horizontal vertical stretch/compression of metal bonded to ligands in octahedral energy level effect

Question

why do the energy levels of the d-orbitals reorder in the way they do when you modify a octahedral ligand configuration already with e_g and t2g(crystal field) and move the ligands on the square plane further away and the z-axis ligands move closer to the metal and vise-versa?

Answer 1

The reordering of the energy levels of the dd-orbitals in an octahedral coordination complex when you modify the ligand positions is related to the crystal field theory and how the metal-ligand interactions affect the dd-orbital energies.

Crystal Field Theory Basics:

In an octahedral complex, the metal ion is surrounded by six ligands at the vertices of an octahedron. This arrangement leads to the splitting of the dd-orbitals into two sets with different energies:

1. egeg​ Orbitals: dz2dz2​ and dx2−y2dx2−y2​ - These orbitals point directly towards the ligands along the axes and experience greater repulsion.
2. t2gt2g​ Orbitals: dxydxy​, dxzdxz​, and dyzdyz​ - These orbitals are oriented between the axes and experience less repulsion.

The crystal field splitting energy (Δ0Δ0​) depends on the strength and arrangement of the ligands around the metal ion.

Effect of Modifying Ligand Positions:

1. Square Plane Ligands Moved Further Away:
2. When you move the ligands in the square plane (x and y directions) further away from the metal ion, the repulsion experienced by the egeg​ orbitals decreases. This is because the ligands are no longer as close to the orbitals oriented along these axes. Consequently, the energy of the egeg​ orbitals will decrease, making them less elevated compared to the t2gt2g​ orbitals.
3. Z-Axis Ligands Moved Closer:
4. Conversely, moving the ligands along the z-axis (up and down) closer to the metal increases the repulsion experienced by the egeg​ orbitals that are oriented along the z-axis. This increased repulsion raises the energy of the egeg​ orbitals relative to the t2gt2g​ orbitals.

Reordering of Energy Levels:

1. Original Configuration (Octahedral): In a typical octahedral field, the egeg​ set is higher in energy compared to the t2gt2g​ set due to direct repulsion from the ligands.
2. After Modifying Ligand Positions:
3. When square plane ligands are moved further away, the energy gap between egeg​ and t2gt2g​ decreases because the egeg​ orbitals experience less repulsion. The egeg​ orbitals may thus be lower in energy relative to the original configuration.
4. When z-axis ligands are moved closer, the repulsion increases, making the egeg​ orbitals even higher in energy relative to the t2gt2g​ orbitals.

Summary:

1. Increased Ligand Distance on the Square Plane: Lowers egeg​ orbital energy relative to t2gt2g​.
2. Decreased Ligand Distance on the Z-Axis: Raises egeg​ orbital energy relative to t2gt2g​.

These changes affect the overall crystal field splitting and the energy levels of the dd-orbitals, thus impacting the electronic structure, bonding, and properties of the complex.

Answer 2

The reordering of the d-orbital energy levels when modifying the octahedral ligand configuration arises from changes in the spatial distribution of the ligands and the corresponding electrostatic interactions with the metal d-orbitals. Bringing ligands closer along a particular axis increases the repulsion and raises the energy of d-orbitals oriented along that axis while moving ligands further away reduces the repulsion and lowers the energy of the respective d-orbitals. This reordering is a direct consequence of the altered crystal field splitting pattern due to the distorted geometry.