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I was doing DFT calculations using VASP of some transition metal compounds and plotted the density of states (DOS) along with the projected density of states (PDOS).

I am wondering how can someone understand what is the oxidation state of a metal ion just by analysing the DOS plot of that compound? I have attached some DOS plots of $TiO_2$

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Paper link : https://iopscience.iop.org/article/10.1149/2.0561701jes

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I am no expert here but, strictly speaking, I think that you can't get it from the DoS. There are many methods for evaluating the amount of charge around an atom:

Broadly speaking, you define a sphere around the atom you want to know the oxidation state of and count the electron charge in the sphere. The difference between the electron charge and atomic number is the oxidation state I guess. Ultimately, it is an ambiguous procedure: e.g. you can change the sphere radius around your atom and get a different number. See the links above for the "best method".

From the DoS, I suppose you can integrate from $-\infty$ to the Fermi level, or in some other range, to find the electron charge; however, this will only tell you the electron charge per unitcell which you likely already know. The DoS doesn't tell you how much charge is around any given atom. Rather, you have to project the DoS onto atomic orbitals (or some other basis). This usually requires integrating in a sphere centered on the atoms, much like the charge analysis above! I think, then, you can integrate the PDoS from $-\infty$ to the Fermi level and find the electron charge centered on a specific atom. Then you can use this to figure out the oxidation.

I think that projecting the DoS onto atomic orbitals etc. isn't conceptually different than other population analysis. Maybe it is worth just using one of the other methods in the links above? Many of them work as post-processing steps to e.g. VASP.

Hope this helps! Ty

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