[Wien] Formation energy of impurity charge states

Tue Apr 23 11:37:23 CEST 2019

Dear Prof Laurence,

You say that Wien2k does not attempt to do any of the charged cell corrections that are in the literature, so besides the alignment of the electrostatic potential (or aligning the core states, as you suggested) are there other correction terms that must be taken into account?

I’m trying to simulate a p-type dopant, so I calculated a neutral supercell with the dopant (DOS shows an impurity band inside the band gap which is missing an electron to be full), calculated a charged supercell by adding an extra electron (DOS shows the impurity band is full) and calculated the same supercell for the pure bulk material.
To calculate the formation energy of the charged state, I tried to align the core states of an atom far from the dopant comparing the values from the charged supercell and from the bulk material, but I observed that variations in the same order of magnitude are are also present in the core states of the same atom in the neutral supercell (comparing to bulk). Since the core states in the neutral supercell should be identical to the bulk, does this mean that the variations I see in the charged supercell might be numerical variations?

Also, I did the structural optimizations using the PBE functional but after that I used the modified Becke-Johnson potential (mBJ) to get a better band gap and DOS.
Calculating the formation energy of the charged state using the PBE functional gives me a positive formation energy but it gives me a negative formation energy when using the mBJ.
Since I depend not only on the total energy of each supercell to do the calculation but also on the value of the Fermi energy of the bulk material, are any of these values not correctly estimated using the mBJ and therefore I should use the values obtained using the PBE?

Finally, regarding the PRL paper by Pantelides, if I understood correctly, their method depends for instance on removing electrons from lower bands and adding them to higher bands. However, such a procedure is not possible in a Wien2k calculation, or is it?

Best regards,
Marcelo

> On 12 Apr 2019, at 20:02, Laurence Marks <L-marks at northwestern.edu> wrote:
> 
> What you are trying to do is generate an estimate of the energy dV*Q where dV is the potential offset, and Q is your charge. The atoms by the charged defect will not be close to the same as the bulk, you want one which is far enough away that it is a viable reference state. You then compare this to your reference material, which does not have to be a supercell and could be just bulk. (Sometimes it is easier to ensure that k-points and other things are identical by using a supercell without the defect.)
> 
> Be aware that Wien2k does not attempt to do any of the charged cell corrections that are in the literature. For these you are on your own! In principle you want to extrapolate with a series of cells of increasing size in order to calculate the defect-defect coupling energy as a function of cell size. And/or calculate the correction. I remember many years ago looking at this with Peter, and I am not sure either of us was terrible convinced by the corrections in the literature.
> 
> Also, be aware that the approach of charged cells assumes that there is no interaction between, for instance, holes and the defect. I recently did a (neutral) calculation of a Ni vacancy in NiO. What I expected to find was two Ni3+, but instead I found a couple of delocalized hole on O sites near the vacancy. (I still need to ponder whether I believe this.) A charged cell calculation where one adds two electrons at the same time as one creates a Ni vacancy will not include the electrostatic interaction between the (negative) vacancy and the delocalized hole.
> 
> Also, there is a recent paper by Pantelides in PRL (with some later comments by others) where he disagrees with the conventional approach. I do not know who is right.
> 
> On Fri, Apr 12, 2019 at 12:34 PM Marcelo Barbosa <marcelo.b.barbosa at gmail.com <mailto:marcelo.b.barbosa at gmail.com>> wrote:
> Dear Prof Laurence,
> 
> First of all, thank you for stepping into the discussion and for clarifying the difference between a pseudo-potential calculation and an all-electron code in this situation.
> 
> Can I then use the core energies obtained using for example "grep :1S case.scf”?
> 
> By the way, I have another question…
> This correction is only needed for a charged cell and, as far as I understood, for the method performed in the case of pseudo-potential calculations the alignment must be done between the charged supercell and a supercell of the same size from the bulk material.
> However, for the procedure you described, the core energy difference should be calculated between the charged supercell and the same supercell in the non-charged state, correct?
> 
> Best regards,
> Marcelo
> 
>> On 11 Apr 2019, at 19:19, Laurence Marks <L-marks at northwestern.edu <mailto:L-marks at northwestern.edu>> wrote:
>> 
>> I think this conversation has gone in an incorrect direction. What you are trying to do is align the relative energies/potential as there is an offset due to subtraction of the mean inner potential (to avoid singularities) that is different for charged and non-charged cells.
>> 
>> With a pseudo-potential calculation, the electrostatic potential is readily available so people use it to align.
>> 
>> With an all-electron code the electrostatic potential can be generated, but there are far easier methods to align! All you need to do is compare the core energies of atoms well away from the defect. This gives you the relevant energy axis shift.
>> 
>> Then you have to make whatever correction you trust....which is not a trivial issue.
>> 
>> On Thu, Apr 11, 2019 at 11:34 AM Marcelo Barbosa <marcelo.b.barbosa at gmail.com <mailto:marcelo.b.barbosa at gmail.com>> wrote:
>> Thank you very much for your help!
>> 
>> Best regards,
>> Marcelo
>> 
>>> On 11 Apr 2019, at 16:16, SM Alay-e-Abbas <alayabbas at gmail.com <mailto:alayabbas at gmail.com>> wrote:
>>> 
>>> --> Since I need to calculate the electrostatic potential, is following method the correct approach? Is it also correct for spin polarized calculations?
>>> For electrostatic potentials you should be using case.vcoul. I don't think that the magnetic order matters here since there is only one output for electrostatic potential (*.vcoul). 
>>> 
>>> --> Create the case.in5 file with the correct plane and number of points to be calculated
>>> and set ny = 1!
>>> 
>>> --> Use “x lapw5 -d” to create the file lapw5.def and then change the unit 9 from “case.clmval” to “case.vtotal”
>>> for electrostatic potentials, it should be case.vcoul.  
>>> 
>>> --> Run lapw5 and get the values in case.rho
>>> The results you should be looking for are in case.rho_onedim
>>> 
>>> On Thu, Apr 11, 2019 at 12:09 PM Marcelo Barbosa <marcelo.b.barbosa at gmail.com <mailto:marcelo.b.barbosa at gmail.com>> wrote:
>>> Dear Alay,
>>> 
>>> Thank you very much for your help!
>>> 
>>> I am able to use your method to select the appropriate plane and the number of points in that plane to be calculated using lapw5.
>>> I just not entirely sure that I correctly understood the rest of the procedure by reading the user’s guide.
>>> 
>>> Since I need to calculate the electrostatic potential, is following method the correct approach? Is it also correct for spin polarized calculations?
>>> 
>>> - Create the case.in5 file with the correct plane and number of points to be calculated
>>> - Set “iuntits” to ATU in case.in5 to get the values in Ry
>>> - Set “cnorm” to VAL in case.in5
>>> - Use “x lapw5 -d” to create the file lapw5.def and then change the unit 9 from “case.clmval” to “case.vtotal”
>>> - Run lapw5 and get the values in case.rho
>>> 
>>> Best regards,
>>> Marcelo
>>> 
>>> 
>>>> On 4 Apr 2019, at 21:30, SM Alay-e-Abbas <alayabbas at gmail.com <mailto:alayabbas at gmail.com>> wrote:
>>>> 
>>>> Hello Marcelo,
>>>> 
>>>> You may do this by selecting an appropriate atom centered plane (with reasonable width) and then setting npy = 1 in case.in5 before running lapw5. See section 8.13.3 of the userguide for more details.
>>>> 
>>>> Best Regards,
>>>> 
>>>> Alay 
>>>> 
>>>> On Thu, Apr 4, 2019 at 5:40 PM Marcelo Barbosa <marcelo.b.barbosa at gmail.com <mailto:marcelo.b.barbosa at gmail.com>> wrote:
>>>> Dear Sirs,
>>>> 
>>>> When comparing the formation energies of two charge states of an impurity in a semiconductor as a function of the Fermi level, it is said that a correction term must be added to align the electrostatic potential from the supercell with the impurity (using a position far from the impurity) and from a supercell of the pure bulk material with the same size (see e.g. DOI: 10.1063/1.1682673).
>>>> 
>>>> The electrostatic potential is calculated in LAPW0, but how can I find the value corresponding to a specific position in my supercell?
>>>> 
>>>> 
>>>> Best regards,
>>>> Marcelo
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>> 
>> 
>> 
>> -- 
>> Professor Laurence Marks
>> "Research is to see what everybody else has seen, and to think what nobody else has thought", Albert Szent-Gyorgi
>> www.numis.northwestern.edu <http://www.numis.northwestern.edu/> ; Corrosion in 4D: MURI4D.numis.northwestern.edu <http://muri4d.numis.northwestern.edu/>
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> 
> 
> 
> -- 
> Professor Laurence Marks
> "Research is to see what everybody else has seen, and to think what nobody else has thought", Albert Szent-Gyorgi
> www.numis.northwestern.edu <http://www.numis.northwestern.edu/> ; Corrosion in 4D: MURI4D.numis.northwestern.edu <http://muri4d.numis.northwestern.edu/>
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