[Wien] 2 ways to calculate bindning energ

[Heinz Haas]

Dear B. Yanchitsky
First a comment on nomenclature: I think the quantity you try to calculate 
is generally called "formation energy".
Concerning accuracy: I think you can only get a reliable value if you 
calculate the pure system with exactly the supercell (and WIEN parameters) 
as for the defect calculation.
Concerning volume: Generally a defect changes the lattice constants. For 
an accurate treatment of the formation energy this effect must be 
included. An hcp system is already quite complicated for this. I suggest 
you first treat an fcc metal (Al) to test your procedures.
Good luck
Heinz
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On Tue, 11 Mar 2008, B. Yanchitsky wrote:

> Dear wien users,
> 
> I'd like to calculate a binding energy of a defect in crystal lattice, for example
> vacancy (hole). The system is hcp be, and I do not count for any effects of lattice distortions,
> and vibrations.
> The first way is through a supercell approach,
> the supercell should be quite big to neglect for interaction of defects through supercells.
> The energy of supercell with N-1 atoms and 1 vacancy is E[N-1]. The energy of Be atom
> in crystal is E[1]. Thus the binding energy Ev_super is
> Ev_super = E[N-1] - (N-1)*E[1].
> 
> The second way is through energy of isolated Be atom, Ei.
> Then binding energy Ev_atom is
> Ev_atom = Ei - E[1].
> 
> What I have got is
> Ev_super= 0.939 eV
> Ev_atom= 4.021 eV
> 
> This is quite close to what I have from a pseudopotential code
> Ev_super= 1.056 eV
> Ev_atom= 3.786  eV
> 
> Some details, the lattice is hcp be (2 atoms per unit cell),
> GGA-13, supercell is 4x4x2 (64 atoms). Energy of isolated was obtained
> through large box. I'm not sure about reached asymptotic (the energy was obtained
> from volume expanded by factor 108),
> but what I have seen, the energy of isolated atom is only increasing vs volume expansion,
> thus making the difference between Ev_super and Ev_atom only larger.
> 
> A pseudopotential test
> on a 96 atoms supercell showed that a supercell provides
> energy accuracy within 0.06 eV,
> Ev_super[96-1]= 0.999 eV
> 
> Any ideas for this conundrum?
> 
>