1. Regarding the energy of the free atom, as I read the archive, it
seems that we have to consider the ghost atoms surrounding the main atom
to get the enrgy of the free atom?! or, it is enough to have the right
basis of the atom and calculate its energy?
It is very desirable to include ghosts, usually they correct the
cohesive energy by 0.1-0.3eV. The example as Roberto suggested provides
an idea, but in practice it would not work, since in such a case atoms
would still be too close.
Generally you have to take a much bigger unit cell (~10-15A), place
there one atom and the ghosts of all its nearest neighbors as in bulk.
Ghost are included by changing the sign of the atom number
%block Chemical_Species_Label
1 31 Ga
1 -7 N #ghost
%endblock Chemical_Species_Label
You still have to provide the same basis and pseudopotential file that
you used for bulk calculations.
2. energy of atom in a crystal: when we calculate the energy of the bulk,
then how do we have the energy of the atom in the structure?
I don't understand this question.
3. I would be grateful if you let me know the additional terms I have to
consider in order to calculate the cohesive energy of a slab too.
You mean surface energy?
For binary compounds it's indeed a problem. You have the cohesive energy
for a pair not for a single atom. But you can find the upper and lower
bounds of the chemical potential of each atom assuming that each atom
might come from the respective bulk (one bound) or from a gas phase
(another bound). Then people normally plot Energy vs. chemical potential
and see which of the surface reconstructions is the most stable
depending on the growth conditions.
I think the best case for you would be to learn about GaAs surface
reconstructions which is quite close to your system and was investigated
very intensely.
Check for example:
GaAs
http://prola.aps.org/abstract/PRB/v54/i12/p8844_1
http://prola.aps.org/abstract/PRB/v62/i12/p8087_1
GaN
http://prola.aps.org/abstract/PRB/v65/i24/e245212
http://prola.aps.org/abstract/PRL/v88/i6/e066103
