How do you predict the relative energy of the dz² in Octahedral crystal field compared to linear crystal field that along the y-axis?

 

The relative energy of the d orbitals in a crystal field depends on the symmetry of the field and the orientation of the orbitals with respect to that field. In octahedral crystal field splitting, the d orbitals split into two sets: ${�}_{2�}$ (dxy, dyz, dzx) and ${�}_{�}$ (dx²-y², dz²).

In a linear crystal field along the y-axis, there is only one set of d orbitals involved, which are along the y-axis (dyz and dyz). This is a simplified scenario where the other d orbitals are not affected due to their orientation.

Now, comparing the relative energies of the dz² orbital in octahedral and linear crystal fields along the y-axis:

1. Octahedral Crystal Field:

   • In an octahedral crystal field, the dz² orbital experiences repulsion from the ligands along the z-axis and is raised in energy compared to the dxy, dyz, and dzx orbitals. This results in the dz² orbital being higher in energy compared to the ${�}_{2�}$ set of orbitals.

2. Linear Crystal Field along y-axis:

   • In a linear crystal field along the y-axis, the dz² orbital, being aligned along the z-axis, does not experience direct repulsion from ligands positioned along the y-axis. Hence, there isn't a significant change in the energy of the dz² orbital.
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Comparatively, in the octahedral crystal field, the dz² orbital will be higher in energy than in the linear crystal field along the y-axis because in octahedral field it is affected by ligands along all axes (x, y, z) leading to a greater splitting of its energy level.