[Wien] Bad formation energies for the charged vacancies

[John Pask]

Dear Peter,

Is the question regarding the computation of total energy per unit  
cell in an infinite crystal with non-neutral unit cells? If so, then  
the total energy diverges -- and so is not well-defined. (So  
neutralizing backgrounds must be added in such cases to obtain  
meaningful results, etc.)

John

On Feb 24, 2010, at 1:18 PM, Peter Blaha wrote:

> I've started some tests after the first query and it seems we might  
> miss a term in the total
> energy.
>
> I created a clmsum-file (density) which is constant and is  
> normalized to one and put this into
> a cell with a single H nucleus.
> So it refers to the test case of a H+ ion in a lattice, where I do  
> not add a constant background, but
> put the "background charge into case.clmsum.
>
> When one switches off the XC-terms, the resulting E-tot contains the  
> integral (rho *V-coul) and since
> rho is constant (equal to Q/volume), we get the average potential in  
> the unit cell (not only the
> interstital, where it is zero anyway) multiplied by the constant rho).
>
> This term is missing when I put a clmsum file with rho=zero, but add  
> a "background charge"
> by case.inm, while the resulting potentials are identical for the  
> two methods.
>
> However, for a charged bulk system there is still a big problem,  
> because V-coul is determined
> only up to a constant and is shifted arbitrarily such that the  
> potential in the interstital is zero.
> In "neutral" calculations such a shift does not matter, since it  
> will be canceled by the sum of
> eigenvalues, but when adding the constant background it matters.
>
> Thus, this correction term depends on RMT ?
>
> At the moment I'm not sure how I should continue. I think in other  
> codes such a correction is
> added, but as mentioned, I guess the correction depends on the  
> arbitrary choice of V-zero.
>
>
> Laurence Marks schrieb:
>> Please see the next email on the list:http:// 
>> *zeus.theochem.tuwien.ac.at/pipermail/wien/2007-January/008713.html
>> I think this is right and you take V0 from case.output0 (it is  
>> printedthere). You should do an empty cell test (no electrons) to  
>> verify thisand the units of V0, perhaps also looking at the code  
>> itself -- andremember to check the limit as the distance between  
>> atoms gets large.
>> On Wed, Feb 24, 2010 at 11:05 AM, Yurko Natanzon<yurko.natanzon at gmail.com 
>> > wrote:> Dear Wien2k users and developers,> I'd like to refresh  
>> the discussion about the total energies of the> charged cells which  
>> took place three years ago:> http://*zeus.theochem.tuwien.ac.at/ 
>> pipermail/wien/2007-January/008711.html>> I'm trying to calculate  
>> the formation energy of the Hydrogen vacancy> in +/-1 charge states  
>> and find that the results are bad (much differ> from the  
>> literature) although the formation energy of the neutral> hydrogen  
>> vacancy is good. So my question arises if we can trust the> values  
>> of the total energies for the charged cells in the recent> version  
>> of Wien2k?>> To investigate this issue further I have performed the  
>> following> tests: I've done the calculations of the total energy of  
>> Mg, MgH2 and> GaN for three cases: neutral cell, cell with one  
>> electron removed (+1> charge) and a cell with an electron added (-1  
>> charge). The results> were compared with the same calculati
> on with another plane-wave code> and are the following:>  
> -----------------------------------------> hcp Mg:> Wien2k:> E(+1)- 
> E(0) = 0.245 Ry> E(-1)-E(0) = -0.199 Ry>> Plane-Wave code:> E(+1)- 
> E(0) = -0.226 Ry> E(-1)-E(0) = 0.281 Ry>> bcc MgH2> Wien2k:> E(+1)- 
> E(0) = 0.277 Ry> E(-1)-E(0) = 0.085 Ry>> Plane-Wave code:> E(+1)- 
> E(0) = 0.024 Ry> E(-1)-E(0) = 0.326 Ry>> fcc GaN> Wien2k:> E(+1)- 
> E(0) = 1.12 Ry> E(-1)-E(0) = -0.717 Ry>> Plane-Wave code:> E(+1)- 
> E(0) = -0.151 Ry> E(-1)-E(0) = 0.443 Ry>  
> ------------------------------------------------->> In wien2k the  
> charged cell was created by changing the number of> electrons in  
> case.in2 and adding the corresponding background charge> in  
> case.inm. One can observe, that the energies have the same order of>  
> magnitude, but the sequence of energies E(+1), E(0) and E(1) is>  
> inverse. It seems, that the system with +1 charge (electron  
> removed)> behaves like the system with -1 charge in the Plane-Wave  
> code. Of> course, the results of tests are no
> t physical, because no supercell> was used and no geometric  
> relaxation was performed (however, it is not> needed for Mg), but if  
> one tries to do all the supercell and> relaxation stuff and tries to  
> calculate the defect formation energy,> the result will be the  
> same.>> I'd be grateful if you comment on this and suggest any  
> corrections> which should be provided to the total energies for the  
> charged cells.>> with kind regards,> Yurko>>> --> Yurko (aka Yuriy,  
> Iurii, Jurij etc) Natanzon> PhD student> Department for Structural  
> Research (NZ31)> Henryk Niewodniczański Institute of Nuclear  
> Physics> Polish Academy of Sciences> ul. Radzikowskiego 152,> 31-342  
> Krakow, Poland> E-mail: Yurii.Natanzon at ifj.edu.pl, yurko.natanzon at gmail.com 
> > _______________________________________________> Wien mailing  
> list> Wien at zeus.theochem.tuwien.ac.at> http:// 
> *zeus.theochem.tuwien.ac.at/mailman/listinfo/wien>
>> -- Laurence MarksDepartment of Materials Science and EngineeringMSE  
>> Rm 2036 Cook Hall2220 N Campus DriveNorthwestern  
>> UniversityEvanston, IL 60208, USATel: (847) 491-3996 Fax: (847)  
>> 491-7820email: L-marks at northwestern dot eduWeb:  
>> www.*numis.northwestern.eduChair, Commission on Electron  
>> Crystallography of IUCRwww.*numis.northwestern.edu/Electron  
>> crystallography is the branch of science that uses  
>> electronscattering and imaging to study the structure of  
>> matter._______________________________________________Wien mailing listWien at zeus.theochem.tuwien.ac.athttp 
>> ://*zeus.theochem.tuwien.ac.at/mailman/listinfo/wien
>
> -- 
> -----------------------------------------
> Peter Blaha
> Inst. Materials Chemistry, TU Vienna
> Getreidemarkt 9, A-1060 Vienna, Austria
> Tel: +43-1-5880115671
> Fax: +43-1-5880115698
> email: pblaha at theochem.tuwien.ac.at
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