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[Michel Côté <michel.cote@umontreal.ca>]

Dear all,

Actually, this problem is addressed by a paper of Axel Becke:

The Journal of Chemical Physics -- October 15, 2002 -- Volume 117, Issue 15,
pp. 6935-6938

Current density in exchange-correlation functionals: Application to atomic
states
Axel D. Becke 

An old and yet unsolved problem in density-functional theory is the strong
dependence of degenerate open-shell atomic energies on the occupancy of the
atomic orbitals. This arises from the fact that degenerate atomic orbitals
of different ml do not have equivalent densities. Approximate density
functionals therefore give energies depending strongly on which orbitals are
occupied. This problem is solved in the present work by incorporating
current density into the calculations using a current-density dependent
functional previously published by the author. ©2002 American Institute of
Physics.

He solved this issue by including a current functional which we do not have
in Abinit, yet!

Michel


Le 12/04/06 05:47, « Nicola Marzari » <marzari@MIT.EDU> a écrit :

> 
> 
> Dear Aloysius,
> 
> for the case of atoms, smearing helps you in reaching self-consistence
> in the presence of level-crossing instabilities (i.e. when you have
> a small gap between the HOMO and the LUMO). The iterations
> to self-consistency might otherwise keep you bouncing around (if level
> "37" is lower than level "36" then 36 is filled, and viceversa).
> 
> Also, they naturally lead to fractional occupations of degenerate
> levels, often giving rise to spherical charge densities.
> 
> Care needs to be paid, though - when you add a fictitious temperature,
> the variational functional that is minimized becomes the
> free energy E-TS ; S will be different from zero, and finite, for
> fractional occupations, but you only want to get the E term from
> abinit (I am not familiar with the output, so I can't advise on
> how to remove -TS).
> 
> In addition, there is still an open question (at least to me)
> on what should be the orbital occupations for the correct ground
> state of an atom. My favourite example is Fe2+ (or analogues), where
> we have one d minority spin electron, and five d minority spin levels.
> 
> We have several choices
> 
> 1) put 1 in one of the 5 d levels, 0 in the others
> 2) 0.5 in two of the d levels, 0 in the others
> 3) 0.33333333 in three levels
> 4) 0.2 in five levels
> 
> 1) gives rise to a cylindrical atom. 4) (If i remember correctly)
> gives the lowest E when you minimize E-TS .
> 
> I never managed to get a satisfactory answer to this question - i.e.
> what would be the right solution. I seem to remember a
> side note of Kohn mentioning that cylindrical atoms, even if they have
> a higher DFT energy when using approximate functional, are close to the
> correct energy you would get with the exact functional (this makes sense
> - the energy of an ensemble of isolated atoms should be piecewise linear
> in the occupation expectation value, as explained in the
> Perdew/Parr/Levy/Balduz 1982 PRL - while GGAs are smooth and roughly
> parabolic). There is also a 1983 paper by Englisch and Englisch (sp ?)
> that mentions that fractional occupations are not v-representable. Oh
> well...
> 
> 
> nicola
> 
> 
>> On 4/12/06, Aloysius Soon <aloysius@physics.usyd.edu.au> wrote:
>> 
>>> Dear users,
>>> I have tried searching the FAQ and forum but can't seem to
>>> find much on atomic calculations (like for computing
>>> cohesive energies).
>>> 
>>> What would the recommend occupt value be? According to the
>>> explanation, a small amount of smearing might help certain
>>> cases but not others and to be used with care. Could anyone
>>> comment on elements like Cu, Ir and O atoms?
>>> 
>>> Thanks for your time.
>>> 
>>> 
>>> 
>>> best regards,
>>> Aloysius
>>> --
>>> Aloysius Soon
>>> Condensed Matter Theory Group
>>> School of Physics A28, Room 361
>>> The University of Sydney, NSW 2006 Australia
>>> Phone: +61 2 903 65389
>>> Fax: +61 2 935 17726
>>> Email: aloysius@physics.usyd.edu.au
>>> Web: http://www.physics.usyd.edu.au/~aloysius/
>>> ==============================================
>>> - CARPE DIEM -
>>> "Gather ye rosebuds while ye may,
>>> Old time is still a-flying,
>>> And this same flower that smiles today,
>>> To-morrow will be dying."
>>>                        ROBERT HERRICK
>>>                        1591-1674
>>> ==============================================
>>> 
>>> 
>> 
>> 
>> 
>> --
>> Pierre-Matthieu Anglade
>> 


-- 
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  Michel Cote                          tel: +1 (514) 343-5628
  Professeur agrégé                   fax: +1 (514) 343-2071
  Département de physique
  Université de Montréal
  C.P. 6128, succ. Centre-ville
  Montréal (Québec) H3C 3J7          Michel.Cote@umontreal.ca
  Canada                   www.phys.umontreal.ca/~michel_cote
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