The spectrochemical series, spin state and magnetism
Whether electrons pair up or spread out depends on which costs less, the pairing energy or the jump across the split. Ligands can be ordered by how large a split they cause, and that order predicts magnetic behaviour.
What a learner can do afterwards
- Compares pairing energy with the splitting energy to assign a high or low spin configuration
- Places common ligands in order of field strength and explains why the order does not follow charge
- Predicts the number of unpaired electrons and converts it to a spin-only magnetic moment
- Explains why tetrahedral complexes are almost always high spin
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High spin or low spin is a contest of two prices. Putting an electron in the upper set costs the splitting energy, Δ. Doubling up inside a lower orbital costs the pairing energy, P. If Δ is larger than P, electrons pair in the lower set and the complex is low spin. If P is larger, electrons spread across the gap and the complex is high spin. The smaller cost wins.
The spectrochemical series ranks ligands by the split they produce: I- < Br- < Cl- < F- < H2O < NH3 < en < CN- < CO. Cyanide and carbon monoxide give large splits and often low spin. Halides and water give small splits and usually high spin. Charge does not decide the order: neutral carbon monoxide ranks far above fluoride. The order reflects how each ligand bonds, including pi bonding covered in the next topic.
Spin-only moment: mu = √(n(n+2)) Bohr magnetons, with n unpaired electrons. To count n in an octahedral complex, high spin puts one electron in each of the five orbitals before any pair, while low spin fills the three lower orbitals before any electron goes up. Iron(II) is d6: high spin gives four unpaired, so mu = √24 ≈ 4.90; low spin gives none. To work backwards, match the measured moment to n, then to the spin state.
As the crystal field topic showed, tetrahedral fields are a special case. The gap is only about four ninths of the octahedral gap for the same metal and ligands, so it is almost always smaller than the pairing energy. Tetrahedral complexes are therefore almost always high spin. Octahedral fields allow both outcomes, which is where the series matters.
Compare the gap with the pairing cost, read the ligand's rank in the series, and let the measured moment confirm the spin state.
Written for this project.
One reading newly written for this dataset; three readings written for this project. Video by Khan Academy.
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Where it sits
8 questions wait behind this lesson, each with its answer explained. Every answer feeds the sky: stars light as they are learned, and dim when it is time to come back.