[Pw_forum] More on F-D smearing

[Nicola Marzari]

Hi Paul,


I think there are different world-views behind the nomenclature -
if you think at the smearing orginating in a convolution of the
density of states, you tend to think at the variational functional as
an energy. I like to think at smearing as a ficititious temperature,
hence the free energy. Maybe we should sort this once for all. Stay
tuned.

> By the way, on the system that I'm studying (crystalline
> Tellurium), the application of a finite temperature actually
> *lowers* the free energy. Obviously this is unphysical....although
> perhaps not totally surprising, given that I'm using a finite
> (but dense : 10x10x10) k-point grid. Its still a little worrying though.

No, no, it is ok, for a regular smearing - the free energy is
quadratic around T=0, and the second-order coefficient is negative.
Have a look at paragraphs 4.2 and 4.3 of http://nnn.mit.edu/phd , in
which the Taylor expansion of the free energy around T=0 is discussed
(there is some subtlety having to do with the fact that the
partial and the total derivative of the free energy with respect
to T are equal, since the free energy is a minimum with respect to
psi_i and f_ij).

So, nothing to worry. Not yet.

			nicola


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Prof Nicola Marzari   Department of Materials Science and Engineering
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