Crystal Field Splitting Calculator
High spin or low spin, and the colour that follows.
Work out Crystal Field Splitting. High spin or low spin, and the colour that follows. Shows the working, not just the answer.
Fe²⁺ is d⁶, Fe³⁺ d⁵, Co³⁺ d⁶, Ni²⁺ d⁸.
Strong-field ligands like CN⁻ and CO give large Δo; I⁻ and Br⁻ give small.
The cost of putting two electrons in the same orbital.
d-orbital occupancy
t2g6 eg0
0 unpaired · Low spin — strong field, Δo beats pairing energy
Whether electrons pair up in the lower t2g set or spread into the higher eg set is a straight competition between the splitting energy Δo and the pairing energy. Strong-field ligands push Δo above the pairing cost and force low spin; weak-field ligands leave it high spin. Only d⁴ through d⁷ have a choice at all. Every other count fills the same way regardless of the ligand, which is why complexes outside that range never change magnetic behaviour when the ligand is swapped. The splitting energy corresponds to a photon in the visible range, which is why transition metal complexes are coloured — and why the colour changes with the ligand. The complex absorbs at the wavelength shown and appears as the complementary colour. The spin-only moment ignores orbital contribution, which is a good approximation for first-row transition metals and a poor one further down.
How the Crystal Field Splitting Calculator works
Enter the d-electron count, the splitting energy and the pairing energy to get the orbital occupancy, the number of unpaired electrons, the spin-only magnetic moment and the wavelength absorbed. Only d⁴ through d⁷ have a high-spin/low-spin choice at all.
Also known as: high spin low spin calculator · crystal field theory calculator · unpaired electrons in a complex · spin only magnetic moment calculator
Frequently asked questions
What decides high spin or low spin?
A direct competition. If the splitting energy Δo exceeds the cost of pairing two electrons in one orbital, electrons pair up in the lower t2g set and the complex is low spin. If pairing costs more, they spread into eg and it is high spin.
Which d counts can be either?
Only d⁴ through d⁷. Below d⁴ there is no pairing decision because the three t2g orbitals are not yet full; above d⁷ every arrangement is forced. That is why only those complexes change magnetism with the ligand.
Why are transition metal complexes coloured?
Because Δo happens to correspond to a photon in the visible range. The complex absorbs at that wavelength and appears as the complementary colour — which is why changing the ligand changes the colour.
What is the spin-only magnetic moment?
√(n(n+2)) Bohr magnetons, where n is the number of unpaired electrons. It ignores orbital contribution, which is a good approximation for first-row transition metals and a poor one further down the table.
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