Hi, as a synthetic chemist, I decided to look into basics of UV spectroscopy. The thing I got stuck with is the enrrgy of a specific transition (for d3 octahedral ion - due to Td-Oh and electron-hole expansions can be generalized to some other configurations):
- For a d³ ion in an octahedral field, my CFSE calculations (with respect to the ⁴F "free ion" ground term) give:
- ⁴A₂g: -1.2Δoct
- ⁴T₂g: -0.2Δoct (so, the ⁴F → ⁴T₂g gap is 1.0Δoct)
- (F)⁴T₁g: +0.8Δoct (2*0.6Δoct-1*0.4Δoct=0.8Δoct).
For the (F)⁴T₁g state, however, the correct value is +0.6Δoct (I checked a handful of textbooks but could not find an explanation. Note that the electron repulsion term x should not be relevant as it is explicitly treated in the next step and the final energy of the ⁴T₁g state is 0.6Δoct-x. (the d3 octahedral Orgel diagram from Housecroft, C. E.; Sharpe, A. G. Inorganic Chemistry, 4th ed.; Pearson: Harlow, England, 2012, p695 with a few notes is attached) Am I missing something?
Dear Pavel
That's indeed an interesting question. I am not a spectroscopist, but here you have my understanding on this matter, which hopefully helps. I have done the numbers myself, and you are absolutely right, using a pure crystal field approximation, the 4T1g state should be at 0.8Δoct.
The thing here is that this (F)4T1g state can mix (due to having the same symmetry) with the higher energy (P)4T1g state. This will result in a slight lowering in energy for the (F)4T1g state and an increase in energy for the (P)4T1g.
The extent of the mixing (and energy stabilisation) cannot be calculated easily, because it depends on several factors including the Racah parameter (note the energy difference between F and P is approximated as 15B, with B being the Racah parameter). For this reason, it is normally calculated from experimental and/or computational data, and this gives an empirical value around 0.6Δoct. Nonetheless, this is still a rather crude approximation, because if you look at the experimental Tanabe-Sugano diagrams for d3 metals, you can observe that the energy difference between the T2g and T1g states is not constant (mainly due to the mixing of the aforementioned (P) and (F) 4T1g states).
Best wishes,
Martí
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