Inorganic chemistry
Magnetic properties and colour of complexes
Unpaired d electrons create magnetic moments, while electronic transitions absorb selected wavelengths and give complexes their characteristic colour. Both properties reveal the ligand-field electronic structure.
IntuitionIntuition: magnetism counts spins; colour records energy gaps
An unpaired electron behaves roughly like a tiny magnetic moment. A photon can promote an electron between ligand-field levels only if its energy matches an allowed transition; the wavelengths removed from white light determine the observed complementary colour.
SchoolSchool level: paramagnetic and diamagnetic ions
Definition: Paramagnetism
A species with one or more unpaired electrons is paramagnetic and is attracted into a magnetic field. A closed-shell species with all spins paired is diamagnetic and is weakly repelled.
The spin-only moment μso uses n unpaired electrons and the Bohr magneton μB. It neglects orbital contributions and spin–orbit coupling, so it is a useful first estimate for many first-row transition-metal ions, not an exact prediction for every complex.
| Unpaired n | μso / μB | Typical case |
|---|---|---|
| 0 | 0 | d⁰ or d¹⁰ |
| 1 | 1.73 | low-spin d⁵ |
| 5 | 5.92 | high-spin d⁵ |
Example: Estimate a spin-only moment
A high-spin octahedral Fe³⁺ ion is d⁵. Estimate μso.
Solution
All five d electrons are unpaired, so n = 5 and μso = √[5(5 + 2)] = √35 = 5.92 μB.
UndergraduateUndergraduate: absorption and selection rules
The energy of a d–d absorption is approximately ΔE = hc/λ. Octahedral d–d transitions are often weak because they are Laporte-forbidden in a centrosymmetric complex; vibronic coupling relaxes the rule. Tetrahedral complexes lack inversion symmetry, so their d–d bands are often more intense.
Charge-transfer bands (ligand-to-metal or metal-to-ligand) can be much more intense than d–d bands. Thus a vivid colour does not necessarily mean a large d–d transition probability, and a pale complex can still be paramagnetic.
Example: Photon energy in the visible
Estimate the energy per mole of photons absorbed at 500 nm.
Solution
Use E = hc/λ per photon, then multiply by Avogadro’s constant: NAhc/λ ≈ 239 kJ mol⁻¹. This is on the scale of many ligand-field splittings.
AdvancedFrom moments and spectra to electronic structure
Magnetic susceptibility is temperature dependent. Curie-like paramagnets approximately obey χM = C/T; deviations can reveal exchange coupling, zero-field splitting, spin crossover or orbital contributions. Diamagnetic corrections from ligands and core electrons should be subtracted when comparing measured moments.
For dⁿ ions, term symbols and Tanabe–Sugano diagrams predict multiple transitions and their changing energies with field strength. Spectral assignments should be checked against oxidation state, geometry, spin state and selection rules rather than inferred from colour alone.
ResearchResearch: spin crossover, molecular magnetism, and photophysics
References
- Ligand Field Theory and Its Applications · B. N. Figgis, M. A. Hitchman, 2000
- On the absorption spectra of complex ions · Y. Tanabe, S. Sugano, 1954