[Wien] Wien Digest, Vol 107, Issue 6

[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
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> Subject: [Wien] Bridging from Physics to Chemistry
> +++++++++++++++++++++++++++++++++++++++++++
> 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
> +++++++++++++++++++++++++++++++++++++++++++

>
> 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   !
> +----------------------------------------------+
>  GroupPage : http://azufre.quimica.uniovi.es/  (being reworked)