Finite-electronic-temperature DFT study

[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


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