The ABINIT Users Mailing List ( CLOSED )

[Nicola Marzari <marzari@MIT.EDU>]

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