Calculator Inputs
Example Data Table
| Complex Type | Geometry | Spin | d Count | Input | Δ (cm-1) | CFSE Factor | CFSE (kJ/mol) |
|---|---|---|---|---|---|---|---|
| Fe²⁺ aqua complex | Octahedral | High spin | d6 | 510 nm | 19607.84 | -0.40 Δo | -92.98 |
| Co²⁺ halide complex | Tetrahedral | High spin | d7 | 625 nm | 16000.00 | -1.20 Δt | -229.86 |
| Ni²⁺ planar complex | Square planar | Low spin | d8 | 540 nm | 18518.52 | -0.60 Δsp | -132.81 |
These values are instructional examples. Real complexes may differ because of covalency, distortion, and experimental conditions.
Formula Used
E = hc / λ
ṽ (cm-1) = 107 / λ(nm)
CFSE = Σ(ni × orbital factori) × Δ
μ = √[n(n + 2)] BM
Adjusted field estimate = CFSE + (number of pairs × pairing energy)
For octahedral fields, this calculator uses t2g = -0.4Δo and eg = +0.6Δo. For tetrahedral fields, it uses e = -0.6Δt and t2 = +0.4Δt. For square planar fields, it uses an approximate teaching sequence: dxz/dyz = -0.4Δsp, dz² = -0.1Δsp, dxy = +0.2Δsp, dx²−y² = +0.7Δsp.
The square planar model is approximate and best used for learning, comparison, and quick estimates.
How to Use This Calculator
- Select the coordination geometry that matches your complex.
- Choose high-spin or low-spin according to ligand strength and known behavior.
- Enter the d-electron count for the metal ion.
- Select the input mode and provide wavelength or splitting energy.
- Optionally enter a pairing energy estimate for comparison.
- Press Calculate to display the result above the form.
- Review CFSE, magnetic moment, occupancy table, and orbital graph.
- Download the result as CSV or PDF when needed.
Frequently Asked Questions
1) What does crystal field splitting energy measure?
It measures how much the metal d orbitals separate in energy when ligands surround the metal ion. That separation controls color, magnetic behavior, and stabilization.
2) Why does geometry change the result?
Different ligand arrangements interact with d orbitals differently. Octahedral, tetrahedral, and square planar fields split the orbitals into different patterns and therefore produce different stabilization energies.
3) What is the difference between high spin and low spin?
High-spin cases maximize unpaired electrons when splitting is relatively small. Low-spin cases pair electrons earlier when splitting is large enough to compete with pairing energy.
4) Can I use absorption wavelength from a UV-Vis spectrum?
Yes. If you know the relevant d-d transition wavelength, enter it in nanometers. The calculator converts it into wavenumber, energy per photon, and molar splitting energy.
5) Why can CFSE be negative?
Negative CFSE means the occupied electron arrangement lies below the barycenter overall. That indicates stabilization relative to the unsplit average d-orbital energy reference.
6) Is the square planar calculation exact?
No. It is an approximate orbital-energy model used for teaching and fast comparison. Real square planar systems can vary with ligand type, covalency, and metal identity.
7) What does the pairing adjustment tell me?
It gives a simple estimate that combines CFSE with an entered pairing penalty. It is useful for comparison, but it is not a complete many-electron term analysis.
8) Are low-spin tetrahedral complexes common?
They are uncommon because tetrahedral splitting is usually small. The calculator still allows them so you can study theoretical strong-field cases and compare trends.