[Pw_forum] multiplicity in lsda calculation

[Nicola Marzari]

> Any comments ? (By the way, it would be helpful to have in the
> docs a note that says that for finite temperature calculations
> the "total energy" printed by the code is actually the total
electronic free energy E-TS, and that the correction for metals
is +1/2 TS.

Summing the "total energy" E-TS + the "correction for metals" 1/2 TS
you obtain E - 1/2 TS, or the "corrected energy" introduced by
Gillan and De Vita.

In the case of Fermi-Dirac or Gaussian smearing, the corrected
energy depends only to orders greater than two in the temperature,
and thus one can use large smearings (.01 to .05 Ry) in true metallic
systems, and still have a reasonably good estimate of the
zero-smearing energy (anything else - e.g. forces or stresses,
will still be greatly influenced by this temperature).

A more general solution to this problem is to use Methfessel-Paxton
or cold-smearing approaches, where the quadratic dependence of the
"total energy" E-TS on temperature is removed "ab-initio".

Finally, in an atom or a cluster you might need to be careful.
If I got all of this correctly (Stefano dG, please chip in), the
"total energy", being E-TS, will have an S term different from
zero as soon as you have degenerate orbitals with fractional
fillings; since what you really need there is E, just add twice
the "correction for metals" to the "total energy"), making sure
that the E you get does not change significantly with T.

:-)

			nicola

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Prof Nicola Marzari   Department of Materials Science and Engineering
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