# Finite-electronic-temperature DFT study

Max latevimax.... at gmail.com
Wed May 6 15:27:51 UTC 2015

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

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