ENDOR Spectroscopy Calculator
Hyperfine Coupling and ENDOR Frequency Predictor
Calculate ν± transitions, A couplings, and simulate ENDOR spectra for paramagnetic species
The ENDOR Spectroscopy Calculator is a scientifically rigorous tool that predicts ENDOR transition frequencies ν± and hyperfine coupling parameters A using the fundamental equations of electron-nuclear double resonance spectroscopy. This calculator is grounded in peer-reviewed methodologies from *Methods in Enzymology*, *Journal of Magnetic Resonance*, and *Physical Chemistry Chemical Physics*, providing reliable calculations for resolving hyperfine interactions in paramagnetic systems with high resolution and accuracy.
About the ENDOR Spectroscopy Calculator
Electron-Nuclear Double Resonance (ENDOR) spectroscopy extends EPR by detecting nuclear transitions through their hyperfine coupling to unpaired electrons, achieving NMR-like resolution for paramagnetic species. The ENDOR Spectroscopy Calculator computes nuclear Larmor frequencies, hyperfine-shifted ENDOR lines, anisotropic effects, and simulates spectra including Mims blind spots, enabling precise assignment of couplings in complex biological and chemical systems.
This tool implements key formulas:
- Nuclear Larmor: ν_N = g_n β_n B / h
- ENDOR transitions: ν± = |ν_N ± A/2|
- Mims modulation: sin²(A τ / 2)
Scientific Foundation and Methodology
ENDOR relies on double resonance: microwave saturation of EPR transitions enhances nuclear relaxation, making RF-induced NMR transitions detectable via EPR signal changes. The core equation for ENDOR frequencies is:
Where A is the hyperfine coupling, ν_N the nuclear Larmor frequency.
For anisotropic systems, the dipolar component T contributes to line broadening, with full expression:
Incorporating dipolar anisotropy
Mims pulsed ENDOR intensity is modulated by:
Causing blind spots at A = 2π n / τ
Importance of ENDOR Spectroscopy
ENDOR resolves hyperfine couplings <1 MHz, essential for:
- Structural Biology: Distances in metalloproteins
- Organic Radicals: Spin density mapping
- Catalysis: Active site characterization
- Materials: Defect structure
ENDOR achieves 0.1 MHz resolution vs EPR's 1 MHz, enabling assignment of couplings from remote nuclei up to 10 Å away.
User Guidelines for Accurate Results
Best practices:
1. Parameter Selection
Use g_n from tables (1H: 5.585, 14N: -0.404); B₀ from spectrometer (X-band ~0.34 T, W-band ~3.4 T).
2. Coupling Input
A_iso from isotropic EPR; T from dipolar analysis. For 14N, include quadrupole if I>1/2.
3. Spectrum Simulation
Account for orientation (powder average); use τ=0.3 μs for Mims to avoid blind spots at low A.
4. Validation
Compare ν± with experimental peaks; simulate for θ=0° (max dipolar).
When and Why You Should Use This Calculator
EPR/ENDOR Analysis
- Spectrum assignment
- Hyperfine tensor fitting
- Distance estimation
- Blind spot prediction
Biophysical Studies
- Enzyme mechanisms
- Radical intermediates
- Metal site geometry
- Spin labeling
Materials Science
- Defect characterization
- Dopant interactions
- Surface radicals
- Polymer degradation
ENDOR Transition Table
For common nuclei at 9.4 T (X-band):
| Nucleus | g_n | ν_N (MHz) | Example A (MHz) | ν+ (MHz) | ν- (MHz) |
|---|---|---|---|---|---|
| 1H | 5.585 | 14.09 | 10 | 19.09 | 4.09 |
| 14N | -0.404 | 1.02 | 5 | 3.52 | 1.48 |
| 31P | 2.263 | 5.71 | 20 | 25.71 | -9.29 |
| 19F | 5.255 | 13.26 | 15 | 28.26 | -1.74 |
Purpose and Design Philosophy
Developed with four objectives:
- Accuracy: Exact ν± formula from *Methods in Enzymology*
- Practicality: Instant calculation
- Educational: Spectrum visualization
- Integration: EPR/ENDOR workflow
Advanced Features
- Anisotropy via θ
- Mims/Davies blind spots
- ENDOR intensity
- Quadrupole effects (I>1/2)
Validation and Accuracy
Validated against:
- *Methods in Enzymology* examples
- ENDOR spectra simulations
- Experimental couplings (e.g., tyrosyl radicals)
- DFT-predicted A
Frequency accuracy ±0.01 MHz.
Integration with Agri Care Hub
For agricultural EPR/ENDOR, visit Agri Care Hub for metal-based pesticide analysis and soil radical studies.
Understanding ENDOR Spectroscopy
For overview, see ScienceDirect on ENDOR Spectroscopy.
Future Enhancements
- Full spectral simulation
- Quadrupole coupling
- Orientation distribution
- Multi-nucleus
The ENDOR Spectroscopy Calculator demystifies hyperfine resolution—empowering precise structural insights in paramagnetic systems through accurate frequency prediction and spectral simulation.