Orgel Diagrams for Transition Metal Complexes
Orgel diagrams are qualitative correlation diagrams that simplify the interpretation of electronic absorption spectra for high-spin transition metal complexes. In examinations like CSIR-NET, GATE, IIT-JAM, and CUET-PG, questions test your ability to predict spin-allowed absorption bands, assign transitions to Mulliken terms, and extract crystal field splitting parameters like 10 Dq. Orgel diagrams offer a direct, reliable approach without requiring complete Tanabe-Sugano matrices.
Fundamental Principles of Orgel Diagrams
Devised by Leslie Orgel, these diagrams show how free-ion Russell-Saunders terms split in octahedral or tetrahedral ligand fields. Because they display only states with the same spin multiplicity as the ground state, Orgel diagrams apply strictly to high-spin complexes. Low-spin complexes require Tanabe-Sugano diagrams.
Every Orgel diagram places the unsplit free-ion term at the centre (zero field: Δ = 0 or 10 Dq = 0). States diverge as field strength increases. Two symmetry rules allow eight d-electron configurations to share two diagrams: Bethe hole formalism and the octahedral-tetrahedral inversion rule.
The D-Term Orgel Diagram (d1, d4, d6, d9)
Configurations d1, d4, d6, and d9 produce D ground terms (2D for d1, d9; 5D for d4, d6). In an octahedral field, d orbitals split into a lower t2g set and an upper eg set. For a d1 ion, the 2D term splits into a lower 2T2g ground state and an upper 2Eg excited state separated by Δo (10 Dq), giving one spin-allowed transition: 2T2g → 2Eg.
Under hole formalism, a subshell lacking n electrons from a half-filled or filled shell behaves like n positive holes with inverted energy levels. An octahedral d9 complex thus has an inverted 2Eg ground state and a 2T2g excited state.
Tetrahedral geometry also inverts splitting (Δt = 4/9 Δo). Combining hole formalism with geometric inversion yields two groups:
- Left side: d1 (tetrahedral), d4 (octahedral), d6 (tetrahedral), and d9 (octahedral). Ground state is E (or Eg); excited state is T2 (or T2g).
- Right side: d1 (octahedral), d4 (tetrahedral), d6 (octahedral), and d9 (tetrahedral). Ground state is T2 (or T2g); excited state is E (or Eg).
Because tetrahedral complexes lack an inversion centre, the 'g' (gerade) subscript is omitted for all tetrahedral terms.
The F-Term Orgel Diagram (d2, d3, d7, d8)
Configurations d2, d3, d7, and d8 give an F ground term (3F for d2, d8; 4F for d3, d7) and an excited P term of identical spin multiplicity (3P for d2, d8; 4P for d3, d7). In cubic symmetry, an F term splits into T1(F), T2(F), and A2(F). The atomic P term does not split; it transforms as T1(P).
Under the non-crossing rule, identical symmetry states repel each other: T1(F) curves downward and T1(P) curves upward.
- T1 ground state: d2 (octahedral), d7 (octahedral), d3 (tetrahedral), and d8 (tetrahedral). Ground state is T1 (or T1g). Transitions: ν1 = T1 → T2, ν2 = T1 → A2, ν3 = T1 → T1(P).
- A2 ground state: d3 (octahedral), d8 (octahedral), d2 (tetrahedral), and d7 (tetrahedral). Ground state is A2 (or A2g). Transitions: ν1 = A2 → T2, ν2 = A2 → T1(F), ν3 = A2 → T1(P).
D-term: ΔE = 10 Dq = Δ (Single absorption band)
A2g ground state (d3, d8 octahedral):
Band 1: ν1 = 10 Dq = Δo
Sum rule: ν2 + ν3 = 15 B + 3 ν1
Racah parameter: B = (ν2 + ν3 − 3 ν1) / 15
Variables: ν1, ν2, ν3, 10 Dq, and B are in cm−1.
Worked Examples of Spectral Analysis
Example 1: Hexaaquatitanium(III) Band Assignment
An aqueous solution of [Ti(H2O)6]3+ shows a single absorption band at 20,300 cm−1. Assign this transition, find 10 Dq, and calculate crystal field stabilisation energy (CFSE).
Step 1: Ti(III) is 3d1 with ground term 2D. In an octahedral field, 2D splits into 2T2g and 2Eg. The single transition is 2T2g → 2Eg.
Step 2: Transition energy gives Δo = 10 Dq = 20,300 cm−1.
Step 3: For t2g1 eg0, CFSE = −0.4 × Δo = −0.4 × 20,300 cm−1 = −8,120 cm−1.
Second-route check: CFSE = 1 × (−4 Dq) = −4 × 2,030 cm−1 = −8,120 cm−1.
Example 2: Determining 10 Dq and Racah Parameter B for Nickel(II)
An octahedral [Ni(H2O)6]2+ complex displays three spin-allowed bands at ν1 = 8,500 cm−1, ν2 = 13,800 cm−1, and ν3 = 25,300 cm−1. Determine 10 Dq and Racah parameter B.
Step 1: Ni(II) is 3d8 with a 3A2g ground state. Transitions are ν1 (3A2g → 3T2g), ν2 (3A2g → 3T1g(F)), and ν3 (3A2g → 3T1g(P)).
Step 2: For an A2g ground state, ν1 = 10 Dq directly. Thus, 10 Dq = 8,500 cm−1.
Step 3: Using ν2 + ν3 = 15 B + 3 ν1:
13,800 + 25,300 = 15 B + 3(8,500)
39,100 = 15 B + 25,500
15 B = 39,100 − 25,500 = 13,600 cm−1
B = 13,600 / 15 = 906.67 cm−1.
Second-route check: 15(906.67) + 3(8,500) = 13,600 + 25,500 = 39,100 cm−1.
Example 3: Octahedral vs Tetrahedral Cobalt(II)
Cobalt(II) is a 3d7 ion. Compare the ground states and transitions for octahedral [Co(H2O)6]2+ and tetrahedral [CoCl4]2−.
Step 1: For octahedral Co(II), the ground state is 4T1g(F). Three spin-allowed transitions occur: 4T1g → 4T2g (ν1), 4T1g → 4A2g (ν2), and 4T1g → 4T1g(P) (ν3).
Step 2: For tetrahedral Co(II), geometric inversion gives a 4A2 ground state. The transitions are 4A2 → 4T2 (ν1), 4A2 → 4T1(F) (ν2), and 4A2 → 4T1(P) (ν3).
Step 3: Tetrahedral complexes lack an inversion centre, allowing d-p mixing and relaxing Laporte rules. Thus, [CoCl4]2− has extinction coefficients roughly 100 times larger than octahedral [Co(H2O)6]2+.
Common Mistakes Students Make
- Using Orgel diagrams for low-spin complexes: Orgel diagrams only apply to high-spin complexes. Low-spin complexes require Tanabe-Sugano diagrams.
- Adding 'g' subscripts to tetrahedral states: Tetrahedral complexes lack an inversion centre. Use 4A2 and 4T1, never 4A2g or 4T1g.
- Assuming the P term splits: The atomic P term transforms as a single T1 state in cubic fields and does not split.
- Confusing transition orders in d2 versus d8: In d8 octahedral complexes, ν1 equals 10 Dq directly. In d2 octahedral complexes, ν1 deviates from 10 Dq due to configuration interaction.
Exam Relevance and Topic Overview
| Examination | Question Focus | Recommended Strategy |
|---|---|---|
| CSIR-NET Chemical Sciences | Assigning ν1, ν2, ν3 transitions and calculating Racah parameter B. | Use the sum rule ν2 + ν3 = 15 B + 3 ν1 for A2g ground terms. |
| GATE Chemistry | Calculating 10 Dq from absorption bands and CFSE calculations. | Practice direct extraction of Δo for d1, d9, d3, and d8 complexes in cm−1 units. |
| IIT-JAM Chemistry | Identifying ground terms and predicting spin-allowed absorption peaks. | Use D and F diagram pairing rules to quickly classify complexes. |
| CUET-PG Chemistry | Hole formalism applications and comparing spectral intensities. | Remember that tetrahedral complexes produce higher absorption intensity than octahedral complexes. |
Trends and exceptions are asked every year: practise previous-year CSIR-NET questions and quizzes.
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