Crystal Field Theory (CFT) is one of the highest-weightage topics in the CBSE Class 12 Chemistry Board Exam under Unit 9: Coordination Compounds. Examiners routinely test d-orbital splitting diagrams in octahedral versus tetrahedral complexes, the relationship between crystal field splitting energy (Δ) and pairing energy (P), and electronic configurations in terms of t2g and eg levels.
Direct Concept Answer: In an octahedral crystal field, the 5 degenerate d-orbitals split into two sets under ligand electrostatic repulsion: the lower-energy t2g triplet (d_xy, d_yz, d_xz) lowered by -0.4Δo, and the higher-energy eg doublet (d_x2-y2, d_z2) raised by +0.6Δo. When ligand field strength causes Δo > P (strong-field ligand), electrons pair up forming low-spin complexes. When Δo < P (weak-field ligand), high-spin complexes form adhering to Hund's rule.
1. Octahedral Splitting vs. Tetrahedral Splitting: Fundamental Comparison
| Property | Octahedral Complexes ([ML6]n±) | Tetrahedral Complexes ([ML4]n±) |
|---|---|---|
| Coordination Number | 6 ligands pointing along Cartesian axes | 4 ligands pointing between Cartesian axes |
| Splitting Pattern | t2g (lower, 3 orbitals) and eg (higher, 2 orbitals) | e (lower, 2 orbitals) and t2 (higher, 3 orbitals) — inverted! |
| Energy Separation Ratio | Δo | Δt = 4/9 Δo (never exceeds pairing energy P) |
| Spin Multiplicity | Can be High-Spin or Low-Spin depending on ligand | Almost exclusively High-Spin because Δt < P |
2. The Spectrochemical Series: Weak-Field vs Strong-Field Ligands
The spectrochemical series ranks ligands in increasing order of crystal field splitting energy (Δ):
I⁻ < Br⁻ < S²⁻ < SCN⁻ < Cl⁻ < N₃⁻ < F⁻ < OH⁻ < C₂O₄²⁻ < H₂O < NCS⁻ < EDTA⁴⁻ < NH₃ < en < NO₂⁻ < CN⁻ < CO- Weak-Field Ligands (Halides, H2O, Ox2-): Δo < P. Electrons enter the eg orbital before pairing occurs in t2g.
- Strong-Field Ligands (CN-, CO, NO2-, en): Δo > P. Electrons pair up completely in the t2g level before entering eg.
3. Electronic Configuration of d4 to d7 Octahedral Ions
| d-Electron Count | Weak Field (Δo < P) High Spin | Strong Field (Δo > P) Low Spin | Board Exam Tip |
|---|---|---|---|
| d4 (e.g., Cr2+, Mn3+) | t2g³ eg¹ (Unpaired: 4) | t2g⁴ eg⁰ (Unpaired: 2) | State Δo vs P condition clearly before writing orbital notation. |
| d5 (e.g., Fe3+, Mn2+) | t2g³ eg² (Unpaired: 5) | t2g⁵ eg⁰ (Unpaired: 1) | [Fe(CN)6]³⁻ is weakly paramagnetic; [Fe(H2O)6]³⁺ is strongly paramagnetic. |
| d6 (e.g., Fe2+, Co3+) | t2g⁴ eg² (Unpaired: 4) | t2g⁶ eg⁰ (Diamagnetic, 0) | [Co(NH3)6]³⁺ is low spin and diamagnetic despite NH3 being intermediate. |
| d7 (e.g., Co2+) | t2g⁵ eg² (Unpaired: 3) | t2g⁶ eg¹ (Unpaired: 1) | Spin-only magnetic formula: μ = √(n(n+2)) Bohr Magnetons (BM). |
4. Frequent Board Exam Traps & Marking Scheme Tips
- Trap 1: Forgetting the Center of Gravity (Barycentre): Always indicate the barycentre line in your splitting diagram. The energy decrease for t2g is -0.4Δo and the increase for eg is +0.6Δo.
- Trap 2: Explaining why Δt = 4/9 Δo: Two reasons are required by CBSE: (1) There are only 4 ligands instead of 6 (4/6 = 2/3), and (2) The ligands do not point directly toward any d-orbital lobes, reducing directional overlap (2/3 × 2/3 = 4/9).
- Trap 3: Subscript 'g' in Tetrahedral notation: Never write t2g or eg for tetrahedral complexes! Tetrahedral complexes lack an inversion centre (gerade symmetry), so use t2 and e only.
5. Frequently Asked Questions (FAQ)
Why are tetrahedral complexes generally high-spin?
Because the crystal field splitting energy in tetrahedral complexes (Δt) is approximately 4/9th of octahedral complexes (Δt = 4/9 Δo), which is almost always smaller than the electron pairing energy (P). As a result, electrons prefer to populate higher energy t2 orbitals rather than pairing up in e orbitals.
What is the formula for calculating CFSE in an octahedral complex?
The formula is: CFSE = [-0.4 × n(t2g) + 0.6 × n(eg)] × Δo + m × P, where n is the number of electrons in the respective subshell and m is the number of extra electron pairs formed due to ligand field splitting.
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