[Wien] Formation energy + some other querries!

XU ZUO xzuo at nankai.edu.cn
Wed Feb 6 15:19:19 CET 2008 

I think you are considering the formation energy of defect. So, you
should chose pure GaN as the zero energy of the formation energy. Dr.
Stephan Lanny and Dr. Alex Zunger gave a nice formula about the defect
formation energy[1].

[1] Stephan Lanny and Alex Zunnger, Dopability, Intrinsic Conductivity,
and Nonstoichiometry of Transparent Conducting Oxides, Phys. Rev. Lett.
98, 045501 (2007).

On Wed, 2008-02-06 at 16:46 +0530, Nandan Tandon wrote:
> By zero energy, we really meant the zero of the energy scale.
> 
> Now i understand that the formation energy can be calculated as:
> Formation energy for GaN with Mn(Ga15,Mn1,N16) : total ENE of
> Ga15MnN16 - 15*total ENE for Ga metal in standard state structure - 1*
> total ENE for Mn metal in standard state structure - 16* total ENE for
> N in standard structure.
> 
> Since in this formula the total energy is with respect to the same
> zero, (as Stefaan has indicated), this formula should work provided
> all the total energies are available.
> This leads to the question of how to evaluate total energy for N in
> standard structure since N would be present only in the gaseous
> phase??????
> 
> Also, just to confirm what Stefaan has said, if one does an atomic
> calculation for H, the total energy evaluated should be around 1Ryd?
> 
> Regards,
> 
> Nandan.
> 
> On 2/6/08, rcais at cal3.vsnl.net.in <rcais at cal3.vsnl.net.in> wrote:
> > For an alloy, formation energy energy is what is conventionally used. Cohesive energy could also be used for an initial assessment. The calculation would  be as follows :
> >  Formation energy for GaN with Mn(Ga15,Mn1,N16) : total ENE of Ga15MnN16 - 15*total ENE for Ga metal in standard state structure - 1* total ENE for Mn metal in standard state structure - 16* total ENE for N in standard structure. Subtracting individual atom energies in weighted amounts from the total energies gives the same result since they cancel out. A positive value suggests a phase that is unstable / metastable) with respect to the metals. Very low negative or positive values of cohesive energy would indicate a definitely unstable phase whereas metastable existence is possible otherwise.
> > Please correct me if I am wrong.
> > Chandrika
> > Anjali :By zero energy do you mean zero point energy?
> >
> >
> > ----- Original Message -----
> > From: Stefaan Cottenier <Stefaan.Cottenier at fys.kuleuven.be>
> > Date: Tuesday, February 5, 2008 7:08 pm
> > Subject: Re: [Wien] Formation energy + some other querries!
> > To: wien at zeus.theochem.tuwien.ac.at
> >
> > >
> > >
> > > 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/
> > > >> -----------------------------------------------------------------
> > > ---------
> > > >> _______________________________________________
> > > >> Wien mailing list
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> > > >>
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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
> > >
> > > e-mail: stefaan.cottenier at fys.kuleuven.be (preferred)
> > >         cottenier at ghi.rwth-aachen.de (avoid)
> > >
> > >
> > > Disclaimer: http://www.kuleuven.be/cwis/email_disclaimer.htm
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-- 
Xu Zuo

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