# How are the eg and t2g states identified in density of states diagrams? (VASP Code)

The 3d orbitals, for example, consist of: dxy, dxz, dyz, d−y², d For environments with spherical symmetry, these 5 orbitals are degenerate, meaning they have the same energy. Spherical symmetry means every direction looks the same from the point of view of the atom. A single atom floating around in free space meets this criteria.

For atoms in a solid, however, spherical symmetry is broken and you may have some other symmetry instead (symmetry here refers to the environment’s symmetry, not the orbital’s). This causes orbital energies to split. For example, the specific case of octahedral crystal symmetry has 2 groupings:

eg: d−y², d
t2g: dxy, dxz, dyz

The eg and t2g sets have different energies from each other. But the members of each set are energetically degenerate. The physical reason for this is that the lobes of the orbital wave functions point in different directions. Some directions place the electrons in regions of greater potential energy than other directions. Notice how this can’t happen for spherical symmetry because every direction is exactly the same.

To identify this in a density of states (DOS) plot, you need to decompose the total DOS into the individual contributions from different orbitals. You’re probably used to seeing total DOS plots, but these are sums of the projected density of states (PDOS) of each orbital.

Here’s an example. Notice how the Ni 3d orbitals are broken up. For Ir, the resulting sets are labeled (a1g is yet another symmetry like eg and t2g).

 LORBIT = 11 files written DOSCAR and lm-decomposed PROCAR
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