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# ISMEAR

ISMEAR = -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.

- ISMEAR=
*N*(*N*>0): method of Methfessel-Paxton order*N*.

**Mind**: For the Methfessel-Paxton scheme the partial occupancies can be negative.

- ISMEAR=0: Gaussian smearing.
- ISMEAR=−1: Fermi smearing.
- ISMEAR=−2: partial occupancies are read in from the WAVECAR or INCAR file, and kept fixed throughout run.

- To set the occupancies specify

FERWE = f1 f2 f3 ... f(NBANDS)

- and for spin-polarized calculations, additionally

FERDO = f1 f2 f3 ... f(NBANDS)

- in the INCAR file. The (partial) occupancies must be specified for all bands and k-points. The band-index runs fastest. The 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.

- In this case a tag

SMEARINGS= ismear_{1}sigma_{1}ismear_{2}sigma_{2}...

- 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 pairs ismear
_{i}/sigma_{i}. The first loop is done using the tetrahedron method with Blöchl corrections.

- ISMEAR=−4: tetrahedron method (use a Γ-centered
**k**-mesh). - ISMEAR=−5: tetrahedron method with Blöchl corrections (use a Γ-centered
**k**-mesh).

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 method 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 either zero or one.
The method of Methfessel-Paxton (ISMEAR>0) also results in a very accurate description of the total energy, nevertheless the width of the smearing (SIGMA) must be chosen carefully. Too large smearing-parameters might result in a wrong total energy, small smearing parameters require a dense mesh of **k**-points. 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 and leads to very similar results. The method of Methfessel-Paxton 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 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→0 )`, giving the extrapolated results. Large SIGMA values lead to a similar error as the Methfessel-Paxton scheme, but in contrast to the Methfessel-Paxton scheme one can not determine how large the error due to the smearing is with systematically reducing SIGMA. Therefore the method of Methfessel-Paxton is more convenient than the Gaussian smearing method. In addition, in the Gaussian smearing method forces and the stress tensor are consistent with the free energy and not the energy for SIGMA→0. Overall the Methfessel-Paxton method is easier to use for metallic systems.

- For semiconductors or insulators use the tetrahedron method (ISMEAR=-5), if the cell is too large (or if you use only a single or two
**k**-points) use ISMEAR=0 in combination with a small SIGMA=0.05.

- For relaxations
*in metals*always use ISMEAR=1 or ISMEAR}=2 and an appropriate SIGMA value (the entropy term should be less than 1 meV per atom). For metals a sensible value is usually SIGMA= 0.2 (which is the default).

**Mind**: Avoid to use ISMEAR>0 for semiconductors and insulators, since it might cause problems.

- For the calculations of the DOS and very accurate
*total energy*calculations (no relaxation in metals) use the tetrahedron method (ISMEAR=-5).