ISMEAR: Difference between revisions

Latest revision as of 07:45, 24 October 2025

ISMEAR = -15 | -14 | -5 | -4 | -3 | -2 | -1 | 0 | [integer]>0
Default: ISMEAR = 1

Description: ISMEAR determines how the partial occupancies f_nk are set for each orbital. SIGMA determines the width of the smearing in eV.

Please consider how-to guide to choose the optimal smearing technique.

Tag options

ISMEAR > 0: method of Methfessel-Paxton order ISMEAR with width SIGMA.

Mind: Methfessel-Paxton can yield erroneous results for insulators because the partial occupancies can be unphysical.

ISMEAR = 0: Gaussian smearing with width SIGMA.

ISMEAR = -1: Fermi smearing with width SIGMA.

ISMEAR = -2: Partial occupancies are read in from the WAVECAR and kept fixed throughout run. Alternatively, you can also choose occupancies in the INCAR file with the tag FERWE (and FERDO for ISPIN = 2 calculations).

ISMEAR = -3: perform a loop over SMEARINGS parameters supplied in the INCAR file.

ISMEAR = -4: Tetrahedron method without smearing.

ISMEAR = -5: Tetrahedron method with Blöchl corrections without smearing.

ISMEAR = -14: Tetrahedron method with Fermi-Dirac smearing SIGMA.

ISMEAR = -15: Tetrahedron method with Blöchl corrections with Fermi-Dirac smearing SIGMA.

Mind: Use a Γ-centered k-mesh for the tetrahedron methods.

@@ Line 1: / Line 1: @@
-{{DISPLAYTITLE:EFERMI_NEDOS}}
+{{TAGDEF|ISMEAR|-15 {{!}} -14 {{!}} -5 {{!}} -4 {{!}} -3 {{!}} -2 {{!}} -1 {{!}} 0 {{!}} [integer]>0 |1}}
-{{TAGDEF|EFERMI_NEDOS|[integer]|21}}
-Description: Choose the number of points in the Gauss–Legendre integration grid used to evaluate the Fermi–Dirac distribution and determine the Fermi level at finite temperature using the tetrahedron method.
+Description: {{TAG|ISMEAR}} determines how the partial occupancies ''f''<sub>n'''k'''</sub> are set for each orbital. {{TAG|SIGMA}} determines the width of the smearing in eV.
-Only relevant when {{TAG|ISMEAR}} = −15 or −14.
+----
-{{Available|6.5.0}}
+Please consider how-to guide to choose the optimal [[smearing technique]].
+== Tag options ==
-----
+*{{TAG|ISMEAR|0|op=>}}: method of Methfessel-Paxton order {{TAG|ISMEAR}} with width {{TAG|SIGMA}}.
+{{NB|mind|Methfessel-Paxton can yield erroneous results for insulators because the partial occupancies can be unphysical.|:}}
+*{{TAG|ISMEAR|0}}: Gaussian smearing with width {{TAG|SIGMA}}.
-During the self-consistent solution of the electronic structure, the Fermi level is obtained by integrating the electronic density of states (DOS) weighted by the Fermi–Dirac occupation function.
+*{{TAG|ISMEAR|-1}}: Fermi smearing with width {{TAG|SIGMA}}.
-By performing a variable transformation, this integral can be efficiently evaluated using Gauss–Legendre quadrature.
-The parameter '''EFERMI_NEDOS''' controls the number of quadrature points used in this integration.
-Increasing the number of integration points generally improves the precision of the computed Fermi level, particularly at low temperatures or in systems with sharp features in the DOS near the Fermi energy.
+*{{TAG|ISMEAR|-2}}: Partial occupancies are read in from the {{FILE|WAVECAR}} and kept fixed throughout run. Alternatively, you can also choose occupancies in the {{FILE|INCAR}} file with the tag {{TAG|FERWE}} (and {{TAG|FERDO}} for {{TAG|ISPIN|2}} calculations).
-However, very high values may lead to unnecessary computational overhead without a significant change in the resulting Fermi level.
-A short convergence test is recommended to find an optimal balance between accuracy and cost.
-==Computation of the number of electrons==
+*{{TAG|ISMEAR|-3}}: perform a loop over {{TAG|SMEARINGS}} parameters supplied in the {{FILE|INCAR}} file.
-The integrated and differential densities of states at <math>T=0</math> are given by
-$$
-n(\epsilon)=\sum_{n\mathbf{k}}\theta(\epsilon-\epsilon_{n\mathbf{k}}), \qquad
-g(\epsilon)=\sum_{n\mathbf{k}}\delta(\epsilon-\epsilon_{n\mathbf{k}}).
-$$
-The total number of electrons can be written either as a sum over Fermi occupations at finite <math>T</math> or as an integral over the DOS:
+*{{TAG|ISMEAR|-4}}: Tetrahedron method without smearing.
-$$
-N_e(\epsilon_F,T)=
-\sum_{n\mathbf{k}}f(\epsilon_{n\mathbf{k}}-\epsilon_F,T)
-=\int_{-\infty}^{\infty}g(\epsilon)f(\epsilon-\epsilon_F,T)\,d\epsilon.
-\tag{1}
-$$
-Making the substitution
+*{{TAG|ISMEAR|-5}}: Tetrahedron method with Blöchl corrections without smearing.
-$$
-x = 1 - 2f(\epsilon-\epsilon_F,T),
-$$
-we obtain
-$$
-\epsilon = k_BT\ln\!\frac{1+x}{1-x}+\epsilon_F, \qquad
-d\epsilon = -k_BT\,\frac{2}{x^2-1}\,dx.
-$$
-Using this change of variable, the integral in Eq. (1) becomes
+*{{TAG|ISMEAR|-14}}: Tetrahedron method with Fermi-Dirac smearing {{TAG|SIGMA}}.
-$$
-N_e(\epsilon_F,T)
-=\frac{1}{2}\int_{-1}^{1}
-n\!\left(k_BT\ln\!\frac{1+x}{1-x}+\epsilon_F\right)\,dx,
-$$
-which is the expression evaluated numerically in VASP using Gauss–Legendre quadrature with {{TAG|EFERMI_NEDOS}} points.
-In practice, this integral is discretized as a weighted sum over <math>N</math> energy grid points:
+*{{TAG|ISMEAR|-15}}: Tetrahedron method with Blöchl corrections with Fermi-Dirac smearing {{TAG|SIGMA}}.
-$$
+{{NB|mind|Use a [[KPOINTS|&Gamma;-centered '''k'''-mesh]] for the tetrahedron methods.|:}}
-N_e(\epsilon_F,T)
-\simeq
-\frac{1}{2}\sum_{i=1}^{N}
-w_i\,
-n\!\left(k_BT\ln\!\frac{1+x_i}{1-x_i}+\epsilon_F\right),
-$$
-where \(w_i\) and \(x_i\) are the Gauss–Legendre weights and abscissas.
-The step functions \(\theta(\epsilon-\epsilon_{n\mathbf{k}})\) entering \(n(\epsilon)\) are evaluated using the tetrahedron method.
-The number of energy points <math>N</math> is defined by {{TAG|EFERMI_NEDOS}}.
-==Related tags and articles==
+== Related tags and articles ==
-{{TAG|ISMEAR}},
 {{TAG|SIGMA}},
+{{TAG|EFERMI}},
+{{TAG|FERWE}},
+{{TAG|FERDO}},
+{{TAG|SMEARINGS}},
 [[Smearing technique]],
 [[K-point integration]]
-[[Category:INCAR tag]]
+{{sc|ISMEAR|Examples|Examples that use this tag}}
-[[Category:Electronic occupancy]]
-[[Category:Electronic minimization]]
-[[Category:Density of states]]
+[[Category:INCAR tag]][[Category:Electronic occupancy]][[Category:Electronic minimization]][[Category:Density of states]]