Skip to Content.
Sympa Menu

forum - Re: [abinit-forum] atomic calculations

forum@abinit.org

Subject: The ABINIT Users Mailing List ( CLOSED )

List archive

Re: [abinit-forum] atomic calculations


Chronological Thread 
  • From: Nicola Marzari <marzari@MIT.EDU>
  • To: forum@abinit.org
  • Subject: Re: [abinit-forum] atomic calculations
  • Date: Fri, 14 Apr 2006 10:40:23 +0200
  • Organization: Massachusetts Institute of Technology


Dear Andrew,

what baffles me is finding an answer to this question:
"What is the correct set of occupation numbers to use in the
calculation of the energy of an atom or an ion, when using LDA/GGA".

One answer is, as you mention, to let the electrons spread equally in the partially-filled subshell.

Another is to take the occupations that minimize the total energy (I
believe that often these two choices are equivalent, but I do not know
if they are always equivalent. E.g. in a d shell with 1 minority
electron, you could have e.g. 5*0.2, 2*0.5, and 3*0.33333, all making
"chemical sense").

A third choice is to use integer occupations, always (e.g. since
fractional occupations ae not v-representable (if I recall correctly
Englisch and Englisch 1984), or simply because a fractional
occupation makes no sense, in an atom, unless if you have the exact
grand-canonical exchange-correlation potential.

A fourth choice is to take ensemble averages of integer occupations results.

I haven't found, in my cursory explorations, a satisfactory answer -
this seems particularly relevant for cases when systematic tests
are done on atomization energies (e.g. by the chemistry community),
where the difference in atomic energies by strategies above are much
larger than the average error in atomization energies.

Note that e.g. letting the electrons spread equally in a partially-filled subshell seems unstisfactory to calculate ionization energies of a transition metal, while you are emptying the d shell
(e.g. you would have have first 5*1.0, then 5*0.8, then 5*0.6, etc...).

Sorry for the long email - any comment, public or private, would be very
welcome.

nicola



Andrew M. Rappe wrote:
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

--
---------------------------------------------------------------------
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

Archive powered by MHonArc 2.6.16.

Top of Page