# Does crystal field splitting energy Δ increase going down a group of transition metals if the ligands are weak field?

• Going down a group, the metal orbitals are more diffuse so there is greter overlap between the metal and the ligand orbitals.
• If there are no π-interactions, i.e. with σ-donor ligands like $\ce{NH3}$, then the $\mathrm{e_g}$ MOs are split further with more metal-ligand overlap, and $\Delta_o$ increases.
• If there are π-acceptor interactions, then the $\mathrm{t_{2g}}$ MOs are split further with more metal-ligand overlap, but $\Delta_o$ still increases as it is the gap between the bonding $\mathrm{t_{2g}}$ and antibonding $\mathrm{e_g^*}$.
• However with π-donor ligands ($\ce{Cl-}$, $\ce{Br-}$ etc), surely more overlap would cause greater splitting of the $\mathrm{t_{2g}}$ orbitals, which would decrease $\Delta_o$, as it is the energy difference between the antibonding $\mathrm{t_{2g}^*}$ and $\mathrm{e_g^*}$.

So, does $\Delta_o$ still increase going down a group if the ligands are π-donors?

I see where you are coming from, but you forgot that even with π-donor ligands, there is still a σ-bonding present in the complex. In the 4d/5d metals, the $\mathrm{e_g}^*$ orbital is pushed up by a lot due to the σ-type overlap.
The $\mathrm{e_g}$ overlap is always stronger than $\mathrm{t_{2g}}$ overlap because the metal $\mathrm{e_g}$ orbitals point directly at the ligands ($\mathrm{d}_{x^2-y^2}$ and $\mathrm{d}_{z^2}$), whereas $\mathrm{t_{2g}}$ orbitals point in between the ligands ($\mathrm{d}_{xy}$, $\mathrm{d}_{xz}$, $\mathrm{d}_{yz}$).
So, yes, the $\mathrm{t_{2g}^*}$ orbital is pushed up higher by the π-donor, but the $\mathrm{e_g^*}$ orbital is pushed up even higher. Thus, for example, the complex $\ce{[RuCl6]^2-}$ has a $(\mathrm{t_{2g}})^4$ configuration (i.e. low spin) even though $\ce{Cl-}$ is a π-donor ligand.