[Pw_forum] Cohesive energy

[Stefano Baroni]

Hi Riccardo:

On Jan 24, 2008, at 12:30 PM, Riccardo Sabatini wrote:

> diamond structure. For what i understood the CE (cohesive energy)  
> is the
> difference between the energy at atoms free and the energy of atoms
> bounded in the structure you want to study.
>
>     My first question is about free energy for reference. To evaluate
> the Si energy alone i made a easy run with one atom in a supercell,  
> big
> enough to delete all the other atom's effects. The result i had is
> around -7.47 Ry. My first question is about this result. I'm  
> following a
> tutorial presentation
> (http://mpdc.mae.cornell.edu/Courses/MAE715/Symposium/Veera- 
> Presentation.ppt)
> and there is listed a value of -7.52 Ry for the Si atom free. I tried
> with different pseudo potentials and with bigger and bigger cells  
> but i
> can't reproduce that result. I think this difference could arise  
> from a
> different pseudopotential used by the author and here comes  my
> question, is there a reference database for pwscf calculations with  
> the
> pseudopotentials used by default ? I tried to search but the NIST
> database i think uses all-electron's calculations (Si atom results to
> have -288 hartree) and so is not very useful for a fast check...

by construction, different pseudopotentials should give equal one- 
electron levels, but the absolute value of the total energy does  
depend on the specific pseudopotential. it is only energy differences  
that are (almost) independent on the specific pseudopotential, as  
long the PP has been constructed correctly ...

>    Anyway, i did the run for the Si in diamond structure.  I tried two
> ways, one with a fcc structure with 2 atoms in the cell and another  
> with
> a sc cell with 8 atoms. The results seem correct but i don't  
> understand
> what result should i take.

either one. the cohesive energy is the total energy of the crystal  
minus the total energy of an equal number of isolated atoms. of  
course, for an infinite system this difference is infinite, and you  
have to decide the refernce with respect to which you want to  
normalize. if you divide by the total number of atoms, you get a  
"cohesive anergy per atom" (which I think is the usual definition).  
for diamond, this is one half the "cohesive energy per cell" (because  
the unit cell has two atoms).

> In the tutorial (the one cited above) there
> is a value called energy/atom and energy/cell. In the first case i
> suppose one has to divide the total energy by the numbers of atoms in
> the cell (2 in the first case and 8 in the second) but i can't figure
> out what is energy/cell (i tried to divide by the volume but the  
> results
> are order of magnitude different).

total energy per cell = the figure spit out by the code
total energy per atom = above / (number of atoms in the unit cell)

beware, though, that when you perform a calculation for non  
elementary cells (as the simple cubic cell with 8 atoms that you were  
mentioning), the result may or may not be directly comparable with  
the result you get with an elementary cell, according to how careful  
you have been in the choice of k points for Brillouin-zone sampling.  
An example may explain this.

suppose you perform a calculation with the 8-atom cell and using only  
the gamma point (k=000) to sample the Brillouin zone. This point  
would correspond to k=(000) for the elementary cell, but you will  
easily convince yourself that k=(100) is a reciprocal-lattice vector  
for the 8-atom cell, while it is not for the 8-atom cell. in  
conclusion, sampling the 8-atom cell with k=(000) should give an  
energy which is exactly (within numerical noise) four times as large  
as the energy of the 2-atom cell, but only if the latter is sampled  
with the (000) AND the (100) points.

>     Is it correct to define a energy for each atom in a cell in  
> this way
> ? (If i remember correctly the difference in energy for the sc
> simulation and for the fcc arise from the difference in volume, one  
> is 4
> times than the other not from the numbers of atoms). If yes, i  
> tried to
> compare the energy/atom for the fcc diamond simulation and for the sc
> diamond simulation and the results are a little different, can this be
> caused by the number of plane waves used ?

I am not sure that what I said would sounds clear to you, unless you  
are already a bit familiar with electronic-structure techniques for  
infinite systems. if you are not, please take a glance, for instance,  
at the excellent textbook by R. Martin

http://www.cambridge.org/uk/catalogue/catalogue.asp?isbn=0521782856

there used to be a few chapters available for free online, but I  
cannot find them anymore

Stefano B.

oh, yes, I was forgetting: please, do not forget to complete your  
signature with your current affiliation - thanks
---
Stefano Baroni - SISSA  &  DEMOCRITOS National Simulation Center -  
Trieste
[+39] 040 3787 406 (tel) -528 (fax) / stefanobaroni (skype)

Please, if possible, don't  send me MS Word or PowerPoint attachments
Why? See:  http://www.gnu.org/philosophy/no-word-attachments.html



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