[Pw_forum] more about phonon frequencies are different when treated as insulator or metal

[Stefano de Gironcoli]

Katalin Gaal-Nagy wrote:

>Are you sure, that the cold smearing of Marzari-Vanderbilt is positive
>definite?
>
have a look to the attached file containing f(x) for gaussian, 
Methfessel-Paxton
and Marzari-Vanderbilt smearing functions .

My understanding of the problems of bad convergence and/or convergence to
"wrong" occupations that sometime occurs with m-p smearing with few k-points
was based on the idea that m-p was not positive definite so that
1)  some eigenstates contribute with negative weight to the charge density
2) the occupation function is non-monotonic and therefore the number of 
electrons
IS NOT a monotonically  increasing function of the Fermi energy as it 
should.

m-v scheme cures the first problem but not the second one and maybe this 
is the
origin of the problems you experienced.

I would expect thatfor a real metal when enough k-points are included in 
the sampling
the function N(E_F) should  become strictly increasing with E_F , both 
with m-p and m-v.
When treating an insulator as a metal some problem can occurs and 
gaussian smearing
is more safe.

stefano
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