[Pw_forum] Bandstructure of a metal slab

Nicola Marzari marzari at MIT.EDU
Fri Jan 16 17:18:31 CET 2004

Dear Vasile,

Fermi-Dirac is used only when trying to mimic a true physical
electronic temperature - in all other cases it is less convenient
to use, since it is comparatively "long-tailed" with respect to a
Gaussian smearing. This means you need to introduce more bands above
the Fermi energy in order to capture all the states with non-zero
occupancy than you would otherwise do with a different smearing.
(It's not a completely fair comparison, since for the same
temperature Gaussian and F-D have different slopes at the
Fermi energy, so in practice one should have a "renormalizing"
factor between the temperatures to compare their efficacy in
improving sampling accuracy).

In general, Gaussian-like smearings are preferable.

If you are interested only in the total energies, you can just use a
Gaussian smearing - but you need to be aware of Gillan (JPhysCondMatt
1989) and De Vita work on how to extract a meanigful corrected energy
taking the semisum of the energy and the free energy.

Methfessel-Paxton and Marzari-Vanderbilt do this automatically for
you, and also provide forces, stresses, and whatever else corrected for
the leading term in the temperature. I personally like the M-V cold
smearing best :-), since it does not resort to introducing negative 
occupancies. Negative occupancies could e.g. give rise to regions of 
negative charge density in a slab, where some of the states above the
Fermi energy extend in the vacuum.

A detailed description of all these techniques is in chapter 4 of
my thesis, found at http://nnn.mit.edu/phd/ . Note that recently
Verstaete and Gonze have also shown that you can do a cold-smearing of
a Fermi-Dirac (i.e. the smearing is used not to recover the 0 
temperature result with fewer k-point, but to recover a 
finite-temperature Fermi-Dirac distribution. It's in PRB, and mentioned
in the ABINIT bibliography).

If you are dealing with atoms and molecules with fractional occupancies,
I would use plain Gaussian smearing, being careful in taking the
limit to T-->0 (the free energy E-TS has a S different from 0 for an
atom with fractional occupancies, so you want the limit for zero T).

I seem to remember that what PWSCF calls energy is actually the
free energy E-TS, when temperature broadening is switched on, and
-TS is what is called "correction for metals". Please correct me
if not the case.

Best luck,

			nicola marzari

PWSCF_PS: is the mailing list archived ? It could build up into a
worthwhile repository.

Vasile Chis wrote:
> Dear Users.
> I have some questions.
> When calculating bandstructure of a metal slab, what type of smearing is 
> to be preferred?
> Fermi-Dirac smearing or Gaussian spreading? And, why?
> Thanks in advance!

Prof Nicola Marzari   Department of Materials Science and Engineering
13-5066   MIT   77 Massachusetts Avenue   Cambridge MA 02139-4307 USA
tel 617.4522758  fax 617.2586534  marzari at mit.edu  http://nnn.mit.edu

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