EPR Spectroscopy Calculator
Spin Hamiltonian & Spectrum Simulator
Predict g-tensor, hyperfine A, ZFS D/E, and CW EPR lineshapes
The EPR Spectroscopy Calculator is a research-grade tool that simulates continuous-wave (CW) EPR spectra using the spin Hamiltonian, g-tensor anisotropy, hyperfine coupling, and zero-field splitting (ZFS) for S=1/2 to S=5/2 systems. Built on peer-reviewed methodologies from *Journal of Magnetic Resonance*, *Physical Chemistry Chemical Physics*, and EasySpin simulation principles, this calculator delivers publication-quality spectral predictions for radical identification, metal center characterization, and spin dynamics analysis.
About the EPR Spectroscopy Calculator
Electron Paramagnetic Resonance (EPR) spectroscopy, also known as ESR, detects unpaired electrons in chemical, biological, and material systems. The EPR Spectroscopy Calculator solves the spin Hamiltonian to predict resonance field positions, line intensities, and spectral patterns under X-band (9.5 GHz) or user-defined microwave frequencies.
Key components:
- Zeeman term: g·μ_B·B·S
- Hyperfine: A·I·S
- ZFS: D[S_z² - S(S+1)/3] + E(S_x² - S_y²)
Scientific Foundation and Methodology
Spin Hamiltonian:
For S=1/2, I=1/2 (e.g., 14N):
3-line pattern
For high-spin (S=5/2):
Fine structure splitting
Importance of EPR Spectroscopy
Critical for:
- Free radicals: Reaction mechanisms
- Transition metals: Oxidation state, geometry
- Photosynthesis: Tyrosyl, quinone radicals
- Materials: Defects, dopants
EPR detects 10¹⁰ spins—1000× more sensitive than NMR—making it ideal for trace paramagnetic species in complex matrices.
User Guidelines for Accurate Results
Best practices:
1. Spin System
S=1/2 for organics; S=5/2 for Mn²⁺, Fe³⁺.
2. g-Values
g_iso ≈ 2.0023 for organic; g > 2.1 for d-metals.
3. Hyperfine
A(¹H) ~ 1–100 MHz; A(¹⁴N) ~ 40 MHz.
4. ZFS
D > 0.1 cm⁻¹ for high-spin; E/D < 1/3.
When and Why You Should Use This Calculator
Organic Chemistry
- Radical trapping
- Spin labeling
- Photoredox intermediates
- Polymerization
Bioinorganic
- Metalloenzyme active sites
- Redox state
- Spin trapping in vivo
- Oxygen evolution
Materials & Agriculture
- Soil paramagnetic centers
- Fertilizer metal speciation
- Nanoparticle defects
- Food oxidation
EPR Parameter Database
Typical values:
| Species | g_iso | A (MHz) | D (cm⁻¹) |
|---|---|---|---|
| DPPH | 2.0036 | — | — |
| Tempol | 2.006 | 43 (¹⁴N) | — |
| Mn²⁺ (aq) | 2.001 |