Valence Bond Theory (VBT)
Valence Bond Theory (VBT) is a fundamental theory in chemistry that explains how atoms form chemical bonds through the overlap of atomic orbitals. It was introduced by Linus Pauling in the 1930s and focuses on the idea that covalent bonds form when half-filled atomic orbitals from two atoms overlap, resulting in a shared pair of electrons
Key Concepts of Valence Bond Theory:
- Atomic Orbital Overlap:
- A covalent bond is formed when two atoms approach each other, and their half-filled orbitals overlap.
- The greater the overlap, the stronger the bond.
- Types of Overlaps:
- Sigma (σ) Bond: Formed by the head-on (axial) overlap of atomic orbitals (e.g., s-s, s-p, or p-p overlap).
- Pi (π) Bond: Formed by the sidewise (lateral) overlap of p orbitals. Pi bonds are weaker than sigma bonds.
- Hybridization:
- To explain molecular geometries, VBT introduces the concept of hybridization, where atomic orbitals mix to form new, equivalent hybrid orbitals (e.g., sp³, sp², sp).
- Bond Strength and Bond Length:
- Greater the overlap, stronger the bond, and shorter the bond length.
- Directionality of Bonds:
- Covalent bonds are directional and depend on the orientation of overlapping orbitals.
Examples of Valence Bond Theory:
- Hydrogen Molecule (H₂):
- Each hydrogen atom has one 1s orbital containing one electron.
- The overlap of these 1s orbitals forms a sigma (σ) bond.
- Methane (CH₄):
- The carbon atom undergoes sp³ hybridization, forming four equivalent sp³ hybrid orbitals.
- Each orbital overlaps with the 1s orbital of hydrogen, forming four sigma bonds with tetrahedral geometry.
- Ethene (C₂H₄):
- Each carbon undergoes sp² hybridization, forming three sigma bonds (two with hydrogen, one with another carbon).
- The unhybridized p orbitals overlap sidewise to form a π bond, resulting in a double bond.
🌟 Key Concepts of VBT in Coordination Compounds:
- Central Metal Atom/Ion:
- Provides empty orbitals to accept electron pairs from ligands.
- Ligands:
- Donor species that provide lone pairs of electrons to form coordinate (dative covalent) bonds with the metal.
- Hybridization:
- The metal atom undergoes hybridization to form hybrid orbitals for bonding with ligands.
- Types of hybridization in complexes:
- sp³ → Tetrahedral geometry
- dsp² → Square planar geometry
- sp³d² → Octahedral geometry (inner orbital complex)
- d²sp³ → Octahedral geometry (outer orbital complex)
- Bond Formation:
- The empty hybrid orbitals overlap with the filled orbitals of ligands, forming coordinate bonds.
- Inner vs. Outer Orbital Complexes:
- Inner orbital complex: Uses inner (n–1)d orbitals (low spin, strong field ligands).
- Outer orbital complex: Uses outer nd orbitals (high spin, weak field ligands).
⚡ Examples of VBT in Coordination Compounds:
1. [Cr(NH₃)₆]³⁺ (Octahedral, Inner Orbital Complex)
- Electronic Configuration of Cr³⁺: 3d³
- Hybridization: d²sp³ (using inner d-orbitals).
- Geometry: Octahedral.
- Magnetism: Paramagnetic (due to three unpaired electrons).
2. [Fe(CN)₆]⁴⁻ (Octahedral, Low Spin Complex)
- Fe²⁺ Configuration: 3d⁶
- Ligand: CN⁻ (strong field ligand, causes pairing of electrons).
- Hybridization: d²sp³ (inner orbital complex).
- Geometry: Octahedral.
- Magnetism: Diamagnetic (all electrons are paired).
3. [FeF₆]³⁻ (Octahedral, High Spin Complex)
- Fe³⁺ Configuration: 3d⁵
- Ligand: F⁻ (weak field ligand, no pairing).
- Hybridization: sp³d² (outer orbital complex).
- Geometry: Octahedral.
- Magnetism: Paramagnetic (due to five unpaired electrons).
4. [Ni(CN)₄]²⁻ (Square Planar Complex)
- Ni²⁺ Configuration: 3d⁸
- Ligand: CN⁻ (strong field ligand, causes pairing).
- Hybridization: dsp².
- Geometry: Square planar.
- Magnetism: Diamagnetic (no unpaired electrons).
Let’s explain the electronic configuration and hybridization of the complex Cr(NH3)6Cr(NH₃)_6Cr(NH3)6^{3+} step by step.
Valence Bond Theory Explanation: [Cr(NH₃)₆]³⁺ Complex
Step 1: Determine the Oxidation State of Chromium (Cr)
The ammonia ligand (NH₃) is neutral.
Let the oxidation state of chromium be x:
x + 6(0) = +3 → x = +3
So, the oxidation state of chromium is +3.
Step 2: Electronic Configuration of Cr³⁺
- Atomic number of Cr = 24.
- Ground-state configuration:
[Ar] 3d⁵ 4s¹(due to half-filled stability). - Cr³⁺ loses three electrons (first from 4s, then from 3d):
[Ar] 3d³
Step 3: Determining Hybridization
- The complex is octahedral → requires six hybrid orbitals.
- Chromium uses:
- Two 3d orbitals,
- One 4s orbital, and
- Three 4p orbitals
- This forms d²sp³ hybrid orbitals.
Step 4: Orbital Diagram for Cr³⁺ Hybridization
| Subshell | Orbitals | Electron Configuration | Hybridization Role |
|---|---|---|---|
| 3d | ↑ ↑ ↑ | Three unpaired electrons | Two orbitals used in hybridization |
| 4s | — | Empty | Used in hybridization |
| 4p | — — — | Empty | Used in hybridization |
| 4d | — — — — — | Empty | Not involved |
Step 5: Final Characteristics of the Complex
- Geometry: Octahedral (due to six coordinated ligands).
- Hybridization: d²sp³ (inner orbital complex).
- Magnetism: Paramagnetic (due to three unpaired electrons).
Conclusion
The complex [Cr(NH₃)₆]³⁺ is an inner orbital octahedral complex with d²sp³ hybridization.
The presence of three unpaired electrons makes it paramagnetic.
🔍 Limitations of VBT in Coordination Compounds:
✅ These limitations are addressed by Crystal Field Theory (CFT) and Molecular Orbital Theory (MOT).
- Does not explain color in complexes.
- Fails to explain magnetic behavior in some cases.
- Does not explain the nature of bonding (like delocalization).
- Doesn’t predict the stability of complexes accurately.
Hybridization and Geometry of Coordination Complexes
| Coordination Number of Central Metal Atom/Ion | Type of Hybridization | Geometry of the Complex | Examples of Complexes |
|---|---|---|---|
| 2 | sp (4s, 4px) | Linear or Diagonal | [CuCl2]–, [Cu(NH3)2]+ |
| 3 | sp2 (4s, 4px, 4py) | Trigonal Planar or Equilateral Triangular | [Cu+ S=C(NH-CH2)2], [Cu+Cl(tu)2]0 |
| 4 | dsp2 (3dx²−y², 4s, 4px, 4py) | Square Planar | [Ni(CN)4]2−, [PdCl4]2− |
| 4 | sp3 (4s, 4px, 4py, 4pz) | Tetrahedral | [NiCl4]2−, [Cu(CN)4]3−, [Ni(CO)4] |
| 5 | dsp3 (3dz², 4s, 4px, 4py, 4pz) | Trigonal Bipyramidal | [Fe(CO)5], [CuCl5]3−, [Ni2+(triars)Br2]0 |
| 5 | sp3d (4s, 4px, 4py, 4pz, 3dz²) | Square Pyramidal | [Co2+(triars)I2]0, [Ni(CN)5]3− |
| 6 | d2sp3 (3dx²−y², 3dz², 4s, 4px, 4py, 4pz) | Inner-Orbital Octahedral | [Ti(H2O)6]3+, [Fe(CN)6]3− |
| 6 | sp3d2 (4s, 4px, 4py, 4pz, 4dx²−y², 4dz²) | Outer-Orbital Octahedral | [Fe+(NO+)(H2O)5]2+, [CoF6]3− |