[Wien] Bridging from Physics to Chemistry

[Víctor Luaña Cabal]

On Mon, Oct 20, 2014 at 03:17:48PM +0200, Salman Zarrini wrote:
> +++++++++++++++++++++++++++++++++++++++++++
> 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 ... .

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,
         Víctor Luaña

--
       \|/a  "After years of working on a problem the genius shout:
      |^.^|     what an idiot I am ... the solution is trivial!'
+-!OO--\_/--OO!------------------------------+-----------------------
!            Dr.Víctor Luaña                   !
! Departamento de Química Física y Analítica   !
! 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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