total energy'' in bulk materials, we recommend the tetrahedron method with Blöchl corrections ({{TAG\|ISMEAR}}=-5). This method also gives a good account of the electronic [[:Category:Density of states\|density]]. In VASP, it is a good idea to always set a smearing method in the {{FILE\|INCAR}} file because the default choice may lead to incorrect results for some materials.
	We recommend to default to Gaussian smearing with a relatively small smearing and to set the Fermi energy to the middle of the bandgap		We recommend to default to Gaussian smearing with a relatively small smearing and to set the Fermi energy to the middle of the bandgap
	{{~~TAG~~\|ISMEAR}} = 0		{{TAGBL\|ISMEAR}} = 0
	{{~~TAG~~\|SIGMA}} = 0.1		{{TAGBL\|SIGMA}} = 0.1
	{{~~TAG~~\|EFERMI}} = MIDGAP		{{TAGBL\|EFERMI}} = MIDGAP
	If you do not know much about your system, we recommend to start with this setup.		If you do not know much about your system, we recommend to start with this setup.
	Below, we explain why this is a good choice and when you should deviate from that.		Below, we explain why this is a good choice and when you should deviate from that.

Schlipf: /* Which method to use */

2025-03-03T14:07:51Z

Which method to use

← Older revision		Revision as of 14:07, 3 March 2025
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	== Which method to use ==		== Which method to use ==

	If you have no prior knowledge of your system always use Gaussian smearing {{TAGO\|ISMEAR\|0}} in combination with a small {{TAGO\|SIGMA\|0.03 to 0.05}}.		If you have no prior knowledge of your system always use Gaussian smearing {{TAGO\|ISMEAR\|0}} in combination with a small {{TAGO\|SIGMA\|0.03 to 0.1}}.
	This applies in particular if you do not know whether your system is an insulator, a semiconductor or a metal and for high-throughput calculations.		This applies in particular if you do not know whether your system is an insulator, a semiconductor or a metal and for high-throughput calculations.
	This is not the default in VASP, so to be on the safe side, you might want to include this setting in all your {{TAG\|INCAR}} files.		This is not the default in VASP, so to be on the safe side, you might want to include this setting in all your {{TAG\|INCAR}} files.

Schlipf: /* Gaussian broadening */

2025-03-03T14:07:32Z

Gaussian broadening

← Older revision		Revision as of 14:07, 3 March 2025
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	You can find an extra line in the {{FILE\|OUTCAR}} file: <tt>energy( SIGMA→0 )</tt>, giving the extrapolated results.		You can find an extra line in the {{FILE\|OUTCAR}} file: <tt>energy( SIGMA→0 )</tt>, giving the extrapolated results.
	However, this value will not be accurate without systematically reducing {{TAG\|SIGMA}}.		However, this value will not be accurate without systematically reducing {{TAG\|SIGMA}}.
	Typically, you will need to use a {{TAG\|SIGMA}} of 0.03 to 0.05 for converged results.		Typically, you will need to use a {{TAG\|SIGMA}} of 0.03 to 0.1 for converged results.
	{{NB\|mind\|The forces and stress are consistent with the free energy and not with the extrapolated energy {{TAG\|SIGMA}}→0 so make sure that forces and stress are converged with respect to {{TAG\|SIGMA}} as well.}}		{{NB\|mind\|The forces and stress are consistent with the free energy and not with the extrapolated energy {{TAG\|SIGMA}}→0 so make sure that forces and stress are converged with respect to {{TAG\|SIGMA}} as well.}}

Huebsch at 14:05, 3 March 2025

2025-03-03T14:05:38Z

← Older revision		Revision as of 14:05, 3 March 2025
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	We recommend to default to Gaussian smearing with a relatively small smearing and to set the Fermi energy to the middle of the bandgap		We recommend to default to Gaussian smearing with a relatively small smearing and to set the Fermi energy to the middle of the bandgap
	{{TAG\|ISMEAR}} = 0		{{TAG\|ISMEAR}} = 0
	{{TAG\|SIGMA}} = 0.05		{{TAG\|SIGMA}} = 0.1
	{{TAG\|EFERMI}} = MIDGAP		{{TAG\|EFERMI}} = MIDGAP
	If you do not know much about your system, we recommend to start with this setup.		If you do not know much about your system, we recommend to start with this setup.

Vaspmaster: /* How to set ISMEAR */

2025-03-03T13:59:46Z

How to set ISMEAR

← Older revision		Revision as of 13:59, 3 March 2025
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	== How to set ISMEAR ==		== How to set ISMEAR ==
	For the calculation of the ''total energy'' in bulk materials, we recommend the tetrahedron method with Blöchl corrections ({{TAG\|ISMEAR}}=-5). This method also gives a good account of the electronic [[:Category:Density of states\|density ~~oIn~~ VASP, it is a good idea to always set a smearing method in the {{FILE\|INCAR}} file because the default choice may lead to incorrect results for some materials.		For the calculation of the ''total energy'' in bulk materials, we recommend the tetrahedron method with Blöchl corrections ({{TAG\|ISMEAR}}=-5). This method also gives a good account of the electronic [[:Category:Density of states\|density]]. In VASP, it is a good idea to always set a smearing method in the {{FILE\|INCAR}} file because the default choice may lead to incorrect results for some materials.
	We recommend to default to Gaussian smearing with a relatively small smearing and to set the Fermi energy to the middle of the bandgap		We recommend to default to Gaussian smearing with a relatively small smearing and to set the Fermi energy to the middle of the bandgap
	{{TAG\|ISMEAR}} = 0		{{TAG\|ISMEAR}} = 0

← Older revision		Revision as of 09:28, 7 July 2026
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	{{TAG\|SMEARINGS}},		{{TAG\|SMEARINGS}},
	[[Integrating over all orbitals]]		[[Integrating over all orbitals]]

			== References ==

	[[Category:Electronic occupancy]][[Category:Electronic minimization]][[Category:Density of states]][[Category:Howto]]		[[Category:Electronic occupancy]][[Category:Electronic minimization]][[Category:Density of states]][[Category:Howto]]

← Older revision		Revision as of 14:07, 3 March 2025
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	You can find an extra line in the {{FILE\|OUTCAR}} file: <tt>energy( SIGMA→0 )</tt>, giving the extrapolated results.		You can find an extra line in the {{FILE\|OUTCAR}} file: <tt>energy( SIGMA→0 )</tt>, giving the extrapolated results.
	However, this value will not be accurate without systematically reducing {{TAG\|SIGMA}}.		However, this value will not be accurate without systematically reducing {{TAG\|SIGMA}}.
	Typically, you will need to use a {{TAG\|SIGMA}} of 0.03 to 0.05 for converged results.		Typically, you will need to use a {{TAG\|SIGMA}} of 0.03 to 0.1 for converged results.
	{{NB\|mind\|The forces and stress are consistent with the free energy and not with the extrapolated energy {{TAG\|SIGMA}}→0 so make sure that forces and stress are converged with respect to {{TAG\|SIGMA}} as well.}}		{{NB\|mind\|The forces and stress are consistent with the free energy and not with the extrapolated energy {{TAG\|SIGMA}}→0 so make sure that forces and stress are converged with respect to {{TAG\|SIGMA}} as well.}}

← Older revision		Revision as of 08:10, 24 October 2025
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	=== Gaussian broadening ===		=== Gaussian broadening ===
	The Gaussian-smearing method leads to very reasonable results in most cases.		The Gaussian-smearing method leads to very reasonable results in most cases.
	Within this method it is necessary to extrapolate from finite {{TAG\|SIGMA}} results to {{~~TAGO~~\|SIGMA\|0}} results.		Within this method it is necessary to extrapolate from finite {{TAG\|SIGMA}} results to {{TAG\|SIGMA\|0}} results.
	You can find an extra line in the {{FILE\|OUTCAR}} file: <tt>energy( SIGMA→0 )</tt>, giving the extrapolated results.		You can find an extra line in the {{FILE\|OUTCAR}} file: <tt>energy( SIGMA→0 )</tt>, giving the extrapolated results.
	However, this value will not be accurate without systematically reducing {{TAG\|SIGMA}}.		However, this value will not be accurate without systematically reducing {{TAG\|SIGMA}}.
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	=== Methfessel-Paxton broadening ===		=== Methfessel-Paxton broadening ===
	The method of Methfessel-Paxton ({{~~TAGO~~\|ISMEAR\|op=>}}) results in a very accurate description of the total energy in metals.		The method of Methfessel-Paxton ({{TAG\|ISMEAR\|op=>}}) results in a very accurate description of the total energy in metals.
	Nevertheless, the width of the smearing ({{TAG\|SIGMA}}) must be chosen carefully.		Nevertheless, the width of the smearing ({{TAG\|SIGMA}}) must be chosen carefully.
	{{TAG\|SIGMA}} should be as large as possible, while keeping the difference between the free energy and the total energy (i.e. the term <tt>entropy T*S</tt>) in the {{FILE\|OUTCAR}} file negligible (1 meV/atom).		{{TAG\|SIGMA}} should be as large as possible, while keeping the difference between the free energy and the total energy (i.e. the term <tt>entropy T*S</tt>) in the {{FILE\|OUTCAR}} file negligible (1 meV/atom).
	The Methfessel-Paxton method is somewhat easier to use than the Gaussian method since the energies can be corrected for the energy term.		The Methfessel-Paxton method is somewhat easier to use than the Gaussian method since the energies can be corrected for the energy term.
	Therefore, we recommend to use this method {{~~TAGO~~\|ISMEAR}} for the calculation of forces and phonon frequencies in metals.		Therefore, we recommend to use this method {{TAG\|ISMEAR}} for the calculation of forces and phonon frequencies in metals.
	{{NB\|warning\| Avoid using {{~~TAGO~~\|ISMEAR\|0\|op=>}} for semiconductors and insulators, since this often leads to incorrect results. Since the occupancies are not monotonous Methfessel-Paxton does not guarantee deterministic results in systems with a gap. Errors for phonons frequencies can exceed 20%. These errors are very hard to spot if you do not look carefully. For insulators, use Gaussian smearing ({{~~TAGO~~\|ISMEAR\|0}}) or the tetrahedron method ({{~~TAGO~~\|ISMEAR\|-5}}).}}		{{NB\|warning\| Avoid using {{TAG\|ISMEAR\|0\|op=>}} for semiconductors and insulators, since this often leads to incorrect results. Since the occupancies are not monotonous Methfessel-Paxton does not guarantee deterministic results in systems with a gap. Errors for phonons frequencies can exceed 20%. These errors are very hard to spot if you do not look carefully. For insulators, use Gaussian smearing ({{TAG\|ISMEAR\|0}}) or the tetrahedron method ({{TAG\|ISMEAR\|-5}}).}}

	=== Fermi-Dirac broadening ===		=== Fermi-Dirac broadening ===
	With the Fermi-Dirac method ({{~~TAGO~~\|ISMEAR\|-1}}), the smearing {{TAG\|SIGMA}} corresponds to the temperature of the electronic system.		With the Fermi-Dirac method ({{TAG\|ISMEAR\|-1}}), the smearing {{TAG\|SIGMA}} corresponds to the temperature of the electronic system.
	You should use this method, if this temperature equivalence is important for you, e.g., if you want to compute some properties based		You should use this method, if this temperature equivalence is important for you, e.g., if you want to compute some properties based
	on the occupations.		on the occupations.
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	The occupancies in the tetrahedron method are exact for the linear extrapolation of the bands.		The occupancies in the tetrahedron method are exact for the linear extrapolation of the bands.
	Partial occupancies arise from the fact that a tetrahedron crosses the Fermi energy.		Partial occupancies arise from the fact that a tetrahedron crosses the Fermi energy.
	We provide also the option to add temperature on top of the tetrahedron method with {{~~TAGO~~\|ISMEAR\|-14}} and {{~~TAGO~~\|ISMEAR\|-15}}.		We provide also the option to add temperature on top of the tetrahedron method with {{TAG\|ISMEAR\|-14}} and {{TAG\|ISMEAR\|-15}}.
	This is particularly relevant if accurate occupancies are required e.g. in the context of [[Transport coefficients including electron-phonon scattering\|transport calculations]].		This is particularly relevant if accurate occupancies are required e.g. in the context of [[Transport coefficients including electron-phonon scattering\|transport calculations]].

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	VASP implicitly computes the Fermi energy such that the sum over all occupations results in the number of electrons.		VASP implicitly computes the Fermi energy such that the sum over all occupations results in the number of electrons.
	In insulators and semiconductors, this choice is not unique if {{TAG\|SIGMA}} is much smaller than the gap.		In insulators and semiconductors, this choice is not unique if {{TAG\|SIGMA}} is much smaller than the gap.
	By default {{~~TAGO~~\|EFERMI\|LEGACY}}, VASP will set the Fermi energy typically close to the lower end of the bandgap.		By default {{TAG\|EFERMI\|LEGACY}}, VASP will set the Fermi energy typically close to the lower end of the bandgap.
	This method is not deterministic, i.e., changes to the number of points for the density of states {{TAG\|NEDOS}} can lead to different values.		This method is not deterministic, i.e., changes to the number of points for the density of states {{TAG\|NEDOS}} can lead to different values.
	It is also fragile with the Methfessel-Paxton method if you forgot to switch to a different smearing method for a gapped system.		It is also fragile with the Methfessel-Paxton method if you forgot to switch to a different smearing method for a gapped system.

	To avoid these issues, we implemented a new method {{~~TAGO~~\|EFERMI\|MIDGAP}}.		To avoid these issues, we implemented a new method {{TAG\|EFERMI\|MIDGAP}}.
	It will compute the middle of the bandgap and use it as starting point for the interval bisection to compute the Fermi energy.		It will compute the middle of the bandgap and use it as starting point for the interval bisection to compute the Fermi energy.
	In systems, with a bandgap significantly larger than the smearing width {{TAG\|SIGMA}} the search will terminate immediately.		In systems, with a bandgap significantly larger than the smearing width {{TAG\|SIGMA}} the search will terminate immediately.
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	== Which method to use ==		== Which method to use ==

	If you have no prior knowledge of your system always use Gaussian smearing {{~~TAGO~~\|ISMEAR\|0}} in combination with a small {{~~TAGO~~\|SIGMA\|0.03 to 0.1}}.		If you have no prior knowledge of your system always use Gaussian smearing {{TAG\|ISMEAR\|0}} in combination with a small {{TAG\|SIGMA\|0.03 to 0.1}}.
	This applies in particular if you do not know whether your system is an insulator, a semiconductor or a metal and for high-throughput calculations.		This applies in particular if you do not know whether your system is an insulator, a semiconductor or a metal and for high-throughput calculations.
	This is not the default in VASP, so to be on the safe side, you might want to include this setting in all your {{TAG\|INCAR}} files.		This is not the default in VASP, so to be on the safe side, you might want to include this setting in all your {{TAG\|INCAR}} files.
	You can also switch to set the Fermi energy in the middle of the gap with {{~~TAGO~~\|EFERMI\|MIDGAP}}.		You can also switch to set the Fermi energy in the middle of the gap with {{TAG\|EFERMI\|MIDGAP}}.
	Keep in mind to check that your calculations are converged with respect to width {{TAG\|SIGMA}}		Keep in mind to check that your calculations are converged with respect to width {{TAG\|SIGMA}}

	For semiconductors or insulators, you can use the tetrahedron method ({{~~TAGO~~\|ISMEAR\|-5}}) if you have at least 4 '''k''' points to form a tetrahedron.		For semiconductors or insulators, you can use the tetrahedron method ({{TAG\|ISMEAR\|-5}}) if you have at least 4 '''k''' points to form a tetrahedron.
	This eliminates the need to converge the smearing width {{TAG\|SIGMA}}.		This eliminates the need to converge the smearing width {{TAG\|SIGMA}}.
	You need to be sure that the bandgap will not close during the relaxation or molecular dynamics calculation otherwise the forces may be inaccurate.		You need to be sure that the bandgap will not close during the relaxation or molecular dynamics calculation otherwise the forces may be inaccurate.

	For relaxations ''in metals'', use {{TAG\|ISMEAR}}=1 or {{TAG\|ISMEAR}}=2 and an appropriate {{TAG\|SIGMA}} value (the entropy term should be less than 1 meV per atom).		For relaxations ''in metals'', use {{TAG\|ISMEAR}}=1 or {{TAG\|ISMEAR}}=2 and an appropriate {{TAG\|SIGMA}} value (the entropy term should be less than 1 meV per atom).
	Often the default value {{~~TAGO~~\|SIGMA\|0.2}} is a reasonable choice for metals.		Often the default value {{TAG\|SIGMA\|0.2}} is a reasonable choice for metals.
	'''Mind again''': Avoid using {{TAG\|ISMEAR\|0\|op=>}} for semiconductors and insulators since it might cause severe problems.		'''Mind again''': Avoid using {{TAG\|ISMEAR\|0\|op=>}} for semiconductors and insulators since it might cause severe problems.

	For the calculations of the density of states (DOS) and very accurate total-energy calculations (no relaxation in metals), use the tetrahedron method ({{~~TAGO~~\|ISMEAR\|-5}}).		For the calculations of the density of states (DOS) and very accurate total-energy calculations (no relaxation in metals), use the tetrahedron method ({{TAG\|ISMEAR\|-5}}).
	You would often do this at the end of a relaxation for the converged structure with a denser '''k'''-point mesh to get an accurate DOS.		You would often do this at the end of a relaxation for the converged structure with a denser '''k'''-point mesh to get an accurate DOS.

	== Other methods ==		== Other methods ==

	If you want to keep the occupancies fixed, use {{~~TAGO~~\|ISMEAR\|-2}}.		If you want to keep the occupancies fixed, use {{TAG\|ISMEAR\|-2}}.
	This may be useful to constraint the electronic state.		This may be useful to constraint the electronic state.
	However, keep in mind that this is only an approximation and the real system would relax the occupancies.		However, keep in mind that this is only an approximation and the real system would relax the occupancies.
	Please refer to the documentation of {{TAG\|FERWE}} in case you want to set the occupancies manually.		Please refer to the documentation of {{TAG\|FERWE}} in case you want to set the occupancies manually.

	To compare the results of different smearings, you can use {{~~TAGO~~\|ISMEAR\|-3}}.		To compare the results of different smearings, you can use {{TAG\|ISMEAR\|-3}}.
	You could use this feature e.g. to converge the {{TAG\|SIGMA}} when Gaussian broadening is used.		You could use this feature e.g. to converge the {{TAG\|SIGMA}} when Gaussian broadening is used.
	Please refer to the documentation of {{TAG\|SMEARINGS}} how to set the smearing methods.		Please refer to the documentation of {{TAG\|SMEARINGS}} how to set the smearing methods.