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ISMEAR = -5 | -4 | -3 | -2 | 0 | N
SIGMA= [real]         FERWE= [real array]          FERDO= [real array]

SIGMA = 0.2

ISMEAR determines how the partial occupancies $ f_{n{\bf k}}$ are set for each orbital. For the finite temperature LDA SIGMA determines the width of the smearing in eV.


$ -1$
Gaussian smearing
1..$ N$
method of Methfessel-Paxton order $ N$.
Mind: For the Methfessel-Paxton scheme the partial occupancies can be negative.

$ -2$
partial occupancies are read in from WAVECAR (or INCAR), and kept fixed throughout run.

If the occupancies are fixed by you, there should be a tag

  FERWE = f1 f2 f3 ... f(NBANDS)
and for spin-polarized calculations
  FERDO = f1 f2 f3 ... f(NBANDS)
in the INCAR file supplying the partial occupancies for all bands and k-points. The band-index runs fastest. The partial occupancies must be between 0 and 1 (for spin-polarized and non-spin-polarized calculations).
Mind: Partial occupancies are also written to the OUTCAR file, but in this case they are multiplied by 2, i.e. they are between 0 and 2.

$ -3$
perform a loop over smearing-parameters supplied in the INCAR file. In this case a tag
  SMEARINGS= ismear1 sigma1  ismear2 sigma2  ...
must be present in the INCAR file, supplying different smearing parameters. IBRION has to be set to -1 and NSW to the number of supplied values (ismear$ i$) . The first loop is done using the tetrahedron method with Blöchl corrections.
$ -4$
tetrahedron method without Blöchl corrections (use a $ \Gamma $-centered k-mesh, see sec.5.5 )
$ -5$
tetrahedron method with Blöchl corrections (use a $ \Gamma $-centered k-mesh, see sec.5.5 )
For the calculation of the total energy in bulk materials we recommend the tetrahedron method with Blöchl corrections (ISMEAR=-5). This method also gives a good account for the electronic density of states (DOS). The only drawback is that the methods is not variational with respect to the partial occupancies. Therefore the calculated forces and the stress tensor can be wrong by up to 5 to 10 % for metals. For the calculation of phonon frequencies based on forces we recommend the method of Methfessel-Paxton (ISMEAR$ >$0). For semiconductors and insulators the forces are correct, because partial occupancies do not vary and are zero or one.

The method of Methfessel-Paxton (MP) also results in a very accurate description of the total energy, nevertheless the width of the smearing (SIGMA) must be chosen carefully (see also 7.4). Too large smearing-parameters might result in a wrong total energy, small smearing parameters require a large k-point mesh. SIGMA should be as large as possible keeping the difference between the free energy and the total energy (i.e. the term 'entropy T*S') in the OUTCAR file negligible (1 meV/atom). In most cases $ N=1$ and $ N=2$ leads to very similar results. The method of MP is also the method of choice for large supercells, since the tetrahedron method is not applicable, if less than three k-points are used.

Mind: Avoid using ISMEAR$ >$0 for semiconductors and insulators, since this often leads to incorrect results (The occupancies of some states might be larger or smaller than 1). For insulators use ISMEAR=0 or ISMEAR=-5.

The Gaussian smearing (GS) method also leads to reasonable results in most cases. Within this method it is necessary to extrapolate from finite SIGMA results to SIGMA=0 results. You can find an extra line in the OUTCAR file 'energy( SIGMA $ \to 0$)' giving the extrapolated results. Large SIGMA values lead to a similar error as the MP scheme, but in contrast to the MP scheme one can not determine how large the error due to the smearing is with systematically reducing SIGMA. Therefore the method of MP is more convenient than the GS method. In addition, in the GS method forces and the stress tensor are consistent with the free energy and not the energy for SIGMA $ \to$ 0. Overall the Methfessel-Paxton method is easier to use for metallic systems.

For further considerations on the choice for the smearing method see sections 7.4,8.6. To summarize, use the following guidelines:

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