Finite-electronic-temperature DFT study

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


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 

In the tutorial on calculating energy and forces, 
for the 300K-FD smearing case, there is a tiny difference between the 
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 

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 
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,

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