What do we mean by spin-splitting energy?

What is the meaning of spin-splitting energy as described here?

• +1 I've edited the question because you had two close votes for "needing more focus". That's because you asked 5 questions in 1 post, so I've just narrowed it down to the first 2 questions. The other 3 questions are commented out, so you can still get them back by looking at the edit history. Those questions can certainly be asked in a separate post! – Nike Dattani Apr 17 at 19:01
• In regards to the original version of this post, questions 1 and 2 warrant separate posts and 3 would effectively be answered by the other two. Splitting questions makes them more searchable later, makes them more approachable for answerers (a person might be able to answer one question but not the other), and makes it easier to evaluate answers (if user answers both questions, is it highly upvoted/downvoted because it answers one of them well/poorly or both). As an added bonus, your separate question posts will generally earn you more rep than a single post. – Tyberius Apr 17 at 19:04
• Thank you guys for your comments. – Chi Kou Apr 17 at 21:10

I see now how your initial questions were related, as they all fall under the scope of crystal field theory. I wrote a bit about this in a previous answer.

At least in the context of molecular crystal field theory, you will usually see the phrase pairing energy rather than "spin-splitting". The distinction is basically just the direction, where the pairing energy is the penalty for having electrons share the same spatial orbital and the spin-splitting energy would be the increased stability from separating a pair.

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 would energy would be larger than the field splitting, leading to high spin configurations.

• Well answered! Thanks a lot sir. – Chi Kou Apr 19 at 11:32
• I think we made the right decision by recommending for this question to be split into at least two, because at first it was 5 questions (what's spin-splitting energy? how do you see it in DOS plot? what's crystal field splitting energy? how do you see it in DOS plot? how are these splittings different?) and we helped the user get in the habit of asking questions in a better format for SE. Your last paragraph seems to answer this though. Maybe this question can be about what spin-splitting energy is, and the other one can be about DOS plots? – Nike Dattani Apr 20 at 20:56

The word "splitting" seems to occur only in one sentence, over the course of the entire paper that you referenced:

"The d-orbital spin-splitting energy is stronger than the weak crystal field splitting energy of the S ligand around the TM atoms"

I can see why you had to ask this question here, because when I search "d-orbital spin-splitting" in quotes (so that we're searching for that exact phrase), only two results come up: this paper and this paper (the same happens if I replace either of the hyphens with spaces.

The phrase "d-orbital splitting" doesn't show up much either, but at least it shows up here where the splitting discussed is $$\Delta_0$$ which is actually the crystal field splitting energy.

In this particular paper, it seems that what they're referring to when they say "d-orbital spin-splitting energy" is the difference in energy between the high-spin and low-spin configurations. The paper goes on to say that because the d-orbital spin-splitting energy is stronger (i.e. larger) than the weak (i.e. small) crystal field splitting energy ($$\Delta_0$$), the system is said to be in the "high-spin state". This would make sense since high-spin states are sometimes characterized as having a small $$\Delta_0$$, for example, in the Wikipedia page in the last link I provided, it shows "$$\Delta_0$$ small" for the high-spin states:

and "$$\Delta_0$$ large" for the low-spin states:

My reading of the relevant paragraph suggests to me that the authors made this conclusion about the "d-orbital spin-splitting" being larger than the crystal field splitting of $$\Delta_0$$ based on Table II, rather than any of the DOS figures. So perhaps the readers are not expected to deduce this by looking at the DOS plots as you ask how to do, but it could be possible, and that's why this nice Q/A system allows us to get answers from multiple people 😊.

• Thanks a lot for your detailed explanation brother. – Chi Kou Apr 19 at 11:30