EPR (ESR) Spectroscopy

What EPR does

EPR looks for one thing: an unpaired electron. Almost every molecule you draw has its electrons neatly paired in bonds and lone pairs, spins cancelling to zero. But radicals, transition-metal ions with partly filled d shells, triplet states, and crystal defects carry an electron with no partner. That lone electron behaves like a tiny bar magnet, and EPR interrogates it.

An electron has two spin states, m_s = +½ and −½. In free space they have identical energy, so there is nothing to detect. Put the sample in a strong magnetic field and the two states split apart — the electronic Zeeman effect — with the gap growing linearly with the field:

    ΔE = g · μ_B · B

    g   = the g-value (≈ 2.0023 for a free electron)
    μ_B = Bohr magneton = 9.274 × 10⁻²⁴ J/T
    B   = applied magnetic field (tesla)

Now shine fixed-frequency microwaves on the sample and ramp the magnet. When the gap ΔE exactly equals the photon energy hν, the electron absorbs a photon and flips from the lower state to the upper one — resonance. The spectrometer records the field at which that absorption happens. That is the entire measurement: find the field where the spins flip.

Step by step: how a spectrum is built

1. Load the sample into a resonant cavity. The cavity stores microwave energy at a single, fixed frequency — most commonly X-band, about 9.5 GHz. A klystron or Gunn diode feeds it. The cavity is placed between the poles of an electromagnet.
2. Split the spin states. The magnet raises the field from below resonance upward. As B climbs, the Zeeman gap gμ_B·B widens from zero toward the microwave photon energy hν.
3. Hit resonance. At the field where gμ_B·B = hν, the population in the lower spin state absorbs microwave photons and is promoted to the upper state. Microwave power drops in the cavity — the detector sees it.
4. Read the g-value. Rearranging the resonance condition, g = hν / (μ_B·B). Because ν is known to high precision and B is measured, the resonance field is the g-value. A free radical sits near g = 2.00; a copper(II) complex might sit at g ≈ 2.2; the shift away from 2.0023 reports on spin–orbit coupling and the electronic structure.
5. Resolve the hyperfine structure. The unpaired electron also feels the tiny magnetic fields of nearby nuclei (¹H, ¹⁴N, ⁶³Cu…). Each magnetic neighbor adds or subtracts a little field, so the single resonance splits into a fingerprint pattern of lines. Counting them tells you how many, and which, nuclei surround the electron.
6. Phase-sensitive detection. The field is wobbled (modulated) at ~100 kHz and read through a lock-in amplifier, which returns the first derivative of the absorption. That's why an EPR spectrum looks like S-shaped wiggles crossing a baseline rather than the bell-shaped peaks of NMR or UV-Vis.

   energy
     ↑        m_s = +1/2   ___----  (upper, spin "up" vs field)
     |               ___----
   ΔE = hν  ← resonance when gap = photon
     |         ---___
     |               ---___  m_s = -1/2  (lower)
     +----------------------------→  magnetic field B
                    B_res

Instrument, frequency bands, and conditions

An EPR spectrometer is essentially a microwave bridge feeding a resonant cavity that sits in a swept magnetic field. The choice of frequency band sets the field at which g ≈ 2 radicals resonate:

Band	Microwave freq.	Field for g ≈ 2	Typical use
L-band	~1 GHz	~0.036 T (360 G)	In vivo imaging, lossy aqueous samples
X-band	~9.5 GHz	~0.34 T (3400 G)	The workhorse — most published spectra
Q-band	~34 GHz	~1.2 T (12,000 G)	Better g-resolution, small samples
W-band	~94 GHz	~3.4 T (34,000 G)	High-field g-anisotropy, rigid systems

• Sample state. Solutions (rapid tumbling averages anisotropy to a clean isotropic spectrum), frozen glasses at 77 K or below (for metals and to freeze out motion), powders, single crystals, or living tissue (in vivo EPR).
• Low temperature. Many transition-metal centers (Fe³⁺, some Cu²⁺, Mn³⁺) relax so fast at room temperature that the lines broaden into nothing. Liquid-helium cryostats (4 K) slow the relaxation and sharpen the signal.
• The g-standard. DPPH (2,2-diphenyl-1-picrylhydrazyl) is the universal field-calibration radical: a single sharp line at g = 2.0036. You measure your unknown against it.
• Concentration. Modern X-band spectrometers detect roughly 10¹⁰–10¹¹ spins — down to nanomolar radical concentrations in favorable cases, far more sensitive than NMR for the species it can see.

Reading hyperfine patterns — counting the neighbors

Hyperfine splitting is where EPR turns from a yes/no detector into a structural tool. An unpaired electron delocalized near magnetic nuclei feels each nucleus's spin as a small extra field. A set of n equivalent nuclei of spin I splits the signal into 2nI + 1 lines, with intensities given by Pascal's triangle (for I = ½) or the appropriate multinomial.

Radical	Coupling nuclei	Lines (2nI + 1)	Intensity ratio
Methyl radical ·CH₃	3 × ¹H (I = ½)	2·3·½ + 1 = 4	1 : 3 : 3 : 1
Ethyl radical ·CH₂CH₃	2 α-H then 3 β-H	3 × 4 = 12	triplet of quartets
Benzene radical anion	6 × ¹H (I = ½)	2·6·½ + 1 = 7	1:6:15:20:15:6:1
Nitroxide (TEMPO)	1 × ¹⁴N (I = 1)	2·1·1 + 1 = 3	1 : 1 : 1
Cu²⁺ (d⁹)	1 × ⁶³Cu (I = 3/2)	2·1·3/2 + 1 = 4	1 : 1 : 1 : 1

The methyl radical is the classic textbook case: its four lines in a 1:3:3:1 ratio, spaced ~23 gauss apart, prove that the electron sees three equivalent protons and therefore lives in a planar sp²-like carbon-centred π orbital. The hyperfine coupling constant (line spacing, in gauss or MHz) measures how much unpaired-electron density sits on each nucleus — a direct spin-density map of the radical.

Worked example: X-band resonance field for a radical

Suppose you run a nitroxide spin label at X-band, ν = 9.50 GHz, and you want to know where a g = 2.0060 line should appear. Solve the resonance condition for the field:

    hν = g · μ_B · B      →      B = hν / (g · μ_B)

    h   = 6.626 × 10⁻³⁴ J·s
    ν   = 9.50 × 10⁹ Hz
    μ_B = 9.274 × 10⁻²⁴ J/T
    g   = 2.0060

    numerator   = h·ν   = 6.626e-34 × 9.50e9  = 6.29 × 10⁻²⁴ J
    denominator = g·μ_B = 2.0060 × 9.274e-24  = 1.860 × 10⁻²³ J/T

    B = 6.29e-24 / 1.860e-23  ≈ 0.3382 T  ≈ 3382 gauss

So the line appears near 3382 G. Run DPPH (g = 2.0036) in the same cavity and it lands at ~3386 G — a 4-gauss shift. That few-gauss difference is the whole point: g-values this close still separate cleanly, which is how EPR distinguishes a carbon radical (g ≈ 2.003) from an oxygen-centred radical (g ≈ 2.01) from a copper center (g ≈ 2.2).

EPR vs NMR — sibling techniques, opposite particles

EPR is the electron-spin analogue of NMR's nuclear-spin resonance. Because the electron's magnetic moment is ~658× larger than a proton's, everything scales up: bigger energy gaps, microwave instead of radio, gauss instead of parts-per-million.

	EPR (ESR)	NMR
Spin probed	Unpaired electron (S = ½…)	Nuclear spin (¹H, ¹³C, …)
Requirement	Sample must be paramagnetic	Works on diamagnetic molecules
Radiation	Microwave (~9.5 GHz, X-band)	Radio (~100–900 MHz)
Field for resonance	~0.34 T (field is swept)	~1–21 T (frequency is swept)
Spectrum shape	First derivative of absorption	Absorption peaks
Fingerprint parameter	g-value + hyperfine (A)	Chemical shift (δ) + J-coupling
Sensitivity	~10¹⁰–10¹¹ spins (very high)	~10¹⁸ spins (much lower)
Splitting from	Nearby nuclei (electron↔nucleus)	Nearby nuclei (nucleus↔nucleus)
Blind to	Closed-shell (paired) molecules	Fast-relaxing paramagnets can broaden lines

Real-world applications

• Spin trapping of reactive oxygen species. The hydroxyl radical (·OH) lives nanoseconds — far too short to observe directly. Add a spin trap like DMPO (5,5-dimethyl-1-pyrroline N-oxide) and the fleeting radical adds to it, forming a stable nitroxide whose EPR pattern identifies the original radical. This is the standard way to prove oxidative stress in biology, food chemistry, and battery aging.
• Site-directed spin labeling (SDSL). Attach a nitroxide (e.g. the MTSL reagent) to a chosen cysteine on a protein. The label's EPR lineshape reports on local mobility, and a pair of labels reports the distance between two points (via the DEER/PELDOR pulsed experiment, measuring dipolar coupling out to ~8 nm). This maps protein conformational changes that crystallography freezes out.
• Metalloenzyme active sites. The copper in cytochrome c oxidase, the Mn₄CaO₅ cluster of Photosystem II, and mononuclear iron centers all give characteristic EPR signatures. EPR is often the only tool that can watch a metal center change oxidation state during turnover.
• Dating and dosimetry. Ionizing radiation creates trapped electron/hole defects (like the E′ center in quartz or CO₂⁻ radicals in tooth enamel and bone). The EPR signal intensity is proportional to accumulated dose, giving ages for archaeological quartz and stalagmites, and retrospective radiation doses for accident victims.
• Oxygen sensing (oximetry). Molecular O₂ is itself a triplet (two unpaired electrons) and it broadens the lines of a nearby spin probe by collisional relaxation. Calibrated probes turn EPR linewidth into a direct readout of oxygen concentration in tumors and tissue.
• Catalysis and materials. EPR follows radical intermediates in polymerizations, tracks color centers and dangling bonds in semiconductors and solar cells, and quantifies conduction electrons in conducting polymers and graphene.

Limitations and pitfalls

• It only sees unpaired electrons. The vast majority of stable organic molecules are EPR-silent. If your species is closed-shell, EPR shows a flat line — you need to generate a radical (electrochemically, photochemically, by irradiation, or by spin trapping) first.
• Fast relaxation broadens signals away. Many transition-metal ions (high-spin Fe³⁺, integer-spin systems, Ni²⁺) relax so quickly that room-temperature lines vanish. You must cool to 77 K or 4 K, which not every lab has.
• Aqueous samples absorb microwaves. Water is lossy at X-band; bulk aqueous samples heat and de-tune the cavity. Use flat cells, capillaries, or drop to L-band for in vivo work.
• Overlapping lines. Complex radicals with several inequivalent nuclei produce dense multiplets that overlap. Spectral simulation (e.g. the EasySpin toolbox) is usually needed to extract g-values and coupling constants.
• Over-modulation and power saturation. Too much field modulation distorts and broadens lines; too much microwave power saturates the transition and flattens the signal. Both are classic beginner artifacts — the linewidth you report can be an instrument setting, not real chemistry.

Who discovered it, and when

EPR was first observed by the Soviet physicist Yevgeny Zavoisky at Kazan State University in 1944, who detected resonant microwave absorption in paramagnetic salts as he varied the magnetic field. Wartime isolation kept his work largely unknown in the West for years. The technique grew up alongside NMR (Bloch and Purcell, 1946), sharing the same quantum idea — spin flips driven at resonance — but aimed at the electron rather than the nucleus.

Through the 1950s and 60s the Oxford and Cornell groups turned EPR into a structural workhorse, cataloguing g-values and hyperfine constants for organic radicals and metal complexes. The nitroxide spin labels that made biological EPR practical came from Harden McConnell's lab in the mid-1960s. Pulsed EPR and the DEER/PELDOR distance experiment matured in the 1990s–2000s, extending the reach from "is there a radical?" to "how far apart are these two points on a folded protein?"