Why do better π-acceptor ligands cause smaller Δ(T) d-orbital splitting?

Consider a formazanate ligand. Then imagine an electron-withdrawing group added to it. I expect a small σ-donating effect, and good π-accepting properties.

My supervisor tells me that an electron-withdrawing group causes a lowering of the π*-orbital energy, leading to a smaller $\Delta_\mathrm{T}$ in the d-orbital splitting of the resulting iron-based molecular orbitals. Why would this be the case?

• @Jan The ligand is a formazanate ligand on which we change one of the substituents into a more electron withdrawing group. – Timon van der Berg Jul 3 '16 at 21:47
• I recommend you give slightly more details about the ligand in question. – orthocresol Jul 3 '16 at 22:17

Since not many people know the ligand formazanate (I hadn’t heard of it before this question), let me quickly supply an image of what it looks like:

Scheme 1: General formazane structure.

Coodination happens from the lower two nitrogens, one of which is deprotonated (hence -ate) and both of which chelate the metal with $\mathrm{sp^2}$-type orbitals. The five formazane atoms form a π system, which can be extended by appropriate $\ce{R}$-groups. And one of these $\ce{R}$-groups is now modified to include an electron-withdrawing group.

I already previously gave a qualitative orbital scheme for a tetrahedral complex including σ and π interactions as given below.

Figure 1: Qualitative MO-scheme of a tetrahedral $\mathrm{d^0}$ complex with σ and π interactions. Originally created for this answer.

The σ donor orbitals transform according to $\mathrm{a_1 + t_2}$, leaving $\mathrm{e + t_1 + t_2}$ for the π ligands. Unfortunately, the picture is a tad clouded, since both σ and π interactions have a $\mathrm{t_2}$ contribution.

Adding an electron-withdrawing group to your ligand will leave the σ interaction unchanged in first approximation, since mainly the ligand’s π system would be affected. The orbital energies of the π system would be reduced. Since we are talking about a metal with a low oxidation state, its orbitals are higher than drawn in the qualitative scheme (which was designed for permanganate). And thus also, the most important π interaction of the ligand will be, as you stated, accepting electrons into its π system.

The exact nature of any effect observed will depend on the original orbital energies. However, the $\mathrm{e}$ orbitals are only affected by the π interaction while the $\mathrm{t_2}$ orbitals are also affected by the σ interaction. The magnitude of π interaction is expected to be the same for both groups of orbitals, since the start from the same value on each side. Thus, the difference between $\mathrm{e}$ and $\mathrm{t_2}$ stems mainly from σ interactions which only affect $\mathrm{t_2}$ due to symmetry.

Because the σ interaction starts with the ligand orbitals being much lower in energy than the metal orbitals, reducing their energy even more will result in a weaker interaction, therefore a lowering of the $\mathrm{t_2}$ level and thus a smaller $\Delta_\mathrm{T}$ or $10~\mathrm{Dq}$ value.