It is a bit beyond the topics of the mailing list, but I still will try
to contribute to your understanding hoping that I'm not getting
oversimplifying:
The terms "closed" and "open" shell in atoms/molecules usually means
that you have only paired electrons (each atomic/molecular orbital is
occupied by a spin-up AND dn electron), or also unpaired electrons.
From this definition it is also clear that any atom/molecule with an
odd number of electrons will be open-shell, and in an open-shell systems
there is a net spin-magnetic moment since the number of up/dn electrons
is (usually) different).
In a bigger molecule you could have several unpaired electrons in
different MOs, but the be arranged in different ways in spin-up or dn,
and one usually classifies them by specifying the "spin-multiplicity"
(singlet, duplet,triplet,...)
And last but not least, one can make an approximation restrict spin-up
and dn-orbitals to be the same or not (restricted/unrestricted).
In solids things are a bit different:
If all electrons are paired and we have an insulator/semiconductor, we
talk about a diamagnet (="closed shell") and it implies again that the
number of electrons is even.
However, in contrast to atoms/molecules, we can have a paramagnetic
METAL, which can have an odd number of electrons and still the up and
dn-electrons are equal. This is a consequence of the large ("infinite")
number of atoms in a 3D solid and the resulting delocalization of the
electronic states, so that ONE atom may have only a small fraction of an
electron in a particular "orbital" (better a Bloch-state).
So the Na atom is a open shell system with 1 unpaired electron, while
metallic Na is a paramagnet (and we do run_lapw, i.e. forcing equal
number and orbitals for up and dn spin).
Also in a solid you can have unpaired electrons (take the metals Fe or
Cr), but then these "open shell" solutions may differ in the way they
have long-range order (something that does of course not exist in
molecules). If the spins on all atoms point into the same direction, we
speak about a ferromagnet (Fe), but they could also be antiferromagnetic
(spin-up on one atom, spin-dn on the next,...) or even more complicated
(spin-spirals, non-collinear (or canted), ....
Cr you can consider as AFM (although, actually it has a long
spin-spiral...).
So for AFM-Cr we do a "spin-unrestricted" calculation with a total
singlet (zero) spin/unit cell), while for ferromagnetic Fe the total
spin is non-zero (note, Fe has a NON-INTEGER spin-moment of 2.2 uB,
something which does (to my knowledge) not exist in a finite system.
And last but not least, an Antiferromagnet in "MO"-language is a system
where there are more occupied orbitals of spin-up on atom 1; but more of
spin-dn on atom 2.
Or if you like: When we do the O2 molecule in a periodic code using a
big supercell, the triplet O2 molecular state is a "ferromagnet", while
the singlet state would be an antiferromagnet.
Thank you for your answer, I know the concepts one by one (at least I
think I know), however, my question is still about their equalization,
for example, when we run an "Anti ferromagnetic" calculation in Wien2k
for a bulk system, which one of the "Closed shell", "open shell",
"Restricted or unrestricted configuration" would be really applied in
this case? For example as I mentioned: A non-spin polarized calculation
in Wien2k(run_lapw) apparently looks like a "closed shell" system which
usually is used for nonmagnetic or Diamagnetic materials.
So, again what is important for me is approximate equalization of these
two groups of definition. And it is always easy to understand to see how
the orbital are filled out for example in "O2" molecule (in the gas
phase or as a impurity in large system)and predict the magnetic or spin
ordering behavior of "O2" molecule, but it would be a bit challenging
when we want to explain for example Anti ferromagnetic behavior of "NiO"
or ferromagnetic behavior of "Gd5Ge4", but not by plotting DOS or band
structure but by presenting the molecule orbitals exactly like what is
doing for "O2" molecule.
--
P.Blaha
--------------------------------------------------------------------------
Peter BLAHA, Inst.f. Materials Chemistry, TU Vienna, A-1060 Vienna
Phone: +43-1-58801-165300 FAX: +43-1-58801-165982
Email: bl...@theochem.tuwien.ac.at WIEN2k: http://www.wien2k.at
WWW: http://www.imc.tuwien.ac.at/staff/tc_group_e.php
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