[Pw_forum] Mermin free energy & Fermi-Dirac smearing

[Nicola Marzari]

Hi Paul,

have a look at this:

http://www.democritos.it/pipermail/pw_forum/2004-January/000785.html

Basically, you should use E-TS/2 to extrapolate a finite-temperature
calculation done with fermi-dirac or gaussian smearing to its zero 
temperature limit. Note that there is never a good reason to do this
- you should use instead methfessel-paxton or marzari-vanderbilt.

If you really want the "physical" E-TS at finite T, then you should
use Fermi-Dirac, and use E-TS in your work - no corrections to it to
extrapolate to zero-temperature (note my comments in the
previous link about the Vertstraete-Gonze approach to use cold
smearing to extrapolate to a finite Fermi-Dirac distribution)

What PWSCF calls "total energy" in the presence of a temperature
is actually E-TS (and I really, really think we should call it
"total free energy", to decrease this permanent state of confusion),
and this E-TS is what you should use. Note that very little has been
done to figure out what the real exchange-correlation functional at
finite-temperature is (in fact, we always use the T=0 one...), and that
it's even more difficult than usual to express from a charge density the
correct free energy of a system, since that contains an ensemble-average
at a given temperature. The Sprik PRL from ~2003 on ions in solution can
be very illuminating on the problem.

Not sure what "demet" is.

				nicola



Paul Tangney wrote:
> Hello,
> 
> I am trying to calculate the total (free) energy of
> a semiconductor with electrons at a high temperature.
> I am doing this by tinkering with the Fermi-Dirac smearing
> scheme in PWSCF. Now, as far as I know, if F-D smearing is
> used purely as a computational device for metals, the
> ground state energy should be calculated (estimated) by
> E_0 = E - TS/2 , where E is the standard Kohn-Sham energy
> and the second term is half the electronic entropy energy.
> Is this correct ?
> 
> What I want is to calculate F = E - TS, the free energy.
> However, when I looked in the code (subroutines "gweights" and
> "w1gauss" ) it appears to me that the ground state energy
> for metals is being calculated as E_0 = E - TS.
> In other words, the correction term is twice what it should
> be. Am I right about this, or am I reading the code wrong ?
> Factors of two can have many origins.
> Is the variable "demet"  TS or TS/2  ?
> 
> If I can figure this out, I can figure out how to get
> the quantity I want.
> 
> Thanks for any help,
> 
> 
> Paul
> 
> 

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Prof Nicola Marzari   Department of Materials Science and Engineering
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