[Wien] Formation energy + some other querries!

[Stefaan Cottenier]

Probably two issues are being confused here. The zero on the energy  
scale *for the eigenvalues* is defined in wien2k as the average of the  
potential in the interstitial. That is an arbitrary convention, and  
this zero is needed to express the Fermi energy and to plot the DOS.  
However, what you need in order to calculate formation energies is the  
*total energy* (:ENE) and not the eigenvalues. The total energy in an  
all electron code has a well-defined zero (in contrast to the energy  
in a pseudopotential calculation). For instance, if for a particular  
unit cell :ENE=-7345.730289 Ry, it means you need that amount of  
energy to bring all electrons and all nuclei in the unit cell to  
infinite distances from each other. That situation -- all particles at  
infinite distances -- corresponds to zero. Exactly the same as in the  
H-atom, where you need exactly 1 Ry (13.6 eV) to bring proton and  
electron at infinite distance from each other (at zero speed).

Moreover, regarding the formula you quote, one can debate whether it  
makes more sense to use the total energy for a Mn and Ga free atom  
(=calculate cohesive energy) or the total energy for bulk Mn and bulk  
Ga (=calculate formation energy). If the bulk phases are known to  
exist, the formation energy is probably what you need (==> the alloy  
will possible split into bulk phases, which are more stable than the  
gas phase). If one of the constituents is a very dilute impurity, I'm  
not sure which of both expression is most meaningful. Anyone a comment?

Stefaan


Quoting Nandan Tandon <nandan.tandon at gmail.com>:

> Dear Prof Blaha
>
> I am still not convinced that the zero of energy is not required.
>
> When we are considering the differences in the single particle energies
> for a particular system, I agree that the arbitrary number representing
> the zero is not required since it cancels but for differences in total
> energies of different systems will require the zero reference.
>
> I will explain my problem in detail :
>
> I wish to find the formation energy for a Mn impurity in GaN. I do a
> supercell calculation (32 atom per unit cell) for pure GaN and Mn
> substituted GaN. I also calculate the energy of a single Mn atom and a
> single Ga atom by putting in a large unit cell. Then the formation energy
> is
>
> FE = E(Ga_16N_16) + E(Mn) - E(Ga)- E(Ga_15MnN_16)
>
> Each of the above total energies are with respect to the respective zero
> energy for that system. Is it that when wien gives the total energy per
> unit cell for any system, it takes care of the reference level?
>
> Regards
>
> Anjali Kshirsagar
>
> On 2/5/08, Peter Blaha <pblaha at theochem.tuwien.ac.at> wrote:
>> > 1. We need to calculate the Formation energies for impurities in some
>> > semiconductor material. Thus an algebra with the total energies   
>> of different
>> > systems. I therefore need to know the zero of my energy. I am not  
>>  able to find
>> > where this value is written. Should be in case.scf0. Can you   
>> please tell us
>> > where to look for average interstitial potential or the zero of   
>> energy for a
>> > particular case?
>>
>> I don't think you need to know the zero of your energy. It is an   
>> arbitrary number.
>>
>> > 2. This problem we are facing with the 06, 07 versions. Earlier,   
>> there was a
>> > provision in case.in1 file that unit could be specified and   
>> accordingly the
>> > k-list will be read from in1 or case.klist file. Now the program   
>> does not allow
>> > us to read the k-list from in1. Why such a change has been made?   
>> Actually I
>> > find that there is a rewind command for the specific unit and if   
>> it is unit 5,
>> > case.in1 is rewind and there is an error. I did not see any such   
>> problem on the
>> > mailing list. We also posted the question but there was no reply   
>> even after
>> > putting it 2-3 times. Hence I want to knwo if we are making any   
>> error or is
>> > there a problem. I will accordingly send you the actual files and  
>>  the error we
>> > are getting.
>>
>> Using unit=5 for the k-vector list is not recommended. It should   
>> still be possible,
>> but you need an extra line before the k-list (put 1.d-15) and the   
>> k-list must be in the new
>> format (4I10 instead of 4I5, check the new klist format).
>> Unfortunately the UG has not been updated properly.
>>
>> > 3. We are also not able to run self-consistency for Monkhost mesh/ special
>> > k-points? Please guide us where to get the information regarding   
>> this. We are
>> > doing slab calculations and for the large supercell we wish to   
>> use Monkhost
>> > mesh for reducing the computations.
>>
>> You can put ANY k-mesh into case.klist; specify TEMP (or GAUSS) for  
>>  the Fermi-method
>> and run an scf-cycle. (KGEN produces a special point mesh anyway,   
>> only for centered
>> lattices it is different due to symmetry constrains).
>>
>> --
>>
>>                                        P.Blaha
>> --------------------------------------------------------------------------
>> Peter BLAHA, Inst.f. Materials Chemistry, TU Vienna, A-1060 Vienna
>> Phone: +43-1-58801-15671             FAX: +43-1-58801-15698
>> Email: blaha at theochem.tuwien.ac.at    WWW:   
>> http://info.tuwien.ac.at/theochem/
>> --------------------------------------------------------------------------
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-- 
Stefaan Cottenier
Computational Materials Engineering (CME) &
Center for Computational Engineering Science (CCES)
RWTH Aachen University
Mauerstrasse 5
DE-52064 Aachen
Germany

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