How Do You Sketch D-Orbital Splitting Diagrams for Td and D4h Symmetries?

[rmjmu507]

Homework Statement

Sketch d-orbital splitting diagrams for a complex in Td symmetry and a complex in D4h symmetry. Label the orbitals as bonding, antibonding, or non-bonding

Homework Equations

The Attempt at a Solution

So I know that in Td symmetry, the d-orbitals split into a lower doubly-degenerate and an upper triply-degenerate level. Also, in D4h symmetry, the d-orbitals split as follows (from low to high energy): doubly-degenerate (xz, yz), singly-degenerate (z^2), singly-degenerate (xy), singly-degenerate (x^2-y^2).

However, I'm not sure how I am supposed to assign bonding characters to these diagrams: for Td, would the lower level simply be sigma and the upper be sigma*? And for the D4h case, would the ordering be as follows: sigma, pi, non-bonding, sigma*/pi*? I'm just taking a guess here - I'm really not sure how to approach this.

Thanks in advance for any help.

 

[nate808]

Dear forum post,

Thank you for your question. I am happy to assist you with your inquiry.

Firstly, you are correct in your understanding of the d-orbital splitting in Td and D4h symmetries. In Td symmetry, the d-orbitals split into a lower doubly-degenerate (e) level and an upper triply-degenerate (t2) level. In D4h symmetry, the d-orbitals split into four levels: doubly-degenerate (xz, yz), singly-degenerate (z^2), singly-degenerate (xy), and singly-degenerate (x^2-y^2).

In terms of assigning bonding characters to these diagrams, you are on the right track. In Td symmetry, the lower e level can be labeled as bonding, while the upper t2 level can be labeled as antibonding. In D4h symmetry, the ordering would be sigma, pi, non-bonding, and sigma*/pi* from low to high energy. Therefore, the sigma and pi levels can be labeled as bonding, while the non-bonding and sigma*/pi* levels can be labeled as antibonding.

I hope this helps clarify your understanding of d-orbital splitting in Td and D4h symmetries. If you have any further questions, please do not hesitate to ask. Keep up the good work in your studies!