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[matthieu verstraete <matthieu.jean.verstraete@gmail.com>]

Hello - all are very valid questions for defect studies, with no
systematic answer in the literature.

> (i) In the charged state, one adds (or removes) an electron from the system,
> and a uniform compensating background charge is then added to the system. 
> The
> question is if the total energy is correctly given by Abinit also in that 
> case.
> This is important, because it is the first term in a relatively complicated
> expression giving the formation energy of charged impurities [see, e.g., 
> van de
> Walle & Neugebauer, J. Appl. Phys. 95, 3851 (2004)].
The corrections schemes are not implemented in abinit. The only thing
you can do is set "charge" to +-1 +-2 etc and have a uniform
background jellium to neutralize the cell. IF you converge the system
size, it will eventually be correct, but this convergence is
notoriously slow (hence the need for the correction schemes).


>
> (ii) In the charged state, the system often is metallic. In that case one 
> has
> to use an occopt parameter value appropriate for metals and a non-zero 
> value of
> tsmear. The problem we ran into is that the total energy depends on the 
> value
> of tsmear, affecting the final formation energy value in a non-negligible 
> way.
> Which tsmear gives the correct formation energy? Would the smallest tsmear
> value be the best? (is it possible to use tsmear=0?). Note that the undoped
> system is an insulator, so does not require tsmear. So one ends up 
> comparing a
> total energy that is calculated with no tsmear, and one with a finite value 
> of
> tsmear, which we find problematic.

1) You can extrapolate to 0 tsmear

2) You can get the tsmear=0 estimate, based on the total energy and
entropy terms (either use cold smearing occopt 4,5 or do it by hand,
as explained in Nicola Marzari's thesis http://quasiamore.mit.edu/phd/
roughly speaking calculating E_internal + 1/2 S)

3) In principle, if you have a defect state in the gap which is nice
and localized, the energy should not change too much. The conduction
band will not be populated unless tsmear ~ e_cond - e_defect, which
gives you a good criterion for tsmear.

4) You should in principle use a single k-point and a huge cell. Is
this the case? For smaller cells, converging wrt k-points is a good
idea, because the bulk states are better represented, but is always a
little unphysical because you are also representing periodic defect
states...

>
> (iii) When one uses a finit value of tsmear, the total energy in the output
> file has an additonal term proportional to kT. What's the meaning of this 
> term,
> considering that, in principle, tsmear is introduced for technical reasons 
> and
> does not necessarily represent a temperature smearing?
It is necessary with any occupation scheme to ensure you have a (free)
energy functional which is variational. If you just add occupation
numbers without an entropy you do not have an energy with a nice
minimum wrt the variation of occupation numbers.


Tell us if it works!

Matthieu

>
> We look forward to comments on the above.
>
> Best regards,
> R. Saniz
>



-- 
~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~~
Dr. Matthieu Verstraete

European Theoretical Spectroscopy Facility (ETSF)
Dpto. Fisica de Materiales,
U. del Pais Vasco,
Centro Joxe Mari Korta, Av. de Tolosa, 72,   Phone: +34-943018393
E-20018 Donostia-San Sebastian, Spain        Fax  : +34-943018390

Mail : matthieu.jean.verstraete@gmail.com
http://www-users.york.ac.uk/~mjv500