Ligand Field Spectra & Color Reference Cheat Sheet

A printable reference covering ligand field splitting, $d\text{-}d$ transitions, wavelength energy, complementary colors, and selection rules for grades 11-12.

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Ligand field spectra explain why many transition metal complexes are brightly colored. This cheat sheet covers how ligands split metal $d$ orbitals, how electrons absorb light during $d\text{-}d$ transitions, and how absorbed wavelength relates to observed color. Students need these ideas to connect electron structure, energy, and visible spectra in coordination chemistry. The core idea is that an octahedral complex has a splitting energy $\Delta_o$ between lower $t_{2g}$ orbitals and higher $e_g$ orbitals. Light is absorbed when photon energy matches the gap, so $\Delta = E = \frac{hc}{\lambda}$ . The color seen is usually the complementary color of the light absorbed, and transition strength depends on selection rules such as the spin selection rule and the Laporte rule.

Key Facts

In an octahedral field, the $d$ orbitals split into lower-energy $t_{2g}$ orbitals and higher-energy $e_g$ orbitals separated by $\Delta_o$ .
In a tetrahedral field, the $d$ orbitals split into lower-energy $e$ orbitals and higher-energy $t_2$ orbitals, with $\Delta_t \approx \frac{4}{9}\Delta_o$ .
A $d\text{-}d$ transition occurs when an electron absorbs a photon and moves between split $d$ orbital energy levels.
Photon energy and wavelength are related by $E = \frac{hc}{\lambda}$ , so shorter wavelength light has greater energy.
For one mole of photons, the absorbed energy is $\Delta = \frac{N_Ahc}{\lambda}$ , often reported in $\text{kJ mol}^{-1}$ .
The observed color of a complex is usually the complementary color of the wavelength region it absorbs most strongly.
A larger $\Delta_o$ causes absorption at shorter wavelength because $\lambda = \frac{hc}{\Delta}$ .
Strong-field ligands such as $\text{CN}^-$ and $\text{CO}$ usually produce larger splitting than weak-field ligands such as $\text{I}^-$ and $\text{Br}^-$ .

Vocabulary

Ligand field splitting: The separation of metal $d$ orbital energies caused by electrostatic and bonding interactions with surrounding ligands.
$\Delta_o$: The energy gap between $t_{2g}$ and $e_g$ orbitals in an octahedral complex.
$d\text{-}d$ transition: An electronic transition in which an electron moves from one split $d$ orbital level to another after absorbing light.
Complementary color: The color observed when a substance absorbs a different color from white light, often the color opposite the absorbed light on a color wheel.
Spectrochemical series: An ordering of ligands from weak-field to strong-field based on how large a $d$ orbital splitting they produce.
Selection rule: A rule that predicts whether an electronic transition is allowed, weakly allowed, or forbidden in a spectrum.

Common Mistakes to Avoid

Confusing absorbed color with observed color is wrong because the complex usually appears as the complementary color of the light it absorbs.
Forgetting the inverse relationship in $E = \frac{hc}{\lambda}$ is wrong because a larger splitting energy means a shorter absorbed wavelength, not a longer one.
Using $\Delta_t = \Delta_o$ for tetrahedral complexes is wrong because tetrahedral splitting is smaller, with $\Delta_t \approx \frac{4}{9}\Delta_o$ .
Assuming every $d\text{-}d$ transition is intense is wrong because many are weak due to the Laporte rule or the spin selection rule.
Ignoring ligand strength is wrong because changing ligands can change $\Delta_o$ , the absorbed wavelength, and therefore the observed color.

Practice Questions

1 A complex absorbs light at $500\,\text{nm}$ . Using $E = \frac{hc}{\lambda}$ , $h = 6.626 \times 10^{-34}\,\text{J s}$ , and $c = 3.00 \times 10^8\,\text{m s}^{-1}$ , calculate the photon energy in joules.
2 A complex absorbs at $620\,\text{nm}$ . Calculate $\Delta$ in $\text{kJ mol}^{-1}$ using $\Delta = \frac{N_Ahc}{\lambda}$ and $N_A = 6.022 \times 10^{23}\,\text{mol}^{-1}$ .
3 If an octahedral complex has $\Delta_o = 240\,\text{kJ mol}^{-1}$ , estimate the absorbed wavelength using $\lambda = \frac{N_Ahc}{\Delta}$ .
4 A cobalt complex changes from pale pink to deep blue after ligand substitution. Explain conceptually how the new ligand field could change $\Delta_o$ , the absorbed wavelength, and the observed color.

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