[Pw_forum] scf calculation for isolated hydrogen atoms

[Gabriele Sclauzero]

Dear Lorenzo

Lorenzo Paulatto wrote:
> On Fri, 12 Feb 2010 13:32:14 +0100, Gabriele Sclauzero <sclauzer at sissa.it>  
> wrote:
>>> I tried to calculate the ground state energy for isolated hydrogen atom
>>> with the following input,however I got the fermi energy level at
>>> -3.5661eV, while it should be -13.6eV.
>> [...]
>> (maybe PAW can give an AE energy estimate).
> 
> With PAW, PBE and spin polarization you can get a total energy for the H  
> atom of -0.998 Ry, but this is not related to Dimpy's problem.

Very nice!

> 
> The problem is that in periodic boundary conditions absolute values of  
> energy (let them be band energies, the Fermi energy or even total energy)  
> have no meaning, but only energies differences matter. I.e. if you  
> consider an isolated system (H1) in two different choices of unit cell  
> (both big enough to ensure convergence) the absolute energies will likely  
> be different, yet the energy differences (e.g. LUMO-HOMO) will remain the  
> same.

You are right, there is a freedom in the choice of the reference level for the  potential, 
but this choice should not change the physical properties of the system (although KS 
levels in principle are only auxiliary quantities).
I still believe that the main problem in Dimpy's result is the self interaction error for 
the 1s level, and even if you align the 1s level to that reference energy you would still 
get a big error.

Try for instance to run ld1.x with the following input:
  &input
     title='H'
     prefix='H_',
     zed=1,
     config='1s1'
     iswitch=1,
     rel=0,
     dft='PZ'
     isic=1,
  /

You get:
      n l     nl                  e(Ry)          e(Ha)          e(eV)
      1 0     1S 1( 1.00)        -1.0000        -0.5000       -13.6057

but if you use isic=0 you'll get:

      n l     nl                  e(Ry)          e(Ha)          e(eV)
      1 0     1S 1( 1.00)        -0.4673        -0.2337        -6.3583

which is much close to what you get from a pw.x LSDA calculation with fixed occupations in 
a very big cell (around -7.3 eV). There is still a 1 eV difference that I cannot explain, 
maybe it is due to something related to what you said.
Or maybe I am completely mistaken and there is some point I cannot get.

> 
> Last, but by any mean no least, I don't see why you should get -1 Ry for  
> the Fermi energy of an isolated Hydrogen. Ef (which means you have used a  
> fictitious smearing to ease convergence) shall be somewhere between the  
> energy of the higher (and only) occupied orbital and the energy of the  
> lowest empty orbital. Both these energies depend on the periodic boundary  
> conditions, hence the Ef for such a system has no meaning. Furthermore, I  
> cannot to see any physical meaning in the Fermi energy of an isolated  
> system represented in periodic boundary conditions.

I completely agree with you on this, one should not give any physical meaning to the Fermi 
energy in a calculation for an isolated atom.

mandi biel,


GS

> 
> best regards
> 

-- 


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| Gabriele Sclauzero, PhD Student                  |
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