Quadruple Bonds in Metal–Metal Clusters

Complete Study Notes
Quadruple Bonds in Metal–Metal Bonded Compounds & Clusters

Exam Relevance: Advanced Inorganic Chemistry | JEE Advanced | NEET | IIT-JAM | CSIR-NET | GATE Chemistry

1. What is a Quadruple Bond?

A quadruple bond is a metal–metal bond with a formal bond order of 4, consisting of:

• 1 σ (sigma) bond
• 2 π (pi) bonds
• 1 δ (delta) bond

Electronic configuration: σ² π⁴ δ²

This is the highest stable bond order commonly observed between two metal atoms.

2. Orbital Contributions to Quadruple Bond

Bond Type	Orbitals Involved	Overlap Type	Strength Order
σ bond	dz² – dz²	Head-on	Strongest
π bonds (2)	dxz–dxz, dyz–dyz	Side-on	Strong
δ bond	dxy – dxy	Face-to-face (4-lobe)	Weakest (~3–5% of total bond energy)

The δ bond is possible only in eclipsed geometry. In staggered conformation, δ overlap → 0 → bond order drops to 3.

3. Classic Examples of Quadruple Bonds

Compound	Metal Pair	M–M Distance (Å)	Configuration	Remarks
[Re₂Cl₈]²⁻	Re–Re	2.24	σ²π⁴δ²	First recognized quadruple bond (Cotton, 1964)
[Mo₂Cl₈]⁴⁻	Mo–Mo	~2.10–2.15	σ²π⁴δ²	Very short bond
Mo₂(O₂CCH₃)₄	Mo–Mo	2.09	σ²π⁴δ²	Paddlewheel structure
Cr₂(O₂CCH₃)₄(H₂O)₂	Cr–Cr	2.36	σ²π⁴δ²	Longest known quadruple bond

4. Role of δ Bond

• Enforces eclipsed conformation
• Contributes very little to bond strength but dramatically shortens M–M distance
• Responsible for intense δ → δ* transition in visible region (deep colors)
• Highly sensitive to oxidation: loss of one δ electron → bond order 3.5

5. Spectroscopic and Structural Evidence

• Very short M–M distances (< 2.5 Å)
• Diamagnetic (all electrons paired)
• Raman spectroscopy: Strong M–M stretching band (~250–350 cm⁻¹)
• UV-Vis: Characteristic δ→δ* band (400–600 nm)
• X-ray crystallography: Eclipsed ligand arrangement

6. Quadruple Bonds in Metal Clusters

Though most common in dinuclear units, quadruple bonds also appear in:

• Edge-sharing bioctahedral clusters
• Some triangular or tetrahedral clusters with localized M–M quadruple bonds
• Example: Certain Re₃ and Mo₆ clusters contain localized quadruple-bonded pairs

7. Comparison with Other Bond Orders

Bond Order	Configuration	Typical Metals	Example
1	σ²	Mn, Fe carbonyls	Mn₂(CO)₁₀
2–3	σ²π⁴ or σ²π⁴δ*	Many	–
4	σ²π⁴δ²	Mo, W, Re, Tc, Cr	[Re₂Cl₈]²⁻
5 (Quintuple)	σ²π⁴δ⁴	Cr, Mo (with bulky ligands)	Cr₂(Ar')₂

8. Key Points for Exams (Must Remember)

• δ bond requires d_xy–d_xy overlap → only in eclipsed geometry
• Shortest M–M bonds are usually quadruple (except quintuple Cr–Cr ~1.80 Å)
• [Re₂Cl₈]²⁻ is the first discovered quadruple bond compound
• Oxidation of quadruple bond compound → δ electron removed → bond order becomes 3.5
• δ → δ* transition gives intense color
• Cr₂(O₂CCH₃)₄ has the longest known quadruple bond due to weak δ overlap

9. Applications & Significance

• Models for metal surfaces and catalysis
• Precursors for molecular wires and nanomaterials
• Test cases for bonding theories beyond double bonds
• Understanding electron-rich metal centers

10. Quick Revision Summary

Quadruple bond = σ + 2π + δ → σ²π⁴δ² → eclipsed geometry → very short M–M → Mo, W, Re classics → δ bond weakest but crucial for structure → δ→δ* visible absorption → oxidation weakens bond significantly.

Related Topic: Quintuple Bond

Quadruple Bonds MCQs

MCQs Asked in CSIR-NET, GATE, and IIT-JAM

CSIR NET Dec 2013

Q1: The electronic configuration of the Re-Re quadruple bond in [Re₂Cl₈]^2- is

1. σ²π⁴δ²
2. σ²π²δ⁴
3. σ⁴π⁴δ²
4. σ²π⁴δ^oδ*²

Correct Answer: A. σ²π⁴δ²

Explanation: Each Re(III) (d⁴) contributes 4 electrons to M-M bonding orbitals, filling σ (2e), two π (4e), and δ (2e) for bond order 4. The δ bond arises from d_xy-d_xy overlap.

CSIR NET Dec 2016

Q2:Quadruple bonds are stabilized by ligands that enforce

1. Staggered conformation
2. Eclipsed conformation
3. 90° rotation between metals
4. Linear M-L-M geometry

Correct Answer: B. Eclipsed conformation

Explanation: Eclipsed ligand arrangement aligns d_xy orbitals for δ overlap; rotation to staggered would break the δ bond, reducing bond order to 3.

CSIR NET June 2017

Q3: Which metal complex exhibits the first confirmed metal-metal quadruple bond?

1. [Mo₂Cl₈]^4-
2. [Cr₂O₄]
3. [Re₂Cl₈]^2-
4. [Tc₂Cl₈]^3-

Correct Answer: C. [Re₂Cl₈]^2-

Explanation: Discovered in 1964, K₂[Re₂Cl₈] was the first with confirmed quadruple bond via X-ray (short Re-Re distance, eclipsed ligands).

CSIR NET June 2018

Q4:In the MO diagram of [Re₂Cl₈]^2-, the HOMO is primarily

1. δ bonding orbital
2. δ* antibonding orbital
3. π* antibonding orbital
4. Non-bonding d orbital

Correct Answer: A. δ bonding orbital

Explanation: The 16 valence electrons fill σ²π⁴δ², making the δ (d_xy) bonding orbital the HOMO, responsible for intense δ→δ* electronic transitions observed in these complexes.

CSIR NET June 2018

Q5: The structures of [Re₂Cl₈]^2- (X) and [Os₂Cl₈]^2- (Y) are made up of two MCl₄ units. For these structures, which statement is correct?

1. (X) and (Y) both have MCl₄ units eclipsed.
2. (X) and (Y) both have MCl₄ units staggered.
3. (X) has both MCl₄ unit staggered and (Y) has both units eclipsed.
4. (X) has both MCl₄ unit eclipsed and (Y) has both units staggered.

Correct Answer: A. has both MCl₄ unit eclipsed and (B) has both units staggered.

Explanation: In [Re₂Cl₈]^2-, the Re-Re quadruple bond (σ²π⁴δ²) requires an eclipsed configuration of the Cl ligands to maximize δ-orbital overlap. In contrast, [Os₂Cl₈]^2- has a triple bond (σ²π⁴δ²δ*²) due to the population of the δ* orbital, allowing a staggered geometry to minimize steric repulsion, as the δ bond is weaker or absent.

CSIR NET June 2019

Q6:The δ bond in metal-metal quadruple bonds arises primarily from overlap of which d-orbitals?

1. d_z² - d_z²
2. d_xz - d_xz
3. d_xy - d_xy
4. d_x²-y² - d_x²-y²

Correct Answer: C. d_xy - d_xy

Explanation: In quadruple bonds like [Re₂Cl₈]^2-, the δ bond forms from direct side-on overlap of d_xy orbitals between metals in eclipsed geometry, contributing to the fourth bonding interaction beyond σ and two π bonds.

CSIR NET June 2019

Q7: The δ bond in metal-metal quadruple bonds arises primarily from overlap of which d-orbitals?

1. d_z² – d_z²
2. d_xz – d_xz
3. d_xy – d_xy
4. d_x²–y² – d_x²–y²

Correct Answer: C. d_xy – d_xy

Explanation: In eclipsed geometry, the δ bond results from side-on overlap of d_xy orbitals, forming the fourth bonding component (σ + 2π + δ).

CSIR NET Dec 2020

Q8:Which factor favors the formation of quadruple bonds in 3d metals compared to 4d/5d metals?

1. Larger radial extension of 3d orbitals
2. Poorer δ orbital overlap in 3d metals
3. Higher effective nuclear charge in 3d series
4. Smaller metal-metal distances in 3d complexes

Correct Answer: B. Poorer δ orbital overlap in 3d metals

Explanation: Quadruple bonds are rare in 3d metals (e.g., Cr₂) due to diffuse 3d orbitals leading to weak δ overlap; 4d/5d metals like Re have more contracted d-orbitals for better overlap.

CSIR NET Dec 2020

Q9: The first compound established to contain a quadruple metal–metal bond is:

1. Cr₂(O₂CCH₃)₄
2. [Re₂Cl₈]^2-
3. [Mo₂Cl₈]^4-
4. Mn₂(CO)₁₀

Correct Answer: B. [Re₂Cl₈]^2-

Explanation: F.A. Cotton in 1964 correctly interpreted the very short Re–Re distance (2.24 Å) and eclipsed geometry in [Re₂Cl₈]^2- as evidence of a quadruple bond.

CSIR NET Dec 2021

Q10:Which complex shows a metal-metal quadruple bond with carboxylate bridging ligands?

1. [Mo₂(O₂CCH₃)₄]
2. [Re₂(O₂CCH₃)₄Cl₂]
3. [Cr₂(O₂CCH₃)₄]
4. [W₂(O₂CCH₃)₄]

Correct Answer: B. [Re₂(O₂CCH₃)₄Cl₂]

Explanation: Paddlewheel complexes like Re₂(acetate)₄X₂ maintain eclipsed geometry for δ bonding, with quadruple bonds confirmed by short M-M distances and spectroscopy.

CSIR NET June 2022

Q11:The Re-Re bond order in [Re₂Cl₈]^2- decreases to 3.5 upon one-electron oxidation primarily because

1. Loss of σ bonding electron
2. Population of δ* antibonding orbital
3. Weakening of π bonds
4. Geometric distortion to staggered

Correct Answer: B. Population of δ* antibonding orbital

Explanation: Oxidation from 16e (σ²π⁴δ², order 4) to 15e (σ²π⁴δ²δ*¹, order 3.5) populates the δ* orbital, which is lowest antibonding in these systems due to similar nodal properties to δ.

GATE 2007

Q12: Considering the quadrupolar nature of M-M bond in [Re₂Cl₈]^2-, the M-M bond order in [Re₂Cl₄(PMe₂Ph)₄]⁺ and [Re₂Cl₄(PMe₂Ph)₄] respectively are

1. 3.0 and 3.5
2. 3.5 and 3.0
3. 3.5 and 4.0
4. 3.0 and 4.0

Correct Answer: B. 3.5 and 3.0

Explanation: In [Re₂Cl₈]^2-, the Re-Re bond is a quadruple bond (bond order 4) with electron configuration σ²π⁴δ². The complex [Re₂Cl₄(PMe₂Ph)₄]⁺ is a mixed-valence Re(II)-Re(III) species (d⁵-d⁴), resulting in 9 electrons in the metal-metal orbitals, giving a bond order of 3.5 (σ²π⁴δ²δ*¹). The neutral [Re₂Cl₄(PMe₂Ph)₄] is Re(II)-Re(II) (d⁵-d⁵), with 10 electrons, yielding a bond order of 3 (σ²π⁴δ²δ*²).

GATE 2008

Q13: Metal-metal quadruple bonds are well-known for the metal

1. Ni
2. Co
3. Fe
4. Re

Correct Answer: D. Re

Explanation: Quadruple bonds are characteristic of second and third row transition metals like rhenium due to better overlap of d-orbitals. [Re₂Cl₈]^2- is the classic example with Re-Re quadruple bond (σ²π⁴δ² configuration).

[1][2]

GATE 2023

Q14: In [Re₂Cl₈]²⁻, the eclipsed conformation is preferred primarily due to:

1. σ bonding
2. π bonding
3. δ bonding
4. Steric repulsion between Cl ligands

Correct Answer: C. δ bonding

Explanation: Maximum δ overlap occurs only in eclipsed geometry. Staggering eliminates δ bonding and increases bond length significantly.

IIT JAM 2015

Q15: In [Re₂Cl₈]^2-, the Re-Re bond distance is shortest due to

1. σ bond only
2. σ and π bonds
3. σ, π and δ bonds
4. backbonding from Cl

Correct Answer: C. σ, π and δ bonds

Explanation: Quadruple bond (one σ, two π, one δ) results in very short Re-Re distance (~2.24 Å). Eclipsed geometry maximizes δ-overlap despite Cl repulsion.

IIT-JAM 2020

Q16: The intense absorption in the visible region of [Re₂Cl₈]²⁻ is due to:

1. LMCT transition
2. δ → δ* transition
3. d–d transition
4. π → π* transition

Correct Answer: B. δ → δ* transition

Explanation: The characteristic low-energy, intense band (around 600–700 nm) arises from the allowed δ → δ* electronic transition.

XYZ

Q17: Which of the following metals most commonly forms stable quadruple bonds?

1. Cr, Mo, W (Group 6)
3. Mn, Tc, Re (Group 7)
4. Fe, Ru, Os (Group 8)
5. Co, Rh, Ir (Group 9)

Correct Answer: A. Cr, Mo, W

Explanation: Especially Mo and W form hundreds of stable quadruply bonded complexes).

XYZ

Q18: In quadruply bonded Mo₂⁴⁺ dimers, the eclipsed conformation is preferred due to:

1. Steric repulsion
2. Maximization of δ-bonding
3. π-bonding only
4. Electronic repulsion

Correct Answer: B. Maximization of δ-bonding

Explanation: The δ bond requires good sideways overlap of d_xy orbitals, which is maximized in eclipsed geometry.

XYZ

Q19: Which of the following orbitals cannot form δ -bond:

1. d_xy
2. d_xz
3. d_x²–y²
4. d_z²

Correct Answer: D. d_z²

Explanation: d_xy, d_xz, d_yz, and d_x²–y² orbitals can form δ-bond because each has four lobes that can overlap.
d_z² orbital has two lobes and a donut-shaped ring, cannot form a delta bond.

Comprehensive Notes on Quadruple Bonds in Metal–Metal Bonded Compounds | Prepared for Competitive Exams (JEE/NEET/CSIR-NET)