Tetrahedral complex and vibronic coupling or different rule for d-d transition?

I'm currently preparing a few slides for an upcoming talk in our group. I would like to mention some of the very basics regarding crystal field and ligand field theory as well, though this will not be the main topic of the talk.


I started from allowed transitions and how the (transition) dipole moment operator causes the transition between two states to be allowed or not (from just pointing out the area under an odd and even function and from group theory basics).


Then I'd like to continue to octahedral complexes. But here you've got two problems, one is the d-d transition that is forbidden and the other one is the Laporte forbidden transititon. When I need to compare this to the next slide with tetrahedral ligand fields I can always say that the Laporte rule doesn't work here since there is no inversion center.


So how is the Laporte rule still achieved for octahedral complexes? Due to something we call vibronic coupling. I always assumed this meant that a vibration, prior to the exitation deforms the octahedron to something that has less symmetry (which is probably happening, too) until I recently heard about transforming your set of *p*-orbital originating $T\_\mathrm{1u}$ along the vibrational mode T1u that is also the dipole moment operator in this case, as x,y,z transforms as $T\_\mathrm{1u}$ in this point group. Transforming $T\_\mathrm{1u}$ along $T\_\mathrm{1u}$ in an octahedral complex gives you, among others also a $T\_\mathrm{2g}$, so the $T\_\mathrm{2g}$ for the transition can also be described in terms of *p*-Orbital and thus you get *p*-orbital contribution. (Please correct me if I've understood anything wrong here).


Now this is a good explanation, what it doesn't explain however is how actual *d*-*d* transitions are allowed now? This means there is either another thing happening here or that there is also a vibronic coupling for the tetrahedral case.


Now, before I read into those group theory explanations I assumed that the *d*-*d* transitions happens because we are not talking about actual d-orbitals but we are talking about electrons in bonds. As the $T\_\mathrm{2g}$ requires a π-type bonding and the $E\_\mathrm{g}$ uses σ-bonding the actual transition is from a π-orbital into a σ-orbital, so *p*-*s* or if you take both sides *pd*-*ps*.


The other alternative would be that also the tetrahedral complex uses vibronic coupling. I can't find much on this though. There are calculations in combination with Jahn-Teller effects but no clear answer as with the octahedral case.


Hence my question: When talking about *d*-*d* forbidden transitions without taking the Laporte rule for odd even parity into account, is the often cited mixing of *d*-states with *p*- and *s*-states from something coming from the bonding situation or is the prohibition lifted due to the same vibronic coupling mechanism as used for partiy forbidden transitions?


