Question

When relaxing the infinitely strong field, the electrons start to feel one another's presence. They will, therefore, give rise to sets of states such as T1g, T2g... for the (t2g)^2 initial configuration. Given that Eg is a doubly degenerated state, which symbolic configurations (arrangements of electrons in dxy, dxz, dyz--> t2g) would fit this state?

Answer 1

Configurations fitting the Eg state for a (t2g)2 initial configuration would involve any two electrons in the dxy, dxz, and dyz orbitals, thus maintaining the double degeneracy of the Eg state.

Step-by-step explanation:

When considering the electron configurations for a t2g level in an octahedral crystal field, the Eg state is described as double degenerate.

In an octahedral complex, the dxy, dxz, and dyz orbitals constitute the t2g set, which are oriented 45° to the coordinate axes.

These orbitals form the lower-energy set since they point between the negative charges located at the vertices of the octahedron.

For a (t2g)2 initial configuration, fitting the Eg state would require two electrons to occupy the t2g set. Possible arrangements could be having one electron each in the dxy and dxz orbitals, or dxy and dyz, or dxz and dyz orbitals.

These configurations would maintain the double degeneracy by not completely filling any single t2g orbital, allowing electrons to repel each other minimally and thus occupying this lower-energy state compared to the higher energy eg orbitals (dz2 and dx2-y2).