[Wien] Bridging from Physics to Chemistry

[Salman Zarrini]

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Dear Victor,

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.

Cheers,

Salman Zarrini
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Subject: [Wien] Bridging from Physics to Chemistry
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Dear Wien2k users,

I get always confused while bridging from Physics to Chemistry in
explaining "spin" and "Magnetism".
So, I would be highly appreciated if anybody kindly equalized (if it
is possible)in DFT the concepts like "Nonmagnetic", "Paramagnetic",
"Ferromagnetic", "Anti-ferromagnetic" and "Ferrimagnetic" in one hand
and "Closed shell", "Open shell", "Spin restricted" and "Spin
unrestricted" configurations in the another hand, specially in the
case of infinite system like an usual bulk (magnetic or nonmagnetic)
which is possible to be easily treated in a plane wave code like Wien2k.

To start, I can just say:  doing a non-spin polarized calculation in
for example Wien2k (run_lapw) equals to a "Closed shell" calculation.

And also, for me a "Ferrimagnetic" looks like a "Spin unrestricted"
configuration ... .

Best regards,

Salman Zarrini
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You are asking an impressive list of things and it is not easy
to answer them. You would need a complete master course for this.

1) Let me start from the electronic structure concept of closed and open
shell. A closed shell corresponds to have all orbital levels empty or
containing a complete collection of electrons. So a ns(2), np(6), nd(10)
or nf(14) are closed shells.  An open shell corresponds to have nl(N),
for 0<N<2*(2*l+1). Remember that in period n the nl orbitals are the
valence ones and the ones involved in chemical bonding.

Closed shells are electronic groups that belong to the fully symmetric
irreducible representation (irrep) for the local symetry group. So they
do not provide many energy levels to your system.

So, when you examine the optical properties of a Cr(+3) impurity in a
Al2O3 corundum crystal is the energy levels of the Cr(+3) open shell
the ones that produce the interesting optical properties. The Al(+3) and
O(-2) ions are closed shells and the provide the chemical ambient where
the 3d impurities do the nice things.

Similarly in the second and third transition metal atoms or in the nf
rare earths. All of them tend to produce rich open shell groups.

2) As for the cooperative magnetism of ferro, ferri, etc I advice you
to explore some good text on the subject: Tipler, Kittel, Ashcroft-Mermin.
The diffrent types of magnetism correspond to different couplings of the
m_s spins in neighbor unit cells of the crystal.

3) The spin restricted and unrestricted SCF techniques correspond
to force the alfa (m_s=+1/2) and beta (m_s=-1/2) electrons having
the same spacial description (restricted) or let the two groups
occupy different regions in space, i.e. different R_{nl}(r) and
R_{nl}^prime(r) orbitals. The unrestricted techniques are very important
as a first step in solving the correlation energy problem.

If you have been lost in this lengthy post don't worry. I told you that
your question was not easy.

Regards,
          V?ctor Lua?a

--
        \|/a  "After years of working on a problem the genius shout:
       |^.^|     what an idiot I am ... the solution is trivial!'
+-!OO--\_/--OO!------------------------------+-----------------------
!            Dr.V?ctor Lua?a                   !
! Departamento de Qu?mica F?sica y Anal?tica   !
! Universidad de Oviedo, 33006-Oviedo, Spain   !
! e-mail:   victor at fluor.quimica.uniovi.es     !
! phone: +34-985-103491  fax: +34-985-103125   !
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