Enter Complex Details
Example Data Table
| Complex | Metal | Oxidation | d-count | Geometry | Ligand field | Expected spin | Unpaired electrons | Magnetic moment |
|---|---|---|---|---|---|---|---|---|
| [Fe(H2O)6]2+ | Fe | +2 | d6 | Octahedral | Weak | High-spin | 4 | 4.90 BM |
| [Fe(CN)6]4− | Fe | +2 | d6 | Octahedral | Strong | Low-spin | 0 | 0.00 BM |
| [Mn(H2O)6]2+ | Mn | +2 | d5 | Octahedral | Weak | High-spin | 5 | 5.92 BM |
| [Co(NH3)6]3+ | Co | +3 | d6 | Octahedral | Strong | Low-spin | 0 | 0.00 BM |
| [NiCl4]2− | Ni | +2 | d8 | Tetrahedral | Weak | High-spin | 2 | 2.83 BM |
| [CoCl4]2− | Co | +2 | d7 | Tetrahedral | Weak | High-spin | 3 | 3.87 BM |
Formula Used
d-electron count ≈ group number − oxidation state
This automatic rule works well for many coordination chemistry teaching problems. Manual mode is included when you already know the correct d-count.
S = n / 2
Here, n is the number of unpaired electrons and S is the total spin quantum number.
Multiplicity = 2S + 1
This gives the spin multiplicity, such as singlet, doublet, triplet, quartet, quintet, and higher values.
μ = √[n(n + 2)] BM
This is the spin-only magnetic moment formula, reported in Bohr magnetons.
CFSE(octahedral) = [(-0.4 × t2g) + (0.6 × eg)]Δo
For octahedral complexes, lower t2g occupancy stabilizes the system while eg occupancy increases energy.
CFSE(tetrahedral) = [(-0.6 × e) + (0.4 × t2)]Δt
For tetrahedral complexes, the lower e set stabilizes the complex and the upper t2 set raises energy.
If both Δ and P are entered, the calculator also compares Δ/P. Larger splitting relative to pairing favors electron pairing and low-spin behavior in relevant cases.
How to Use This Calculator
- Enter the complex name if you want a labeled report.
- Choose the metal and oxidation state for automatic d-electron counting, or switch to manual mode.
- Select the coordination geometry. This version supports octahedral and tetrahedral fields.
- Choose weak, intermediate, or strong ligand field behavior.
- Optionally enter Δ and P using the same units to compare splitting and pairing directly.
- Leave spin preference on automatic, or force high spin or low spin for teaching and comparison.
- Press Calculate Spin State to see the result above the form.
- Use the CSV and PDF buttons to export the summary for revision, lab notes, or class handouts.
FAQs
1. What does high spin mean?
High spin means electrons occupy higher-energy orbitals before pairing when the crystal field splitting is small. This usually creates more unpaired electrons and stronger paramagnetism.
2. When does low spin occur?
Low spin occurs when crystal field splitting is large enough that pairing in lower orbitals is energetically preferred. Strong-field ligands often produce this outcome in octahedral d4 to d7 complexes.
3. Why are tetrahedral complexes usually high spin?
Tetrahedral splitting is typically smaller than octahedral splitting. Because the energy gap is modest, electrons usually avoid pairing and remain unpaired in higher orbitals.
4. Why is the d-electron count important?
The d-electron count determines how electrons fill split d orbitals. That filling pattern controls the number of unpaired electrons, spin state, magnetic behavior, and crystal field stabilization.
5. Is the magnetic moment exact?
No. This calculator reports the spin-only magnetic moment. Real measurements may differ because of orbital contributions, spin-orbit coupling, temperature effects, and experimental conditions.
6. Can this calculator replace spectroscopy?
No. It is a fast educational and screening tool. Experimental methods such as UV-Vis, magnetic susceptibility, EPR, or Mössbauer spectroscopy are still needed for confirmation.
7. Why is there no high or low spin distinction sometimes?
For some octahedral d-counts, especially d0 to d3 and d8 to d10, the practical occupancy pattern does not change in a way that needs separate high-spin and low-spin labels.
8. Can I use manual d-electron mode?
Yes. Manual mode is useful when you already know the d-count, want to test textbook problems, or need to override the automatic approximation for special cases.