ISMEAR = -5 | -4 | -3 | -2 | 0 | N
SIGMA= [real] FERWE= [real array] FERDO= [real array]
ISMEAR determines how the partial occupancies are set for each orbital. For the finite temperature LDA SIGMA determines the width of the smearing in eV.
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).
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) . The first loop is done using the 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 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 and 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 ISMEAR0 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 )' 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 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:
For metals a sensible value is usually SIGMA= 0.2 (which is the default).