[Pw_forum] F-D Smearing etc..

[Nicola Marzari]

Hi Paul,


I've uploaded in http://nnn.mit.edu/paul a plot of E-TS (free),
E (total), and E-TS/2 (corrected) for bulk Al, and Gauassian smearing.
This should show you what to expect for the change in temperature
of the different quantities. The analytical proofs are in the thesis.

Note that if you were using Methfessel-Paxton or Marzari-Vanderbilt,
the free energy wouldn't have a quadratic term, and would look
almost identical to the corrected energy of the plot attached.

> 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.

All codes calculate exactly what you want, i.e. F=E-TS minimized
with respecte to occupation numbers and orbitals. They do this either
using a direct minimization recipe on all those degrees of freedom
(this is the "ensemble-DFT" philosophy, now available in the CVS of
Quantum-Espresso, thanks to Paolo Umari and Ismaila Dabo), or
they reach iteratively  selfconsistency (PWSCF and all other
codes). Once you are *fully* selfconsistent (i.e. the eigenvectors
of your Hamiltonian, populated with occupations given by the
thermal-distribution of their eigenvalues, produce a charge
density that is identical to the previous one), you have the same
ground state of the direct minimization.

I think we should continue this is in private - but again, have a
careful look at the reference first.


				nicola


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Prof Nicola Marzari   Department of Materials Science and Engineering
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