[Wien] 2 ways to calculate bindning energy

[B. Yanchitsky]

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?

-- 
Bogdan Yanchitsky
Institute of Magnetism
Vernadsky Blvd., 36-b
03142  Kiev
UKRAINE

Tel. (+380-44) 444 34 20
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