Ligand field spectra explain why many transition metal complexes are brightly colored. This cheat sheet covers how ligands split metal orbitals, how electrons absorb light during 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 between lower orbitals and higher orbitals. Light is absorbed when photon energy matches the gap, so . 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 orbitals split into lower-energy orbitals and higher-energy orbitals separated by .
- In a tetrahedral field, the orbitals split into lower-energy orbitals and higher-energy orbitals, with .
- A transition occurs when an electron absorbs a photon and moves between split orbital energy levels.
- Photon energy and wavelength are related by , so shorter wavelength light has greater energy.
- For one mole of photons, the absorbed energy is , often reported in .
- The observed color of a complex is usually the complementary color of the wavelength region it absorbs most strongly.
- A larger causes absorption at shorter wavelength because .
- Strong-field ligands such as and usually produce larger splitting than weak-field ligands such as and .
Vocabulary
- Ligand field splitting
- The separation of metal orbital energies caused by electrostatic and bonding interactions with surrounding ligands.
- The energy gap between and orbitals in an octahedral complex.
- transition
- An electronic transition in which an electron moves from one split 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 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 is wrong because a larger splitting energy means a shorter absorbed wavelength, not a longer one.
- Using for tetrahedral complexes is wrong because tetrahedral splitting is smaller, with .
- Assuming every 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 , the absorbed wavelength, and therefore the observed color.
Practice Questions
- 1 A complex absorbs light at . Using , , and , calculate the photon energy in joules.
- 2 A complex absorbs at . Calculate in using and .
- 3 If an octahedral complex has , estimate the absorbed wavelength using .
- 4 A cobalt complex changes from pale pink to deep blue after ligand substitution. Explain conceptually how the new ligand field could change , the absorbed wavelength, and the observed color.
Understanding Ligand Field Spectra & Color Reference
Ligands do more than sit around a metal ion. Their negative charge or electron pairs point toward particular parts of space, so they repel electrons in some metal orbitals more strongly than in others. The exact arrangement matters.
In an octahedral complex, ligands approach along the x, y, and z directions. Orbitals aimed along those directions feel the greatest repulsion. Changing the ligand changes this repulsion because different ligands interact with the metal in different ways.
Some donate electron density strongly. Others can accept electron density from the metal.
This is why the spectrochemical series is useful. It is an experimental ranking of ligands by the size of splitting they tend to produce, not a simple ranking by charge alone.
Electron configuration determines which transitions are possible. First find the metal oxidation state, then count its d electrons. Next fill the split orbitals using the usual rules about energy and electron pairing.
For some electron counts, there is a choice between placing electrons in higher orbitals or pairing them in lower orbitals. This depends on whether the splitting energy is larger or smaller than the pairing energy. Weak field ligands often give high spin complexes with more unpaired electrons.
Strong field ligands can give low spin complexes with fewer unpaired electrons. This affects magnetic behavior as well as the spectrum.
A complex with unpaired electrons is paramagnetic. A complex with all electrons paired is diamagnetic.
Not every absorbed transition gives an equally dark band. The spin rule means an electron normally keeps the same spin during a transition. Transitions that would change the total spin are weak.
The Laporte rule makes many d to d transitions weak in centrosymmetric octahedral complexes. This is because both starting and ending d orbitals have the same symmetry type. Real complexes are not perfectly still, however.
Molecular vibrations can briefly distort the structure and relax this restriction. Tetrahedral complexes lack a center of symmetry, so their d to d bands are often stronger. Charge transfer transitions can be much stronger than d to d transitions.
In these, electron density moves between ligand and metal. They often dominate the color of ions such as permanganate or chromate.
When reading a spectrum, focus on the absorption maximum, usually reported as a wavelength. Use the color wheel carefully. The color listed is the light removed from white light, while the sample appears in the opposite region.
A broad absorption band can remove several nearby colors, producing shades such as greenish blue or yellow brown rather than a pure color. Concentration and path length change how intense a solution looks, but they do not usually change the transition energy itself. Solvent, temperature, geometry, and oxidation state can shift band positions.
In exam problems, make a table with ligand strength, metal oxidation state, d electron count, geometry, spin state, expected splitting size, absorbed region, and observed color. This prevents a color answer from becoming a guess.