Understanding eg and t2g Symmetry in DOS Graphics

[Hyla Brook]

Dear all,

I found in many references the authors pointed out the eg and t2g band in the DOS graphics, and wrote in the text accordingly that it had eg symmetry (or t2g symmetry). How did they conclude that just from one Dos graphics (sometimes d projected)?

Best regards

 

[Rajini]

Hi,
i really don't know what a DOS graphics is. But in transition metal complexes the electrons in the d orbital are usually placed in Eg (Eg is above T2g) and T2g states. And the way these electrons are placed gives information on spin-state and electronic structure as well.
hope it helps.

 

[Hyla Brook]

Hi,
i really don't know what a DOS graphics is. But in transition metal complexes the electrons in the d orbital are usually placed in Eg (Eg is above T2g) and T2g states. And the way these electrons are placed gives information on spin-state and electronic structure as well.
hope it helps.

Hi, Rajini. Thank you for your reply. DOS means density of states. I agree with you that Eg is above T2g, but what I feel confused is that how can one know which peaks correspond to, for example, the Eg band from a single d-projected DOS graph? I guess I should provide a picture here for illustration(attachment). This is the spin polarized d-project DOS graph of Ni in Ni2MnGa(L21 structure), the author pointed out the eg peaks in it(saying in the text that they have the dz^2 and d(x^2-y^2) character). What the base is this?

 

[Rajini]

Hi,
Yes, it is known that DOS means density of (phonon) states. When you appended 'graphics' to DOS i was confused. For your question i really don't know the answer. Please read that paper fully..maybe somewhere they gave some reference..or you can lookup into solid-state physics books. sorry.

 

[kanato]

The eg manifold generally consists of the d(x^2-y^2) and the dz^2, whereas the t2g manifold consists of dxy, dyz, dxz. You could tell which is which by doing the individual projections. Also, since t2g contains 3 states and eg only contains 2, you could hazard a guess just by which set of peaks has greater area under them.

 

[Hyla Brook]

The eg manifold generally consists of the d(x^2-y^2) and the dz^2, whereas the t2g manifold consists of dxy, dyz, dxz. You could tell which is which by doing the individual projections. Also, since t2g contains 3 states and eg only contains 2, you could hazard a guess just by which set of peaks has greater area under them.

Hi, Kanato. You are right if individual projections could be made, we could tell the eg and t2g. I think that depends on the whether the program one use for calculation could do that job. For the second way you propose, it is a good idea that inspires me, and the question is, could we distinguish what we are looking for from the other peaks and what are the relative energy level of them? If this is solved, an appropriate guess could be made, I think.

 

[kanato]

The only sure fire way to identify the t2g vs. eg states is by doing the projections. There are some things you can look for to make an educated guess otherwise, such as looking at the formal electron configuration. Typically d states have a smaller bandwidth than s or p states, so you expect large peaks to be them. Also, within LDA a partially filled d subshell will almost always straddle the Fermi level. From there, if the DOS is clean enough you can make a guess as to which is eg or t2g based on the area. You can also consider the local symmetry, if you have a transition metal within an octahedron of anions, the orbitals which point directly toward those anions (the eg) will have a larger Coulomb repulsion with the anions as compared to the t2g states which have their density in pointing at the faces of the octahedron. This resulting in the eg being higher in energy.

But I stress again that the only way to know for sure is to do the projections.

 

[Hyla Brook]

The only sure fire way to identify the t2g vs. eg states is by doing the projections. There are some things you can look for to make an educated guess otherwise, such as looking at the formal electron configuration. Typically d states have a smaller bandwidth than s or p states, so you expect large peaks to be them. Also, within LDA a partially filled d subshell will almost always straddle the Fermi level. From there, if the DOS is clean enough you can make a guess as to which is eg or t2g based on the area. You can also consider the local symmetry, if you have a transition metal within an octahedron of anions, the orbitals which point directly toward those anions (the eg) will have a larger Coulomb repulsion with the anions as compared to the t2g states which have their density in pointing at the faces of the octahedron. This resulting in the eg being higher in energy.

But I stress again that the only way to know for sure is to do the projections.

Many thanks to you for the very nice discussion!