Turn spin-energy levels into a spectrum
Magnetic resonance asks a very practical question: at what field and frequency can an oscillating magnetic field drive a transition between spin states? From that simple starting point we get EPR spectra, hyperfine patterns, anisotropic powder lineshapes and reaction-yield detected resonance.
Use the resonance condition to connect microwave frequency, magnetic field and effective g-value.
Predict qualitatively how hyperfine coupling, anisotropy and linewidth shape an EPR spectrum.
Distinguish CW, time-resolved, pulsed and reaction-yield detected magnetic resonance.
Resonance
Match the photon energy to the spin splitting
Resonance occurs when the drive matches an allowed energy difference
What it is: A transition becomes efficient when the oscillating field frequency matches the energy gap between spin eigenstates.
What it changes: It allows the weak transverse microwave/RF field to coherently transfer population or create coherence between states.
What you observe: A peak, derivative line, echo response or reaction-yield change at a particular field/frequency.
What it is: The orientation-dependent magnetic response that converts field into electron-spin splitting.
What it changes: Changing \(g_\mathrm{eff}\) shifts the field required to satisfy \(h\nu=g_\mathrm{eff}\mu_BB\).
What you observe: Different resonance positions for different molecular orientations or electronic structures.
For an isotropic \(S=\tfrac12\) electron spin, the first resonance condition is
For \(g\approx2\), X-band EPR around \(9.5~\mathrm{GHz}\) resonates near \(0.34~\mathrm T\). Q-band moves to roughly \(1.2~\mathrm T\), and W-band around \(94~\mathrm{GHz}\) is near \(3.35~\mathrm T\). The exact field depends on \(g\).
Hyperfine structure
Nuclear spins split electron-spin transitions
Hyperfine lines are a map of which nuclei the electron spin can feel
What it is: Electron–nuclear coupling makes the electron-spin transition energy depend on the nuclear-spin projection.
What it changes: One electron resonance is divided into several transitions corresponding to different nuclear configurations.
What you observe: Multiplets whose spacing and anisotropy encode local spin density and geometry.
What it is: Symmetry-related nuclei share the same coupling; chemically or geometrically distinct nuclei generally do not.
What it changes: Equivalent nuclei create regular combinatorial patterns, whereas inequivalent nuclei generate many nonuniform lines.
What you observe: Characteristic EPR multiplets and resolved nuclear fingerprints.
For one electron coupled isotropically to one nucleus, a simple high-field Hamiltonian is
To first order, the allowed EPR transitions obey \(\Delta m_S=\pm1\) and \(\Delta m_I=0\). One \(I=\tfrac12\) nucleus therefore gives two hyperfine components. Several equivalent nuclei produce the familiar multiplet patterns; inequivalent nuclei create more complicated splittings.
When does this simple picture fail?
At low fields, for strong hyperfine coupling, for large anisotropy or when several interactions have comparable size, \(m_S\) and \(m_I\) may no longer be good quantum numbers. Then the full Hamiltonian has to be diagonalized rather than interpreted as a simple first-order splitting pattern.
Anisotropy
One molecule can resonate at different fields in different orientations
For an axial \(g\)-tensor with principal values \(g_\perp\) and \(g_\parallel\), the effective \(g\)-value for a field at angle \(\theta\) to the symmetry axis is
The corresponding resonance field is \(B_\mathrm{res}=h\nu/(\mu_Bg_\mathrm{eff})\).
Axial \(g\)-tensor resonance
The anisotropy is modest at X-band, but the same \(g\)-difference maps onto a larger absolute field separation at higher microwave frequency.
This plots the resonance condition for an axial \(g\)-tensor, not a simulated powder spectrum. A real powder spectrum also requires orientation weighting, transition probabilities, linewidths and any hyperfine or ZFS interactions.
Powder spectra
A frozen sample contains all molecular orientations at once
In a single crystal, you can rotate one known molecular orientation relative to the field. In a frozen solution or powder, every orientation is present. The spectrum therefore accumulates resonance contributions from the entire orientation sphere.
Characteristic edges and turning points appear near principal tensor orientations, but the intensity is not just a histogram of \(B_\mathrm{res}(\theta)\). The correct spectrum also includes the orientational measure, transition matrix elements and broadening.
Linewidths
Relaxation determines how sharp a resonance can be
A spectral line has a width because phase coherence is finite
What it is: Broadening experienced by every member of the ensemble because each spin loses phase coherence in time.
What it changes: Shorter \(T_2\) broadens the Lorentzian component of the line through the time–frequency uncertainty relation.
What you observe: A broader resonance even in a perfectly homogeneous sample.
What it is: A distribution of static or slowly varying resonance frequencies caused by field inhomogeneity, \(g\)-strain, unresolved hyperfine or structural heterogeneity.
What it changes: Different spins dephase relative to each other without necessarily losing their individual microscopic coherence.
What you observe: Broadened ensemble lines that can often be partly refocused by an echo.
For a simple exponentially decaying transverse coherence, the homogeneous absorption line is Lorentzian. Its frequency-domain full width at half maximum is
Real EPR lines can also contain unresolved hyperfine structure, \(g\)-strain, conformational distributions and other inhomogeneous broadening. Those contributions are often summarized through an effective \(T_2^\ast\), but \(T_2^\ast\) is not the same microscopic quantity as the true homogeneous \(T_2\).
Experimental modes
“EPR” is not one experiment
Continuously irradiate while sweeping field or frequency. Excellent for resonance positions, hyperfine patterns and steady-state lineshapes.
Observe transient spin polarization after a photochemical or kinetic trigger. Particularly useful for radical pairs and triplet states.
Manipulate coherences with microwave pulses and read out echoes or time-domain signals. Enables precise relaxation and distance measurements.
Drive spin resonance but detect it through a change in reaction yield instead of conventional microwave absorption.
RYDMR
Detect resonance through chemistry
Reaction-yield detected magnetic resonance is especially natural for radical pairs. An RF or microwave field perturbs the spin evolution. If that changes how much singlet or triplet character reaches a spin-selective reaction channel, the resonance can be detected as a change in chemical yield.
Conceptually, the chain is
This is magnetic resonance without requiring conventional inductive detection of the spin magnetization.
Selected reading
Examples from my work
Reaction-yield detected magnetic resonance spectroscopy of radical pairs in cryptochrome-4a
Using reaction yield as the observable for a radical-pair magnetic-resonance experiment.
Free Radic. Biol. Med. (2026) →Revealing the Impact of g-Tensor Anisotropy on the Charge Recombination in Donor–Acceptor Dyads Under High Magnetic Fields
Why anisotropic resonance physics can feed back into radical-pair kinetics.
JACS (2025) →Weak Radiofrequency Field Effects on Biological Systems Mediated through the Radical Pair Mechanism
How oscillating magnetic fields interact with radical-pair spin dynamics.
Chemical Reviews (2025) →Key external literature
Where to read next
These are deliberately selected from outside my own work: foundational papers or reviews that are especially useful for this topic.
Nuclear Induction
F. Bloch · Physical Review (1946). A foundational treatment of driven spin precession, resonance and relaxation in magnetic resonance.
Open DOI →EasySpin, a comprehensive software package for spectral simulation and analysis in EPR
S. Stoll and A. Schweiger · Journal of Magnetic Resonance (2006). A widely used practical and theoretical reference for modern EPR spectral simulation.
Open DOI →