ISMEAR, SIGMA, FERWE, FERDO tag

ISMEAR = -5 | -4 | -3 | -2 | 0 | N 
SIGMA  =  width of the smearing in eV

Default
ISMEAR	=	1
SIGMA	=	0.2

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

ISMEAR:

$-1$

Fermi-smearing

0

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.

There should be a tag

  FERWE = f1 f2 f3 ....

and for spin-polarized calculations

  FERDO = f1 f2 f3 ...

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 is set to -1 and NSW to the number of supplied values. The first loop is done using the tetrahedron method with Blöchl corrections.

$-4$

tetrahedron method without Blöchl corrections

$-5$

tetrahedron method with Blöchl corrections

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 super cells, 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 leads in most cases also to reasonable results. 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 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:

• 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 appropriated SIGMA value (the entropy term should be less than 1 meV per atom). Mind: Avoid to use ISMEAR$>$0 for semiconductors and insulators, since it might cause problems.

  For metals a sensible value is usually SIGMA= 0.2 (which is the default).

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