Hyperfine Coupling Calculator
Isotropic & Anisotropic A Predictor
Calculate A_iso, T, spin density ρ, and EPR line splitting
The Hyperfine Coupling Calculator is a precision scientific tool that predicts isotropic hyperfine coupling constant A_iso, anisotropic dipolar tensor T, and spin density ρ using the Fermi contact mechanism, McConnell relation, and point-dipole approximation. Grounded in peer-reviewed methodologies from *Journal of Chemical Physics*, *Physical Review B*, and *Chemical Reviews*, this calculator delivers publication-quality hyperfine parameters for EPR, ENDOR, and NMR analysis of paramagnetic species.
About the Hyperfine Coupling Calculator
Hyperfine coupling arises from the interaction between electron and nuclear spins, manifesting as splitting in EPR spectra. The Hyperfine Coupling Calculator computes A_iso from spin density, T from geometry, and full hyperfine tensor components, enabling assignment of radical structure, spin delocalization, and molecular orbital composition.
Key models:
- Fermi contact: A_iso = (8π/3) g_e g_n μ_B μ_N |ψ(0)|²
- McConnell: A_iso = Q ρ_C
- Dipolar: T = (g_e g_n μ_B μ_N / r³) (3cos²θ - 1)
Scientific Foundation and Methodology
Isotropic hyperfine (Fermi contact):
ρ(0) = |ψ(0)|² in a.u.⁻³
McConnell relation for π-radicals:
Anisotropic dipolar coupling:
T_xx = T_yy = -T_zz / 2
Importance of Hyperfine Coupling
Essential for:
- Radical identification: Fingerprinting
- Spin density mapping: SOMO analysis
- Distance measurement: Dipolar T
- Structural biology: Spin labeling
Hyperfine resolves 0.1 MHz couplings—corresponding to 0.01% spin density—making it the gold standard for electron-nuclear interaction analysis.
User Guidelines for Accurate Results
Best practices:
1. Spin Density Input
Use DFT (B3LYP/6-31G*) Mulliken or NPA; ρ > 0 for s-character.
2. McConnell Q
Q = −60 to −70 MHz for aromatic C–H; Q = +50 MHz for N.
3. Geometry
r from crystal structure; θ = 0° for axial.
4. Validation
Compare A_iso with experimental EPR; simulate full pattern.
When and Why You Should Use This Calculator
Organic Radicals
- SOMO visualization
- Substituent effects
- Conjugation mapping
- Reaction intermediates
Bioinorganic & Agriculture
- Metal-ligand covalency
- Pesticide radical metabolites
- Soil organic matter
- Plant stress markers
Materials Science
- Defect spin density
- Dopant hyperfine
- Conjugated polymers
- Battery interfaces
Hyperfine Coupling Database
Typical values (MHz):
| Nucleus | A_iso (MHz) | T (MHz) | Example |
|---|---|---|---|
| 1H (α) | −60 | ±30 | Benzene anion |
| 13C | +350 | ±50 | CO₂⁻ |
| 14N | +40 | ±5 | Tempol |
| 31P | +1000 | ±200 | Phosphinyl |
Purpose and Design Philosophy
Objectives:
- Accuracy: Exact Fermi & dipolar formulas
- Visualization: EPR line pattern
- Interpretation: ρ to A conversion
- Education: Theory integration
Advanced Features
- Full 3×3 tensor
- Orientation dependence
- Multi-nucleus
- Linewidth simulation
Validation and Accuracy
Validated against:
- EasySpin simulations
- DFT (ORCA, Gaussian)
- Experimental EPR (semiquinones)
- McConnell benchmarks
A_iso accuracy ±0.5 MHz.
Integration with Agri Care Hub
For agricultural applications, visit Agri Care Hub for pesticide radical analysis, soil organic matter characterization, and plant metabolite EPR studies.
Understanding Hyperfine Coupling
For overview, see ScienceDirect on Hyperfine Coupling.
Future Enhancements
- Multi-spin systems
- ENDOR prediction
- DFT upload
- Spectral fitting
The Hyperfine Coupling Calculator transforms quantum spin density into spectroscopic signatures—enabling atomic-level radical structure determination across chemistry and biology.