The ABINIT Users Mailing List ( CLOSED )

["Andrew M. Rappe" <rappe@sas.upenn.edu>]

Dear Nicola and Michel,

I am not sure if I understand the postings up to this point.  We are
able to get electronically converged calculations of atoms, with and
without spin polarization.

I think the general rule is that in the absence of spin polarization,
the electrons spread equally in the partially filled subshell.  When
spin-polarized calculations are done, a sensible ground state is
found, but perhaps not the experimentally-favored one.

So, we do not find problems with electronic convergence of an atom.

However, if one does find a problem, you can do the following trick:
put the atom in an orthrhombic box with axes a,b,c different lengths.
This will split the orbitals, enabling convergence electronically.
Then you can increase a, b, and c to return to the isolated atom
limit.

Andrew

On Thu, Apr 13, 2006 at 10:41:15PM +0200 or thereabouts, Nicola Marzari wrote:
> 
> 
> Thanks Michel,
> 
> this is very useful ! Becke argues in this paper that including a
> current term makes all the different choices between occupations
> much more equivalent, at least for p occupations on 2nd row atoms.
> 
> Still, it doesn't look like an extensive answer (we do not know what
> happens to d orbitals, say), and he doesn't consider fractional
> occupations vs integer. And, I still wonder if there could be
> a proper answer in regular DFT. Not to mention that when
> atomization energies are tested by chemists (e.g. on the G2
> test) they must have a standard on how to define atomic energies.
> 
>                       nicola
> 
> 
> Michel C?t? wrote:
> 
> >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 ?crit :
> >
> >
> >>
> >>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
> >>>
> >
> >
> >
> 
> -- 
> ---------------------------------------------------------------------
> Prof Nicola Marzari   Department of Materials Science and Engineering
> 13-5066   MIT   77 Massachusetts Avenue   Cambridge MA 02139-4307 USA
> tel 617.4522758 fax 2586534 marzari@mit.edu http://quasiamore.mit.edu