Bonding Theories in Coordination Compounds

Introduction

How do ligands actually bond to metal atoms? Why do some complexes have specific geometries? Why are some magnetic while others aren’t? These questions puzzled chemists for decades after Werner proposed his theory. The answer came from Valence Bond Theory (VBT), proposed by Linus Pauling in the 1930s.

Valence Bond Theory: The Basic Idea

Core Concepts

1. Ligands donate electron pairs to empty orbitals of the metal
2. The metal-ligand bond is a coordinate covalent bond (both electrons from ligand)
3. Metal orbitals hybridize to accommodate ligand electron pairs
4. The type of hybridization determines the geometry
5. Magnetic properties depend on the number of unpaired electrons

The Process

graph LR
    A[Metal atom/ion] --> B[Hybridization of orbitals]
    B --> C[Empty hybrid orbitals]
    D[Ligands] --> E[Electron pair donation]
    C --> F[Coordinate bond formation]
    E --> F
    F --> G[Coordination complex]

    style A fill:#e74c3c
    style D fill:#2ecc71
    style G fill:#3498db

Hybridization and Geometry

Common Hybridization Schemes

Understanding Through Examples

Example 1: [Ni(CN)₄]²⁻ (Square Planar, Diamagnetic)

Step 1: Electronic Configuration

• Ni = [Ar] 3d⁸ 4s²
• Ni²⁺ = [Ar] 3d⁸

Step 2: Distribution in d orbitals

3d: ↑↓ ↑↓ ↑↓ ↑ ↑

Step 3: Effect of CN⁻ (strong field ligand) CN⁻ causes pairing of electrons:

3d: ↑↓ ↑↓ ↑↓ ↑↓ __

Step 4: Hybridization One empty 3d + one 4s + two 4p = dsp²

dsp²: [__] [__] [__] [__] ← 4 empty hybrid orbitals
      ↑↓  ↑↓  ↑↓  ↑↓  (4 CN⁻ ligands donate electron pairs)

Result:

• Geometry: Square planar
• Magnetic nature: Diamagnetic (all paired)
• Inner orbital complex

Example 2: [NiCl₄]²⁻ (Tetrahedral, Paramagnetic)

Step 1: Electronic Configuration

• Ni²⁺ = [Ar] 3d⁸

Step 2: Distribution

3d: ↑↓ ↑↓ ↑↓ ↑ ↑

Step 3: Effect of Cl⁻ (weak field ligand) Cl⁻ does NOT cause pairing - electrons remain unpaired

Step 4: Hybridization One 4s + three 4p = sp³

sp³: [__] [__] [__] [__] ← 4 empty hybrid orbitals
     ↑↓  ↑↓  ↑↓  ↑↓  (4 Cl⁻ ligands donate)

Result:

• Geometry: Tetrahedral
• Magnetic nature: Paramagnetic (2 unpaired electrons)
• Outer orbital complex

Example 3: [Co(NH₃)₆]³⁺ (Octahedral, Diamagnetic)

Step 1: Electronic Configuration

• Co = [Ar] 3d⁷ 4s²
• Co³⁺ = [Ar] 3d⁶

Step 2: Distribution

3d: ↑↓ ↑ ↑ ↑ ↑

Step 3: Effect of NH₃ (moderate field ligand) NH₃ causes pairing:

3d: ↑↓ ↑↓ ↑↓ __ __

Step 4: Hybridization Two empty 3d + one 4s + three 4p = d²sp³

d²sp³: [__] [__] [__] [__] [__] [__] ← 6 empty hybrid orbitals
       ↑↓  ↑↓  ↑↓  ↑↓  ↑↓  ↑↓  (6 NH₃ donate)

Result:

• Geometry: Octahedral
• Magnetic nature: Diamagnetic
• Inner orbital complex (uses 3d)

Example 4: [CoF₆]³⁻ (Octahedral, Paramagnetic)

Step 1: Electronic Configuration

• Co³⁺ = [Ar] 3d⁶

Step 2: Distribution

3d: ↑↓ ↑ ↑ ↑ ↑

Step 3: Effect of F⁻ (weak field ligand) F⁻ does NOT cause pairing

Step 4: Hybridization One 4s + three 4p + two 4d = sp³d²

3d: ↑↓ ↑ ↑ ↑ ↑ (remain unpaired)

sp³d²: [__] [__] [__] [__] [__] [__] ← 6 empty hybrid orbitals
       ↑↓  ↑↓  ↑↓  ↑↓  ↑↓  ↑↓  (6 F⁻ donate)

Result:

• Geometry: Octahedral
• Magnetic nature: Paramagnetic (4 unpaired)
• Outer orbital complex (uses 4d)

Interactive Demo: Visualize d Orbital Shapes

Explore the 3D shapes of d orbitals and how they orient in space during hybridization.

Inner vs Outer Orbital Complexes

Comparison Table

Why Does This Matter?

1. Magnetic properties: Inner complexes often diamagnetic, outer often paramagnetic
2. Stability: Inner orbital complexes are generally more stable
3. Color: Different electronic arrangements = different colors
4. Reactivity: Affects how the complex reacts

The Spectrochemical Series

Ligands arranged by their ability to cause electron pairing:

Weak field ligands ←→ Strong field ligands

Predictions from the Series

Magnetic Moment Calculation

Formula

where n = number of unpaired electrons, BM = Bohr Magneton

Quick Reference Table

Special Cases

1. Tetrahedral Complexes

Always sp³ hybridization (no d orbitals involved) Always high spin (weak field) Usually paramagnetic

Examples:

• [FeCl₄]⁻
• [CoCl₄]²⁻
• [NiCl₄]²⁻

2. Square Planar Complexes

Always dsp² hybridization Always low spin (strong field causes pairing) Usually diamagnetic

Common with:

• Ni²⁺ (d⁸)
• Pd²⁺ (d⁸)
• Pt²⁺ (d⁸)
• Au³⁺ (d⁸)

3. d⁸ Configuration Special Case

For d⁸ ions (Ni²⁺, Pd²⁺, Pt²⁺):

• Weak field ligand → tetrahedral (sp³), paramagnetic
• Strong field ligand → square planar (dsp²), diamagnetic

This is why the same Ni²⁺ behaves so differently!

Limitations of VBT

What VBT Explains Well:

✓ Geometry of complexes ✓ Magnetic properties ✓ Inner vs outer orbital distinction

What VBT Cannot Explain:

✗ Color of complexes (why are they colored?) ✗ Quantitative prediction of magnetic moments ✗ Spectral properties (UV-Vis absorption) ✗ Why certain ligands are strong field vs weak field ✗ Thermodynamic stability quantitatively

These limitations led to the development of Crystal Field Theory (next topic)!

Memory Tricks

Hybridization Patterns

“2 Linear SP” → CN 2 = sp = linear “4 Square Dancers Prefer Squash” → CN 4 = dsp² OR sp³ “6 Octahedrons Double-Spaced Perfectly” → CN 6 = d²sp³ OR sp³d²

Strong Field = Pairing

“Strong ligands FORCE electrons together” CN⁻, CO → Strong → Pairing → d²sp³ → Diamagnetic

“Weak ligands LET electrons spread” F⁻, Cl⁻ → Weak → No pairing → sp³d² → Paramagnetic

Common Mistakes

Practice Problems

Level 1: Basic Understanding

Q1. Draw the orbital diagram and predict the geometry and magnetic nature: a) [Fe(CN)₆]⁴⁻ (Fe²⁺: d⁶) b) [FeF₆]⁴⁻ (Fe²⁺: d⁶)

Q2. Why is [Ni(NH₃)₆]²⁺ paramagnetic while [Ni(CN)₄]²⁻ is diamagnetic?

Q3. Calculate the magnetic moment of: a) [Mn(H₂O)₆]²⁺ (high spin d⁵) b) [Co(NH₃)₆]³⁺ (low spin d⁶)

Level 2: Application

Q4. [CoF₆]³⁻ is paramagnetic with 4 unpaired electrons, while [Co(C₂O₄)₃]³⁻ is diamagnetic. a) Write electronic configurations for both b) Identify hybridization for each c) Explain the difference

Q5. Arrange the following in increasing order of unpaired electrons: [Fe(CN)₆]⁴⁻, [Fe(CN)₆]³⁻, [Fe(H₂O)₆]²⁺, [Fe(H₂O)₆]³⁺

Q6. A complex of Ni²⁺ has 2 unpaired electrons and tetrahedral geometry. Identify possible ligands.

Q7. Why do all tetrahedral complexes have sp³ hybridization and not dsp²?

Level 3: JEE Advanced

Q8. The magnetic moment of [Mn(CN)₆]³⁻ is 2.8 BM, while [MnCl₆]³⁻ is 4.9 BM. a) Calculate number of unpaired electrons in each b) Explain the difference using VBT c) Identify hybridization in each case

Q9. A complex of Co³⁺ (d⁶) with ammonia is diamagnetic and has octahedral geometry. However, when excess HCl is added, NH₃ ligands are replaced by Cl⁻ and the resulting complex is paramagnetic with 4 unpaired electrons. a) Write formulas for both complexes b) Explain the magnetic behavior change c) Identify hybridization change

Q10. [Cr(NH₃)₆]³⁺ and [Cr(H₂O)₆]³⁺ both have the same number of unpaired electrons despite different ligands. Explain.

Q11. A square planar complex of Pt²⁺ with formula [PtCl₂(NH₃)₂] exists. Predict: a) Hybridization b) Magnetic nature c) Number of geometrical isomers

Q12. Explain why: a) Low spin octahedral complexes are more common for 2nd and 3rd row transition metals b) Square planar geometry is rare for first-row transition metals (except Ni²⁺)

Solutions to Selected Problems

Q1. a) [Fe(CN)₆]⁴⁻: d²sp³, octahedral, diamagnetic (CN⁻ strong field → pairing) b) [FeF₆]⁴⁻: sp³d², octahedral, paramagnetic (4 unpaired) (F⁻ weak field)

Q2.

• [Ni(NH₃)₆]²⁺: NH₃ not strong enough to cause complete pairing in 3d⁸ → paramagnetic
• [Ni(CN)₄]²⁻: CN⁻ very strong → forces pairing → square planar, diamagnetic

Q3. a) μ = √[5(5+2)] = √35 = 5.92 BM b) μ = √[0(0+2)] = 0 BM

Q6. Weak field ligands like Cl⁻, Br⁻, I⁻ (don’t cause pairing)

Q8. a) [Mn(CN)₆]³⁻: 2 unpaired (2.8 ≈ √8) [MnCl₆]³⁻: 4 unpaired (4.9 ≈ √24) b) CN⁻ strong field → some pairing; Cl⁻ weak field → no pairing c) [Mn(CN)₆]³⁻: d²sp³ (inner); [MnCl₆]³⁻: sp³d² (outer)

Summary Table: Common Complexes

Related Topics

Within Coordination Compounds

• Werner’s Theory — Why coordination compounds form
• Isomerism — Geometry affects isomerism
• Crystal Field Theory — Better explanation of color and magnetism
• Stability Constants — Thermodynamic stability

Cross-Chapter Connections

• Chemical Bonding — Hybridization theory basics
• Atomic Structure — Electronic configurations
• d-Block Elements — Properties of transition metals
• Magnetism — Diamagnetism and paramagnetism