Questions: Metal-Metal Bonding

Question 1

The quadruple bond in [Re₂Cl₈]²⁻ consists of which types of orbital interactions?

• A. Four equivalent sigma bonds
• B. One sigma (d_z²-d_z²), two pi (d_xz-d_xz and d_yz-d_yz), and one delta (d_xy-d_xy) bond
• C. Two sigma and two pi bonds, like a C≡C triple bond with an extra sigma
• D. One sigma, one pi, and two delta bonds

Answer: (B)

The quadruple bond uses four of the five d-orbitals on each metal. The d_z² orbitals overlap head-on (sigma). The d_xz and d_yz pairs overlap laterally (two pi bonds). The d_xy orbitals overlap face-to-face (delta bond). The d_x²−y² orbitals on each metal point at the chloride ligands and are used for metal-ligand bonding, not metal-metal bonding. The delta component is uniquely characteristic of metal-metal bonding — it has no analogue in organic chemistry — and it requires the chloride ligands to be eclipsed rather than staggered, because staggering would destroy the d_xy-d_xy overlap.

Question 2

The eclipsed geometry of the chloride ligands in [Re₂Cl₈]²⁻ is a direct consequence of the delta bond between the two rhenium atoms.

• T. True
• F. False

Answer: True

Delta bonds form from face-to-face overlap of d_xy orbitals on adjacent metals. This overlap is maximized when the ligands on the two metals are eclipsed (aligned) and goes to zero when they are staggered (rotated 45°). The delta bond energy is sufficiently large to overcome the steric preference for staggered ligands, locking the complex in the eclipsed conformation. This is a striking example of electronic structure dictating molecular geometry: without the delta bond, the eight chlorides would prefer a staggered arrangement to minimize Cl-Cl repulsion.

Question 3

A dinuclear metal complex has the metal-metal MO configuration σ²π⁴δ²δ*²π*². What is the effective bond order?

• T. True
• F. False

Answer: False

This question requires calculation. Bond order = (bonding electrons − antibonding electrons)/2. Bonding: σ²π⁴δ² = 8 electrons. Antibonding: δ*²π*² = 4 electrons. Bond order = (8 − 4)/2 = 2. This configuration represents a net double bond. The filled delta and delta* cancel (no net delta bonding), and two of the four pi electrons are canceled by the two pi* electrons, leaving the sigma bond and one net pi bond. If someone claimed the answer was 'true' for bond order 3, that would be wrong — careful counting of antibonding electrons is essential.

Question 4

Explain why the metal-metal bond in [Mo₂(CH₃COO)₄] (Mo-Mo distance ~2.09 Å) is much shorter than a typical Mo-Mo single bond (~2.8 Å), and describe the bonding.

Model answer: The short Mo-Mo distance indicates a bond order much higher than one. [Mo₂(CH₃COO)₄] contains a Mo-Mo quadruple bond: σ²π⁴δ². Each Mo is in the +2 oxidation state (d⁴), contributing 4 electrons; the total of 8 metal electrons fills the σ, two π, and δ bonding MOs exactly. No antibonding orbitals are occupied, giving the maximum bond order of 4. The acetate ligands bridge the two metals, holding them in proximity, and the eclipsed arrangement of the bridging carboxylates is enforced by the delta bond. The short bond distance (comparable to a Mo≡Mo triple bond in some compounds) reflects the quadruple bond's high electron density between the nuclei.

The discovery of the quadruple bond in [Re₂Cl₈]²⁻ by F.A. Cotton in 1964 opened an entirely new chapter in inorganic chemistry. It demonstrated that metals could form bonds with no organic analogue and led to the broader study of multiply bonded transition metal compounds.