ISMEAR determines how the partial occupancies are set for each wavefunction. For the finite temperature LDA SIGMA determines the width of the smearing in eV.
There should be a tag
and for spin-polarized calculations
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.
There should be a tag
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 tetrahedron method with Blöchl corrections.
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 9.4). 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, but the difference between the free energy and the total energy (i.e. the term ' entropy T*S') in the OUTCAR should be negligible (usually less than 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. In this case the tetrahedron method is not applicable if less than three k-points are used.
Mind: Avoid to use ISMEAR>0 for semiconductors and insulators, it might result in problems, because this function gives occupancies which are larger than 2. For insulators you can always use the tetrahedron method (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. There is an extra-line in the OUTCAR file 'energy(SIGMA )' stating the results of this extrapolation. Large SIGMA values lead to a similar error as the MP scheme, but in contrast to the MP scheme there is no way to figure out, how large the error due to the smearing is. Therefore the method of MP seems to be superior to the GS method. In addition forces and stress are consistent with the free energy and not the energy for SIGMA 0. Usually the Methfessel-Paxton is therefore easier to use.
For further considerations on the choice for the smearing method see sections 9.4,10.6. To summarize, use the following guidelines:
For metals a sensible value is usually SIGMA= 0.2 (that's the value we use for most transition metal surfaces).