# Metal 3d to ligand hybridization in Td

asked by Guillaume Radtke (2019/05/21 10:22)

Dear Quanty Developers,

I would like to include metal/ligand hybridization in the calculation of a TM L23 edge in Td symmetry and I wonder how to include it in Quanty. More specifically, my problem lies in the fact the (12) 2p ligand orbitals decompose according to a1 + t1 + e + 2*t2 in Td. What would be the “cleanest” to account for the ligand in this case ? Forget about symmetry ? Or add two “ligand d shells” and find a way to remove one set of e orbitals ?

Thank you in advance for your answer,

Best Regards,

G. Radtke

## Answers

Dear Guillaume,

The situation for Td should be very similar to the Oh case that is discussed in depth here. You only consider the symmetry adapted linear combinations of p-orbitals that can interact with the d-orbitals. Compared to the example on the site, for Td symmetry you will need to define the hybridization operators Vt2 and Ve. If you have doubts you can also have a look at the Quanty input file generated using Crispy. I hope this answers your question.

Marius

Dear Marius,

In fact, Td is not quite the same as Oh as the t2 IRREP occurs twice when decomposing the representation spanned by the 12 ligand p orbitals (and e only once, if I'm correct). My question is therefore how to account properly for these two Vt2 and Vt2' while having only one Ve ?

Guillaume.

Hi Guillaume,

You are correct; there should be a second set of orbitals with T2 symmetry. Probably the best way is to add a second shell of ligands. You will need however to define the energy of these ligands w.r.t. the 3d orbitals of the metal and the first set of ligand orbitals. In Quanty this is done via $\Delta$ and $U_{dd}$.

Marius