[Wien] Bridging from Physics to Chemistry

[Salman Zarrini]

++++++++++++++++++++++++++++++++++++++++++++++++++++++++
Dear Prof. Blaha,

Thank you for your prompt and nice answer.
So can you confirm me please that, in comparison of a "paramagnetic"  
METAL and a "antiferromagnetic" solid I would say that "paramagnetic"  
METAL is a kind of a "closed shell" system while a "antiferromagnetic"  
solid is a "open shell" but both of them have zero spin/unit  
cell,singlet state or so to speak, a "paramagnetic" METAL is a  
"singlet closed shell" system but "antiferromagnetic" is a "singlet  
open shell" system.

I have to more questions which your answer would be highly appreciated:

1. What happen in a bulk case that we start a scf spin-polarized  
calculation (runsp_lapw) where all the spin for example are aligned up  
in initialization (instgen_lapw -> case.inst) but at the end no spin  
magnetic moment or a nonmagnetic system would be harvested. Means we  
started from a "Open shell" system (in this case triplet or even more)  
but the SCF finished by a "closed shell" system, is it meaningful such  
changes?

2. Do you think does it make sense talking about paramagnetic behavior  
or call a system paramagne in the DFT calculation? as in one hand the  
"zero kelvin" is the temperature considered in all the DFT level  
calculations and codes, and in another hand we know that  
"paramagnetic" behavior shows up at higher than specific temperatures  
like "curie and neel" in solid states

Best regards,

Salman Zarrini
++++++++++++++++++++++++++++++++++++++++++++++++++++++++


Quoting "Peter Blaha" <pblaha at theochem.tuwien.ac.at>:

> 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: blaha at theochem.tuwien.ac.at    WIEN2k: http://www.wien2k.at
> WWW:   http://www.imc.tuwien.ac.at/staff/tc_group_e.php
> --------------------------------------------------------------------------