What kind of bonds can form between benzene and transition metals in π-complexes?

Question

I'm trying to draw the six π-orbitals (3 bonding, which are filled, and 3 anti-bonding) of a benzene ring when it complexes with metal d-orbitals and which metal orbitals have the correct symmetry ($\sigma$, π, $\delta$) to overlap with each of them. I know that metal orbitals will only form a bonding interaction with ligand orbitals if they have matching symmetry but I am not sure which ones will interact.

I think a π bond is formed between $e_{1g}$ of benzene and $d_{xy}$ and $d_{yz}$. Also a $\sigma$ bond is formed between $a_{2u}$ of the benzene and $d_{z^2}$ and $a_{2u}$. No δ bond is formed.

Answer 1

In theory benzene and a transition metal could form σ, π, δ, and even φ bonds as the symmetry allows this.

Here are the orbitals of benzene, calculated at the PBE0/def2-TZVPP level of theory in the D_6h point group with Gamess.

The (valence) orbitals of chromium on the same level of theory in the same point group are as follows:

The linear combination of these orbitals would yield orbitals that have the above mentioned bond symmetries. We will ignore for now that they will most likely not occupied in a complex like bis(benzene)chromium.

• benzene a_2u + Cr s → σ
• benzene a_2u + Cr d_z² → σ
• benzene e_1g + Cr d_xz → π
• benzene e_1g + Cr d_yz → π
• benzene e_2u + Cr d_xy → δ
• benzene e_2u + Cr d_x²-y² → δ

If we look at f-orbitals (that is of course not very feasible for chromium), we could construct another bond type:

• benzene a_1g + Cr f_x(x2−3y2) → φ

The necessary orbital looks like this:

Of course which of these bonds will form or not depends on the metal in question, the occupation of the orbitals and more. After all, there are also p orbitals which can overlap to form σ and π bonds.

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Colour code: Occupied orbitals are shown in blue and orange, while virtual orbitals are shown in yellow and red. Phases have been assigned randomly. The total density of the molecule uses a violet contour.