Allyl Ligand Molecular Orbitals and Metal Interaction

The allyl ligand, specifically the allyl anion (CH₂ = CH‐CH₂−), is a three-carbon system with a delocalized π system. It is an example of an ambidentate ligand, meaning it can bond to a metal center in different ways (e.g., η¹ or η³).

Molecular Orbitals of Allyl Anion

The three p-orbitals on the carbon atoms combine to form three π molecular orbitals (MOs):

• π₁ (or 1π): This is the lowest energy MO and is bonding. It has zero nodes between carbon atoms.
• π₂ (or 2π): This is a non-bonding MO. It has one node passing through the central carbon atom.
• π₃ (or 3π): This is the highest energy MO and is antibonding. It has two nodes between carbon atoms.

The allyl anion has 4 π electrons (2 from the double bond and 2 from the negative charge). These electrons fill the π₁ and π₂ orbitals. Thus, π₁ and π₂ are filled, and π₃ is empty.

Interaction with Metal d-orbitals

Ligands interact with metal centers through donation of electron density from the ligand to the metal (σ-donation) and acceptance of electron density from the metal into empty ligand orbitals (π-back donation).

Sigma Donation

In general, σ-donation from a ligand occurs from a filled ligand orbital to an empty metal orbital. For π systems, the highest occupied molecular orbital (HOMO) is typically involved in donation. In the allyl anion, the HOMO is the π₂ (2π) orbital.

However, in some contexts, especially when describing bonding in organometallic compounds involving π ligands like allyl, the term "σ-donation" can refer to the overall donation of electron density from the filled bonding orbitals of the ligand's π system to the metal. The lowest energy bonding MO, π₁ (1π), provides significant electron density and interacts effectively with metal orbitals having appropriate symmetry to form a stable bond. Based on the options provided, the 1π orbital is considered for σ-donation.

Pi Back Donation

π-back donation involves the donation of electron density from a filled metal d-orbital to an empty ligand orbital. This typically occurs into the lowest unoccupied molecular orbital (LUMO) of the ligand. For the allyl anion, the LUMO is the π₃ (3π) orbital, which is antibonding and empty. This orbital has the correct symmetry to overlap with filled metal d-orbitals, allowing for back-donation.

Therefore, considering the typical interactions and the options provided, the 1π orbital is used for σ-donation (representing donation from the filled bonding part of the π system) and the 3π orbital is used for π-back donation (as it is the empty antibonding orbital).

Summary of Molecular Orbital Use

• σ-donation: Utilizes the 1π molecular orbital.
• π-back donation: Utilizes the 3π molecular orbital.

The orbitals used for σ‐donation and π back donation with metal d‐orbitals, respectively, are 1π and 3π.