[Wien] Bridging from Physics to Chemistry

[Peter Blaha]

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
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Peter BLAHA, Inst.f. Materials Chemistry, TU Vienna, A-1060 Vienna
Phone: +43-1-58801-165300             FAX: +43-1-58801-165982
Email: blaha at 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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