[Pw_forum] F-D Smearing etc..

[Paul Tangney]

Hi Nicola,
I obviously wasn't clear.
I agree that E-TS should be called the free energy.
E-TS/2, on the other hand,  is the estimate of the
ground state energy for T=0....when T is used as a
computational device.

I don't agree that F = E-TS should be
lower than the ground state energy (i.e. F, when T=0)
which is what I'm seeing in my simulations.
Of course -TS is always negative because S and T are
positive, but the magnitude of TS should be smaller than
the difference between E(T>0) and E(T=0).

I can't download your thesis from where I am right now,
but I'm pretty sure that the Kohn-Sham ground state is
always lower than the ground state of the Mermin functional
for finite T, and equal to it at T=0.

I think the code is not actually calculating what I want.
What I want is F=E-TS, minimized with respect
to the occupation numbers and the orbitals. I don't think
the code calculates this...it just goes to self consistency
with occupations determined by a F-D distribution.
I'm not sure about this, but I think that what the code
calculates can, in principle, depend on when (i.e. at which
iteration) the excited states are occupied. If at the first
iteration we have a really crap band structure, and then we
occupy it with our F-D dist, this occupation can determine
what happens in the rest of the self consistent calculation.
We might get something different if we began by only occupying
valence bands, and then at iteration 5 (say) started imposing
the F-D distribution.

I don't know if this is why F decreases as T increases
in my calculations.

Anyway, I'm still worried....but its almost Sunday, so I'll have a
day of rest.

Regards,

Paul


-- 
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Dr. Paul Tangney
Theory of Nanostructured Materials Facility
The Molecular Foundry
Lawrence Berkeley National Lab.         E-mail: PTTangney at lbl.gov
1 Cyclotron Road, Bldg 66                  Phone: (510) 642-2635
Berkeley, CA 94720                         Fax :  (510) 643-9345
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