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What are the signs (if any) in DOS plots that tell us whether we have a big or small crystal-field splitting energy, or spin-splitting energy? I already asked and got an answer to: What do we mean by spin-splitting energy?

I am asking in the context of this paper which discusses a comparison between spin-splitting energy and crystal field splitting energy, and shows multiple DOS plots.

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    $\begingroup$ Just a comment: the ligand field theory is inherently a multireference theory, so for quantitative estimations of these energies it is advised to go beyond the energy band model and use a multireference method instead, e.g. use the ab initio ligand field theory (AILFT) method in the ORCA software $\endgroup$
    – wzkchem5
    Nov 14, 2021 at 13:59

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I'm going to reproduce the part of my answer from the linked question that relates to the spin-splitting.

I don't believe the spin-splitting or field splitting can be read from the DOS. The way they are mentioned in the paper seems to suggest they are giving a qualitative explanation for seeing all the compounds in high spin configurations. The spectrochemical series gives an ordering of ligands based on how much field splitting they should cause. Since S is known to be a weak-field ligand, it makes sense that the spin splitting energy would be larger than the field splitting, leading to high spin configurations.

As for the crystal-field splitting, perhaps not from the DOS on its own, but the PDOS could help you identify the gap in energy between states formed from different types of d-orbitals.

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