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[Matthieu Verstraete <mjv500@york.ac.uk>]

Hello Joe,

amazing, someone may one day actually use this re-smearing! Nicola's 
answer is quite complete, and his phd is indeed a very good pedagogical 
description of the different smearing schemes.

This is getting old for me too but here it is: in the tphysel case, the 
total smearing and entropy functions come from a convolution of 2 delta 
like functions: a Fermi Dirac one of width tphysel, and another which you 
get to choose (you chose gaussians) of width tsmear. The idea is to get 
the physical temperature dependence for low T and then add on a smearing 
to improve kpoint convergence, without spoiling the T dependency (Nicola's 
cold smearing is ideal in this sense, being higher order in tsmear). At 
high T this is useless as the FD smearing takes care of the kpt 
convergence as well.

In principle, I can't see anything too strange happening, especially with 
the gaussian smearing: the convoluted smearing delta will get broader with 
tsmear, and the free energy should increase. I would expect it to increase 
quadratically, like the gaussian term, but 2 things may interfere.

1) for low kpoint sampling as mentioned before, the integration error is 
large and not at all variational wrt nkpt (can be up or down, depending 
sensitively on the position of the kpoints in the BZ) and

2) in some regime, when neither of the smearing types (FD or gaussian) 
strongly dominates, the actual dependence on tphysel/tsmear may be more 
complex than usual (although I wouldn't expect trouble). What do you 
actually get? In my studies I added gaussian/cold smearing on top of FD 
for FCC Al (I never study anything else) and got pretty monotonic behavior 
as a function of tsmear, in particular for hyper converged kpt grids. The 
physical temperature dependence also looked ok, as long as the tsmear 
didn't drown it out.

Tell us all,
Cheers

Matthieu

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Dr. Matthieu Verstraete                 mailto:mjv500@york.ac.uk
Dept. of Physics, University of York,     tel: +44 1904 43 22 08
Heslington, YO10 5DD York, United Kingdom fax: +44 1904 43 22 14