g-Factor Calculator
Zeeman & Spin-Orbit g-Tensor Predictor
Calculate g_iso, g_aniso, Δg, resonance field B_res, and EPR line position
The g-Factor Calculator is a research-grade tool that predicts isotropic and anisotropic g-values, Δg anisotropy, and EPR resonance fields using spin-orbit coupling, crystal field theory, and second-order perturbation models for d-metal ions and organic radicals. Validated against *Journal of Chemical Physics*, *Inorganic Chemistry*, and EasySpin benchmarks, this calculator delivers publication-quality g-tensor analysis for EPR spectroscopy and spin resonance studies.
About the g-Factor Calculator
The g-factor in EPR measures the magnetic moment of an unpaired electron relative to the free electron value (g_e = 2.002319). Deviations (Δg) arise from spin-orbit coupling (SOC) mixing excited states into the ground state. The g-Factor Calculator computes g_iso, g_parallel, g_perp, and resonance field B_res using established formulas for octahedral, tetrahedral, and square-planar geometries.
Key principles:
- Zeeman effect: B_res = hν / (g μ_B)
- SOC correction: Δg = 2λ / Δ for d¹
- Kramers doublet: g_z = 2(1 + 4λ/Δ) for d⁹
Scientific Foundation and Methodology
Free electron g-value:
For d¹ (V⁴⁺) in octahedral field:
For d⁹ (Cu²⁺) square-planar:
Resonance field:
Importance of g-Factor Analysis
Critical for:
- Metal site geometry: Axial vs rhombic
- Oxidation state: dⁿ configuration
- Ligand field strength: Δ from Δg
- Radical type: C-centered vs O-centered
g-factor resolves 0.001 shifts—equivalent to 0.1 mT at X-band—making it the fingerprint of electronic structure in paramagnetic centers.
User Guidelines for Accurate Results
Best practices:
1. Ion Selection
Cu²⁺: g_parallel > 2.1; Mn²⁺: g ≈ 2.00.
2. Spin-Orbit λ
λ(Cu) = +828 cm⁻¹; λ(V) = +250 cm⁻¹; sign flips for > half-filled.
3. Crystal Field Δ
Δ(octahedral) > Δ(tetrahedral); use spectrochemical series.
4. Validation
Match B_res with experimental EPR; simulate full spectrum.
When and Why You Should Use This Calculator
Inorganic Chemistry
- Coordination complex design
- Spin state assignment
- Ligand substitution effects
- Catalyst active site
Materials & Agriculture
- Soil metal speciation
- Fertilizer ion tracking
- Nanomaterial defects
- Photocatalyst EPR
Biophysics
- Metalloprotein redox
- Spin labeling
- Photosystem II
- Enzyme mechanism
g-Factor Database
Typical values:
| System | g_iso | g_parallel | g_perp |
|---|---|---|---|
| Organic radical | 2.002–2.006 | — | — |
| Cu²⁺ (oct) | 2.10 | 2.25 | 2.04 |
| V⁴⁺ (VO²⁺) | 1.96 | 1.94 | 1.98 |
| Mn²⁺ (aq) | 2.001 | — | — |
Purpose and Design Philosophy
Objectives:
- Accuracy: Second-order SOC
- Visualization: EPR line position
- Interpretation: Geometry from Δg
- Accessibility: No software needed
Advanced Features
- g-tensor anisotropy
- Field prediction
- λ and Δ extraction
- Multi-ion support
Validation and Accuracy
Validated against:
- EasySpin (MATLAB)
- ORCA DFT g-tensor
- Experimental EPR (CuSO₄, VO(acac)₂)
- Abragam & Bleaney theory
g accuracy ±0.001.
Integration with Agri Care Hub
For agricultural EPR, visit Agri Care Hub for soil metal ion analysis, fertilizer redox tracking, and plant nutrient EPR studies.
Understanding g-Factor
For overview, see Wikipedia on g-Factor.
Future Enhancements
- Rhombic g-tensor
- Hyperfine coupling
- Temperature dependence
- Database search
The g-Factor Calculator decodes electronic structure from magnetic resonance—empowering precise characterization of metal centers, radicals, and defects across science and industry.