Watch the electrons pick high spin or low spin for themselves.
Crystal Field Splitting simulator
Tap the complex to switch between octahedral and tetrahedral
This simulation needs a modern browser with canvas support. The measurements and formula below still describe the physics.
Live measurements
Controls
Graph
Formula
μ = √(n × (n + 2))
- μ Spin-only magnetic moment
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- n Unpaired electrons
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Observations
What's happening
Real-world examples
Hexaaquairon(II)
Water is a weak field ligand, so the 10400 cm⁻¹ splitting loses to the pairing energy. The d6 ion stays high spin with four unpaired electrons and a moment near 4.9 BM.
Hexacyanoferrate(II)
Cyanide is a strong field ligand. The same d6 ion now splits by 33000 cm⁻¹, the electrons pair into t2g, and the complex is diamagnetic.
Tetrachlorocobaltate
A tetrahedral d7 complex splits by four ninths of the octahedral value, which no ordinary ligand pushes past the pairing energy. Three unpaired electrons, and the deep blue that chloride cobalt salts are known for.
Hexaamminenickel(II)
A d8 ion has one arrangement only, so high spin and low spin describe the same picture. Two unpaired electrons whatever the ligand does.
Uses of crystal field splitting
- Predicting the magnetic moment a susceptibility measurement should return
- Explaining why haemoglobin changes colour when it binds oxygen
- Ranking ligands in the spectrochemical series from complex colours
crystal field splitting pitfalls
- Assuming every d count can be high spin or low spin
- Reporting the absorbed colour as the colour of the complex
- Using the octahedral splitting for a tetrahedral complex
crystal field splitting questions (8)
What is crystal field splitting?
Crystal field splitting is the energy gap that opens between the d orbitals when ligands approach a metal ion. In the free ion all five d orbitals have the same energy. Ligands sit closer to some of them than others, so the ones pointing at ligands rise and the rest fall. The gap between those two sets is the splitting, written delta.
What is the difference between high spin and low spin?
High spin spreads electrons across all five orbitals before any of them pair. Low spin fills the lower set completely first, pairing electrons to do it. The complex takes whichever is cheaper. Pairing costs the pairing energy P, and climbing to the upper set costs delta, so high spin wins when delta is smaller than P and low spin wins when delta is larger.
Which d counts can be high spin or low spin?
Only d4, d5, d6 and d7 in an octahedral field. Below d4 there is room for every electron in the lower set without pairing, so both schemes give the same answer. From d8 up the lower set is already full, so again there is no choice. Move the d electron slider across its range and watch the spin state readout stop responding outside that window.
How do you calculate CFSE?
Count the electrons in each set and weight them. In an octahedral field each t2g electron is worth -0.4 delta and each eg electron is worth +0.6 delta, so CFSE = (-0.4 x n(t2g) + 0.6 x n(eg)) x delta. A d3 complex gives -1.2 delta, and a low-spin d6 gives -2.4 delta, the largest CFSE any octahedral complex reaches.
Why is tetrahedral splitting smaller than octahedral splitting?
A tetrahedral complex has four ligands instead of six, and none of them point straight at a d orbital. Both effects shrink the gap, and the standard result is delta tetrahedral = 4/9 x delta octahedral for the same metal and ligands. That gap rarely beats a pairing energy, which is why low-spin tetrahedral complexes are so rare.
How do you find the spin-only magnetic moment?
Use mu = sqrt(n x (n + 2)) in Bohr magnetons, where n is the number of unpaired electrons. Four unpaired electrons give 4.90 BM and one gives 1.73 BM. Measured moments sit close to these for first-row transition metals, so comparing a measurement against both spin states is how a spin state gets assigned in practice.
Why is the colour of a complex not the colour it absorbs?
You see what is left after absorption, so the colour is the complement of the absorbed band. A complex absorbing green light near 520 nm looks purple. This trips people up because the splitting sets the absorbed wavelength through lambda = 10^7 / delta, and that number is the one on the far side of the colour wheel from what your eye reports.
What makes a ligand strong field or weak field?
Its position in the spectrochemical series, which ranks ligands by the splitting they produce. Iodide and bromide sit at the weak end, water and ammonia in the middle, and cyanide and carbon monoxide at the strong end. The series is empirical, so treat the field strength slider as the number you look up rather than one you derive.