Finite-electronic-temperature DFT study

[Max]

Dear CP2K users and developers,


I am interested in performing a finite-electronic-temperature
study of some systems at a few tens of 10^3K. And I would like
to know if I can use CP2K for this.

It seemed to me that I could do so by activating smearing
(force_eval/dft/scf/smear) with a Fermi-Dirac distribution.
But in the tutorial on the calculation of energy and forces
(http://www.cp2k.org/howto:static_calculation), it is said
that the printed final free energy corresponds to the one
extrapolated for vanishing electronic entropy energy.
So I'm wondering if I'm missing some theoretical points
of the implementation that prevent the use of this feature
in finite-electronic-T cases.

I thank you in advance for your help.


All the best,
Max

[M. Brehm]

As far as I understand, electronic smearing and finite electronic temperature is often used just to reach convergence of the wave function at all. In these cases, it is desirable to extrapolate back to zero electronic temperature. If I remember it right, CP2k writes the contribution from the smearing to the electronic energy to the log file at some point ("electronic entropic energy", or something like this) before it performs the extrapolation. So you should be able to read this value from the log file.

[Sasha Batyrev]

Should not Mermin functional be used for consistent description of high temperature electrons, as it was done in cpmd according to A.Alavi's formalism?

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[Max]

Hi,

Thanks a lot, M. Brehm and I. Batyrev, for your kind replies.

The study of high-temperature electrons must indeed be done within the
framework of the Mermin extension of DFT. It seems to me that the
quantities required for evaluating the free energy functional

    \[ F = E_{KS} + \mu\,N -T\,S \]

are computed in CP2K when the Fermi-Dirac (FD) smearing is switched on.
This is the case for $\mu$ the chemical potential and for $S$ the electronic
entropy.

In the tutorial on calculating energy and forces, (http://www.cp2k.org/howto:static_calculation),
for the 300K-FD smearing case, there is a tiny difference between the values
reported for the free energy

  Total energy:  -31.29788686349247

and the estimate of the ground-state energy for T->0

  ENERGY| Total FORCE_EVAL ( QS ) energy (a.u.):  -31.297887031736590

I was wondering which kind of extrapolation was used? and if the quantities
computed at SCF convergence were similarly corrected? I'm mostly interested
in the forces

  \[ \frac{\rm{d}F}{\rm{d}\bf{R}_I} = \frac{\partial E_{KS}}{\partial \bf{R}_I}}

I went through the sources and could not find the place where such an
extrapolation could have been made. I have to say that I'm not familiar
at all with the code, so I may be really wrong!

Nevertheless I found that at convergence, there is a step which consists in
undoing the density mixing used during the SCF procedure, so as to have a
density which is consistent with the final wavefunction. Could the tiny
difference come from this update? In the tutorial, I've now noticed that for
the case without smearing, one observes a similar difference between the
energy values priinted at the "Total energy" and
"ENERGY| Total FORCE_EVAL" lines.


Regarding the forces, if there is no corrections other than undoing the
density mixing at convergence, do they correspond to the forces calculated
for the equilibrium density?

All the best,
Max