The ABINIT Users Mailing List ( CLOSED )

[Nicola Marzari <marzari@MIT.EDU>]

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 Côté 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 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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