Calculate Δ from wavelength, predict spin states, and explore the color and magnetism of transition metal complexes
Visible range: 400-700 nm
Crystal Field Theory: Explains the color and magnetic properties of transition metal complexes by considering ligand-metal interactions as purely electrostatic.
d-Orbital Splitting: Ligands approach along axes, raising energy of orbitals pointing toward ligands (eg in octahedral) and lowering others (t2g).
Color Origin: d-d transitions absorb specific wavelengths. The complementary color is observed. Larger Δ → shorter λ absorbed → blue-shifted color.
Spin States: Strong field ligands (CN⁻, CO) cause large Δ → low spin. Weak field ligands (H₂O, F⁻) cause small Δ → high spin.
Crystal Field Splitting Energy (Δ) is the energy difference between sets of d-orbitals in transition metal complexes that results from the electrostatic interaction between the metal ion and surrounding ligands. This phenomenon is fundamental to understanding the color, magnetism, and reactivity of coordination compounds.
In an isolated transition metal ion, all five d-orbitals (dxy, dxz, dyz, dx²-y², dz²) have the same energy (they are degenerate). When ligands approach the metal ion to form a complex, this degeneracy is "lifted" — the orbitals split into different energy levels depending on their spatial orientation relative to the ligands.
The energy gap between these split d-orbitals is the crystal field splitting energy, denoted as Δo (octahedral), Δt (tetrahedral), or Δsp (square planar).
In octahedral geometry (six ligands along ±x, ±y, ±z axes), the five d-orbitals split into two groups:
In tetrahedral geometry (four ligands at alternating corners of a cube), the splitting is inverted and smaller:
In square planar geometry (common for d8 ions like Pt²⁺, Pd²⁺, Ni²⁺):
Problem:
The hexaaquatitanium(III) ion, [Ti(H₂O)₆]³⁺, appears purple in solution and absorbs green light at approximately 510 nm. Calculate the crystal field splitting energy Δo.
Solution:
Step 1: Identify the given information
Step 2: Use the relationship between energy and wavelength
E = hc/λ
where h = 6.626 × 10⁻³⁴ J·s, c = 2.998 × 10⁸ m/s
Step 3: Calculate energy per photon
E = (6.626 × 10⁻³⁴ J·s)(2.998 × 10⁸ m/s) / (510 × 10⁻⁹ m)
E = 3.894 × 10⁻¹⁹ J per photon
Step 4: Convert to kJ/mol (multiply by Avogadro's number)
Δo = (3.894 × 10⁻¹⁹ J)(6.022 × 10²³ mol⁻¹) / 1000
Δo = 234.4 kJ/mol
Step 5: Interpret the result
Answer: Δo = 234 kJ/mol
This corresponds to the d-d transition: t2g¹ → eg¹
The magnitude of Δ determines how electrons are distributed among the d-orbitals, particularly for d⁴-d⁷ configurations where a choice exists:
| Configuration | Weak Field (Δ < P) | Strong Field (Δ > P) | Example Ions |
|---|---|---|---|
| d⁴ (Oct) | High Spin (t2g³eg¹) | Low Spin (t2g⁴) | Cr²⁺, Mn³⁺ |
| d⁵ (Oct) | High Spin (t2g³eg²) | Low Spin (t2g⁵) | Fe³⁺, Mn²⁺ |
| d⁶ (Oct) | High Spin (t2g⁴eg²) | Low Spin (t2g⁶) | Fe²⁺, Co³⁺ |
| d⁷ (Oct) | High Spin (t2g⁵eg²) | Low Spin (t2g⁶eg¹) | Co²⁺, Ni³⁺ |
Where P is the pairing energy — the energy cost of placing two electrons in the same orbital:
Ligands can be arranged in order of increasing crystal field splitting strength:
I⁻ < Br⁻ < S²⁻ < SCN⁻ < Cl⁻ < NO₃⁻ < F⁻ < OH⁻ < H₂O < NCS⁻ < CH₃CN < py < NH₃ < en < bipy < phen < NO₂⁻ < CN⁻ < CO
Weak field ← increasing Δ → Strong field
Weak Field Ligands:
Strong Field Ligands:
The color of transition metal complexes arises from d-d transitions — electrons absorbing photons of specific wavelengths to jump from lower to higher d-orbitals:
| Complex | λ absorbed (nm) | Color Absorbed | Color Observed | Δ (kJ/mol) |
|---|---|---|---|---|
| [Ti(H₂O)₆]³⁺ | 510 | Green | Purple/Violet | 234 |
| [Cu(H₂O)₆]²⁺ | 800 | Red | Blue | 150 |
| [Ni(H₂O)₆]²⁺ | 720 | Red | Green | 166 |
| [Co(NH₃)₆]³⁺ | 475 | Blue | Yellow/Orange | 252 |
| [Fe(CN)₆]³⁻ | 420 | Violet | Yellow | 285 |
Important relationships:
Determining metal ion concentrations by measuring absorbance of colored complexes. Used in environmental testing (heavy metals), clinical chemistry (Fe²⁺/Fe³⁺), and quality control. Beer-Lambert law relates concentration to absorbance at λmax.
Predicting paramagnetism (unpaired electrons) vs diamagnetism (all paired). High spin complexes have more unpaired electrons → stronger magnetic moments. SQUID magnetometry measures magnetic susceptibility to determine electron configuration.
Engineering active sites in metalloenzymes and industrial catalysts. Controlling d-orbital energies affects substrate binding, electron transfer rates, and reaction pathways. Examples: cytochrome P450 (oxidation), Wilkinson's catalyst (hydrogenation).
Designing pigments, dyes, and optical materials. Prussian blue, ruby (Al₂O₃:Cr³⁺), and ceramic glazes rely on d-d transitions. Tuning λ absorbed by changing ligands or metal ions creates desired colors without organic chromophores.
Understanding hemoglobin (Fe²⁺), myoglobin, and electron transport proteins (cytochromes). Spin state changes upon O₂ binding affect function. MRI contrast agents (Gd³⁺ complexes) and anticancer drugs (cisplatin Pt²⁺) utilize coordination chemistry.
UV-Vis spectroscopy identifies metal oxidation states and coordination environments. Electronic absorption spectra reveal Δ values. Combined with IR, EPR, and XAS techniques to fully characterize complex structure and bonding.
Wrong: "[Cu(H₂O)₆]²⁺ absorbs at 800 nm (red), so it looks red."
Correct: "It absorbs red light, so we see the complementary color, which is blue."
Wrong: "Both octahedral and tetrahedral [NiCl₄]²⁻ have the same Δ."
Correct: "Tetrahedral splitting is inherently smaller. For the same ligands and metal, Δt is only 4/9 of Δo, making tetrahedral complexes almost always high spin."
Wrong: "d³ and d⁸ octahedral complexes can be either high spin or low spin."
Correct: "Only d⁴, d⁵, d⁶, and d⁷ octahedral complexes have a choice between high and low spin. d³ is always high spin (t2g³), and d⁸ has only one arrangement (t2g⁶eg²)."
Wrong: "λ = 500 nm → E = hc/λ = (6.626 × 10⁻³⁴)(3 × 10⁸)/500 = 3.975 × 10⁻²² J/mol"
Correct: "Convert nm to m first (500 nm = 5 × 10⁻⁷ m), calculate energy per photon, then multiply by Avogadro's number to get kJ/mol: 239 kJ/mol."
While CFT successfully explains colors and magnetism, it treats ligand-metal interactions as purely electrostatic. Ligand Field Theory (LFT) incorporates molecular orbital theory, recognizing that metal-ligand bonding involves orbital overlap (σ and π bonding).
LFT better explains the spectrochemical series (π-acceptor ligands like CO cause large Δ through back-bonding) and provides a more accurate picture of covalency in metal complexes. For advanced applications, consider using Angular Overlap Model (AOM) or computational methods (DFT).