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EPR, Methods
EPR, Methods Richard Cammack, King’s College, London, UK ã 2017 Elsevier Ltd. All rights reserved.
N, Nþ
Symbols A B0 B1 B2 g h H I k mI mS
hyperfine coupling constant static magnetic field microwave magnetic field radiofrequency magnetic field electron g factor Planck’s constant Hamiltonian operator nuclear spin operator Boltzmann constant nuclear spin angular momentum electron spin angular momentum
Q S T Tl T2 h l mB n nn t
Introduction Electron paramagnetic resonance (EPR) is also known as electron spin resonance (ESR) or electron magnetic resonance (EMR) spectroscopy; no single name has become generally accepted. It is a means of investigating materials that are paramagnetic, i.e. having unpaired electrons. These include organic free radicals, compounds of transition metal ions and defects in solids. Since the development of the X-band continuouswave spectrometer in the 1950s and 1960s, the basic design of the EPR spectrometer has remained relatively unchanged, while a wide variety of applications in physics, chemistry and biochemistry have been devised. Examples are the observation of radical intermediates in chemical reactions; the determination of electron density distributions on radicals; the observation of rapid motion of spin labels in solution; and the determination of coordination geometry of metal ion sites. Advances in solid-state microwave electronics have led to instrument extensions in many different ways, for specialist applications. Examples are ENDOR and TRIPLE and ESEEM, to measure hyperfine interactions, and low-frequency EPR imaging. The principles of typical applications will be described, with reference to the relevant equipment and sample requirements.
Characteristics of the EPR Spectrum EPR involves the interaction of electromagnetic radiation, usually in the microwave region, with the paramagnetic material in a magnetic field. Because paramagnetic centres are less common than nuclear spins, the method is more selective than the analogous technique of NMR. There are some differences in practice between NMR and EPR that result from the much This article is reproduced from the previous edition, Copyright 1999, Elsevier Ltd.
Encyclopedia of Spectroscopy and Spectrometry, Third Edition
populations of electron energy levels separated by a magnetic field quality factor of a resonator electron spin operator absolute temperature longitudinal (spin–lattice) relaxation time transverse (spin–spin) relaxation time filling factor of a resonator microwave wavelength Bohr magneton microwave frequency nuclear Larmor frequency delay in pulse sequence
greater magnetic moment of the electron compared to that of nuclear spins. The bandwidth of the spectrum is much greater than the parts-per-million scale of NMR. It is impossible to adjust the frequency over such a wide range, owing to the geometry of microwave waveguides, so it is the usual practice to observe the EPR spectrum at fixed frequency by sweeping the magnetic field. The relaxation rates of electron spins are faster than for nuclear spins, so that in some cases (particularly transition metals such as iron) it is necessary to cool the sample to cryogenic temperatures to observe the spectrum. The spectrum is characterized by a number of parameters which give information about the nature of the paramagnetic centres and their surroundings.
Zeeman Interaction The g factor defines the energy of the Zeeman interaction. This splits the energy levels of the paramagnet (Figure 1). At the resonance condition the energy DE required to reverse the direction of the electron spin in a magnetic field B0 is equal to the energy of the microwave quantum hn, given bym DE ¼ hv ¼ gmB B0 where h is Planck’s constant and mB the Bohr magneton. In an EPR spectrum the signals are obtained by increasing the B0 field. The g factor is inversely proportional to B0. For a free electron in a vacuum, g is a constant that is very precisely known (ge¼2.002 319 3044. . .). In a paramagnetic molecule, g varies from this, under the influence of spin–orbit interactions. These increase considerably with atomic number, and are particularly important for lanthanides. In the spin Hamiltonian formalism the effects of spin–orbit coupling are described by treating g as a spectroscopic variable, the ‘spectroscopic splitting factor’, which is characteristic of the paramagnetic centre. Therefore the EPR spectrum may be considered as a spectrum of g factors.
http://dx.doi.org/10.1016/B978-0-12-803224-4.00138-2
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Table 1 Isotope
% Natural abundance
Nuclear spin, I
mN
1
H
99.985
1 2
þ2.793
2
H
0.015
1
þ0.857
13
1.11
1 2
þ0.702
14
99.63
1
þ0.404
15
0.37
1 2 5 2 1 2 1 2 3 2 5 2 1 2 7 2 3 2 3 2 5 2 5 2
0.283
C N N
17
0.037
19
100
31
100
33
0.76
O F P S
55
100
57
2.19
59
100
63
69.09
65
30.91
95
15.72
97
9.46
Mn Fe Co Cu Cu Mo Mo
Figure 1 (a) Principle of electron paramagnetic resonance. (b) Effect of hyperfine splitting with a nucleus, l¼1/2.
Hyperfine Interaction The interaction between the magnetic moment of the electron and nuclear spins is a valuable feature of EPR spectra. It introduces splittings of the electron energy levels (Figure 1b). Each nuclear spin I induces a splitting into [2Iþ1] levels. The magnitude of the splitting is defined by the hyperfine coupling constant, A, which is expressed in energy units (usually MHz). Where there are several nuclei, for example protons in a radical, each level is further split by each nuclear hyperfine interaction. The hyperfine coupling can be observed as splitting of the EPR spectrum, if the coupling is greater than the line width. The magnitude of the splitting is given the symbol a, expressed in magnetic field units. The value of A depends on the nuclear moment, and the extent of interaction of the unpaired electron spin density with the nucleus; A has a sign as well as magnitude. If A > 0, the state in which electron and nuclear spins align antiparallel is of lower energy. Measurements of the magnitude and sign of hyperfine couplings provide some of the most detailed experimental evidence for electronic structures of molecules. They have been used to verify the results of molecular orbital calculations. In EPR spectra of transition ions, the hyperfine interaction gives rise to characteristic splittings, for example for copper
Some nuclei with magnetic moments
1.89 þ2.629 þ1.132 þ0.643 þ3.444 þ0.090 þ4.649 þ2.226 þ2.385 0.913 0.933
(I ¼ 32, 4 lines) and manganese (I ¼ 52, 6 lines) (Figure 2a). It can be used to identify paramagnetic centres and determine the electron density distribution over radicals. Isotopic substitution can be used (Table 1) to identify specific metals, for example 57Fe for natural iron. Interactions with nuclei of ligands, sometimes called superhyperfine splittings, allow the determination of the electron density distribution in transition metal complexes. Nuclei with spins greater than S ¼ 12 have a quadrupole moment and this gives rise to further splitting of the energy levels.
Interactions between Electrons (Fine Structure Interactions) The magnetic moment of the electron is 658 times that of the proton, so that interactions between electrons are of greater energy than those between nuclear spins, and are detectable over greater distances. This has a number of consequences. For example, when two or more electron spins are present in a paramagnetic centre such as a transition ion with spin S > 12 or an organic triplet state (S¼1), coupling of the electron spins gives rise to fine structure splittings (known as zero-field splittings) which strongly influence the apparent g factor. If the spin is an integral value, the splitting between the energy levels may be larger than the X-band microwave quantum, and no EPR signal is detected. However, for an odd number of electron spins there are always energy levels that can only be split by the magnetic field. As a consequence paramagnets with halfintegral spin, such as high-spin FeIII and CoII, are EPRdetectable (see Figure 2b). For the latter ions, with S ¼ 52, g factors may extend from 10 to 0. EPR spectra of transition ions are often measured in the solid state so that the spectrum is broadened by anisotropy of the g factor.
EPR, Methods
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Figure 2 EPR spectra of transition ions; (a) manganese ions in aqueous solution; note the six-line hyperfine splitting owing to the 55Mn nucleus (I¼52); (b) high-spin FeIII in metmyoglobin, frozen at 77 K; note the g factors at 6.0 and 2.0.
Electron spin–spin interactions occur between paramagnetic centres in solution and in the solid state. This causes splitting or broadening of the EPR signal. For solid paramagnetic materials the broadening may be so great as to render the X-band EPR spectrum undetectable. For EPR spectra in the solid state, the material must usually be magnetically dilute, for example doped into a diamagnetic host material. Paramagnets in biological materials such as proteins are usually fixed within the protein matrix and are thus detectable. Spin–spin interactions give rise to characteristic changes in line shape, and enhancement of the electron-spin relaxation rate, from which it is possible to estimate distances between the paramagnetic centres.
Anisotropy The Zeeman, dipolar hyperfine and fine structure interactions are all anisotropic, meaning that the energy of interaction depends on the angle between the paramagnetic centre and the applied magnetic field. In solution spectra of small molecules, the anisotropy is averaged, and spectral lines are narrow. Note, however, that the isotropic hyperfine interaction does not average to zero and so there is still hyperfine splitting (e.g. Figure 2a and Figure 3a). For randomly oriented samples in the solid state (so-called powder spectra), the distribution of molecules in different orientations gives rise to characteristic broadening of the line shape (Figure 2b and Figure 3c).
Figure 3 EPR spectra of radicals; (a) benzoquinone anion radical in solution; (b) the nitroxide TEMPOL in solution and (c) in a photosynthetic reaction centre.
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Effects of Temperature, Electron-Spin Relaxation and Spectral Linewidths Temperature has a number of effects on the EPR spectrum. The populations of the electron energy levels N and Nþ (Figure 1a) differ by a small amount because of the Boltzmann distribution: Nþ DE gmB B0 ¼ exp ¼ exp N kB T kB T where kB is the Boltzmann constant and T the absolute temperature. At room temperature and a magnetic field of 0.32 T, the difference is about 0.07% of the unpaired electrons. It increases at higher microwave frequencies (hence higher fields), and at lower temperatures. The spin–lattice relaxation, with a characteristic time T1, is responsible for maintaining the population difference between levels N and Nþ. The spin–spin relaxation time T2 reflects the lifetime of the excited state and its effect on the line width. If the electron-spin relaxation rate is too rapid, the lifetime of the excited state is short and the EPR spectrum becomes broadened. At high temperatures the spectrum may become too broad for detection, hence the use of cryogenic temperatures for some transition ions. However, if the spin–lattice relaxation is too long, the population difference NNþ cannot be maintained, and the amplitude of the signal is attenuated, a situation known as microwave power saturation. Electron-spin relaxation times may be estimated by measuring the amplitude of the signal as a function of applied microwave power.
Figure 4 Outline of a typical continuous-wave EPR spectrometer.
Operation of the Spectrometer The outline of a conventional continuous-wave EPR spectrometer is shown in Figure 4. The term ‘continuous-wave (CW)’ refers to the fact that microwaves are applied throughout the measurement. It is designed to optimize the weak EPR signals originating from the sample, against a background of noise from the source. The microwave source is a reflex klystron (a type of thermionic valve) or a Gunn diode (a semiconductor device). The detector is a microwave diode. The operating frequency is typically in the X-band (9.5 GHz). This frequency is a compromise; higher frequencies increase the ratio N: Nþ (and hence sensitivity) but require smaller cavities and thus smaller sample size (and hence number of spins being measured). A typical sample volume is of the order of 0.1 cm3. The microwave circuit is known as the microwave bridge, to emphasize that it is a balanced circuit. The source is tuned to the resonant frequency of the cavity. Microwaves pass through waveguides to the cavity via a circulator, which ensures that signal arising from the sample in the cavity passes to the detector. The reference arm serves to balance the signal with the input microwave power. The circuit is optimally tuned by matching its impedance with the cavity using the iris, to a condition known as critical coupling. In this situation the intensity of the microwave field B1 at the sample is enhanced by the Q-factor of the cavity, typically several thousand-fold. When electron paramagnetic resonance occurs in the sample, a small amount of power is transmitted to the detector and is amplified and recorded.
EPR, Methods
The homogeneous B0 field is provided by an electromagnet. EPR spectra are obtained by modulation of the field by a small amount, at a frequency of 100 kHz. A lock-in amplifier detects the EPR signal in phase with the modulation. Modulation and phase-sensitive detection is a standard method of noise rejection and enhances the signal-to-noise ratio, and hence the sensitivity of the technique, by as much as 105. It gives rise to the characteristic first-harmonic (first-derivative) line shape. Although the absorption spectrum could be derived from this by integration, spectra are usually retained as the derivative form as it emphasizes narrow hyperfine splittings and other features.
Temperature Control The form of the paramagnetic material may be solid, liquid or gas, and so appropriate temperature control of the sample is needed. The temperature of the sample may be controlled by flowing gas through a quartz vacuum jacket. For low temperatures, helium is used. The sample may be held in a Dewar of liquid nitrogen or helium. For smaller resonator designs such as loop-gaps, the whole resonator is immersed in a cryostat containing helium or nitrogen.
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example through a waveguide of length l which prevents microwave leakage. The applied magnetic field B0 is modulated with Helmholtz coils in the walls of the cavity. The B0 and Bl fields are oriented at right angles, which gives a maximum magnetic resonance interactions for S ¼ 12 paramagnets. For paramagnets with an integer spin, the resonant transition is forbidden in this geometry. Parallel mode cavities are used for this situation, in which Bl is parallel to B0. In the loop-gap resonator (Figure 5b), the coupling loop acts as an antenna to transmit microwave power to and from the bridge to the split-ring resonator element. The number of gaps is variable, depending on the sample size. The microwave magnetic field Bl circulates in the ring, while the electric component is mostly confined to the gaps. Magnetic field modulation is also by external coils (not shown). Loop-gap resonators have better filling factors than rectangular cavities, so that the resonator can be smaller and the sample tube larger. They are particularly effective for lossy samples such as aquesous solutions. Other designs of cavity are possible, including cylindrical resonators constructed of an inert dielectric material such as sapphire (alumina).
Computer Control and Data Acquisition
Resonators The quality, or Q factor, of the microwave cavity or resonator is a measure of its efficiency at concentrating microwave energy. For a resonant a.c. circuit it is given by Q¼
2pðEnergy storedÞ ðEnergy dissipated per cycleÞ
The filling factor is the fraction of the microwave magnetic field Bl which bisects the sample. Two examples of resonators used in EPR are illustrated in Figure 5. Rectangular cavities (Figure 5(a)) are of metal which is coated with silver and gold for high conductivity. The sample is positioned at the maximum of the microwave magnetic field, Bl. It may be irradiated with ultraviolet or visible light, in this
Most operations of the instrument are under computer control. The spectrum is recorded as a series of data points, along a linear axis of magnetic field. The signal-to-noise ratio can be improved by repetitive scanning and signal averaging. Fourier transform techniques are normally only used for analysis of pulsed EPR experiments. There is a range of different software for analysis of the spectroscopic data, in particular for simulation.
Sample Holders and Sample Preparation The holders for EPR samples are constructed of a diamagnetic, nonconductive material such as quartz. Electrically conductive
Figure 5 Resonators for EPR spectroscopy. (a) Rectangular cavity; (b) loop-gap resonator.
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materials such as metals cannot be used as they reflect microwaves and prevent penetration of microwaves into the sample. It is not possible to measure EPR spectra of large aqueous samples at frequencies above 1 GHz because of microwave power losses. For measurements in an X-band rectangular
cavity, specially constructed flat cells are used, with a thickness of about 0.3 mm (Figure 6). They are placed in the centre of the cavity, which is a nodal plane of the electric vector, hence minimizing dielectric losses. Oxidation–reduction reactions are used to generate organic or inorganic compounds in their paramagnetic oxidation states, for example quinones in their semiquinone states, or transition metal ions in their paramagnetic states (Table 2). Electrolytically generated radicals may be obtained by means of electrodes placed in the cell above and below the cavity. For kinetic measurements, paramagnets may be generated by mixing solutions and flowing them into a cell inside the cavity (Figure 6 (centre)). For short-lived states of transition metals in solution, samples may be obtained by rapid freezing, in which samples are mixed and squirted into a bath of isopentane at 140 K.
Multifrequency EPR
Figure 6 Sample holders for aqueous samples.
Table 2
Examples of paramagnetic transition ions
Metal ion
Paramagnetic oxidation states
Other states
Vanadium Chromium Manganese Iron Cobalt Nickel Copper Molybdenum
VIV CrIII, CrVI MnII, MNIV FeIII CoII NiI, NiIII CuII MoV
VV, VIII MnIII FeII CoI, CoIII NiII CuI MoIV, MoVI
Note – other oxidation states and isotopes exist for these elements.
Table 3
Although the majority of EPR spectra are still taken at X-band frequency, there are advantages for some applications to use lower or higher microwave frequencies, or a range of frequencies. To operate at each frequency it is usually necessary to use a different microwave bridge and cavity. These frequencies are identified by their frequency bands, as listed in Table 3. In high-frequency spectrometers, superconducting magnets are used. Up to 100 GHz, the microwaves may be obtained by mixing with lower-frequency radiation in a heterodyne arrangement. For higher frequencies, the radiation may be regarded as far infrared, and Fabry–Pe´rot resonators are used which consist of two parabolic mirrors to concentrate the radiation. In low-frequency spectrometers the magnetic field is produced by Helmholtz coils and the resonator is a coil similar to that used in NMR. Some features of the EPR spectrum increase with magnetic field, such as the separation between g factors. Others, such as the separation between hyperfine splittings, do not change, to first order. By altering the microwave frequency it is possible to resolve the effects of multiple electron–nuclear and electron–electron interactions. The EPR spectra of organic radicals at X-band (9 GHz) are dominated by hyperfine splittings by
Microwave wavebands and frequencies
Band
Frequency (GHz) (app.)
l (mm)
Field for g¼2 (mT)
Typical applications
Radiofrequency L S X K Q V W D G
0.25 1 4 9.5 24 35 65 96 140 250
1200 300 75 31.6 12.5 8.6 4.6 3.12 2.14 1.2
8.93 35.7 143 339 857 1250 2322 3430 5000 8931
EPR imaging Aqueous sample EPR Hyperfine splittings Routine spectroscopy
The definitions of bands follow EPR convention and the frequencies are approximate.
Electron spin–spin interactions g factor anisotropy in radicals Large zero-field splittings Even spin system
EPR, Methods
protons and other nuclei. At W-band (96 GHz) the spectra are dominated by the anisotropy of the g factor.
Electron–Nuclear Double Resonance (ENDOR) and TRIPLE Resonance The hyperfine interactions with nuclei adjacent to the paramagnetic centre are often too small to be observed because they are smaller than the EPR line width. Electron–nuclear double resonance is a technique which detects these interactions. In addition to the microwave field Bl a radiofrequency field, B2, is applied at right angles. A commercial design uses a coil wound around the sample tube in a special cavity. The energy levels and transitions relevant to the ENDOR measurement are illustrated in Figure 7. The microwave field, at the EPR resonant frequency, partially saturates the signal, equalizing the populations of the mS¼12 levels. The radiofrequency is swept, and when the latter is at the resonant frequency of the interacting nuclear spins this provides further pathways for electron spin relaxation and the EPR signal is enhanced. The resulting spectrum consists of a pair of lines. The positions of the lines depend on the relative magnitudes of the hyperfine coupling, A, and the nuclear Zeeman frequency,
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nn (the NMR frequency of the nucleus) (Figure 7). In the case where nn > A/2, as for protons, which have a large nuclear moment, the lines will be centred at nn and separated by A. When A/2 > nn, as in the case of strong couplings to other nuclei, the ENDOR spectrum consists of two lines centred at A/2 and separated by 2nn. Hyperfine interactions of the order of a few megahertz can be resolved and provide information about nuclei at distances up to 0.5 nm. An additional advantage of ENDOR is that the number of lines is additive, rather than multiplicative. If there are numerous nuclear spins in the paramagnetic molecule, each type of hyperfine splitting will give just one pair of lines and so the ENDOR spectrum is simpler than the EPR spectrum. This feature is particularly useful in the interpretation of the complex spectra of radicals. TRIPLE resonance is another method which resolves further a spectrum containing multiple hyperfine couplings. It is analogous to the Overhauser effect in NMR. By continuously applying radiofrequency radiation at the resonant frequency of one line in the spectrum, other lines in the ENDOR spectrum are suppressed or enhanced if they are connected to the same transition. This method makes it possible to determine the sign of A, which is used in molecular orbital calculations.
Figure 7 Energy levels for an electron interacting with an I ¼ 12 nucleus, showing the transitions relevant to ENDOR and electron-spin echo envelope modulation (ESEEM), (dotted lines).
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Pulsed EPR Pulsed EPR spectrometers are now commercially available and have some of the same electronic features as NMR spectrometers. The layout of the microwave bridge is similar to that of Figure 4, but in addition a pulse programmer controls the microwave supply through diode switches. The microwave pulses, of duration 5–50 ns, are amplified by a travellingwave tube amplifier, to a power up to 1 kW. The cavity has a lower Q-factor than for CW EPR to allow the microwave field to build up more quickly. The main differences between pulsed EPR and pulsed NMR arise from the broad bandwidth of the EPR spectrum.
Flash Photolysis For the spectra of radicals that are dispersed over a narrow range of frequency, it is possible to detect a free-induction decay (FID). This makes it possible to derive a spectrum by Fourier transformation and observe the spectrum of a transient species induced, for example, by a laser flash which is synchronized with the microwave pulse programmer (Figure 8a). Normally, however, the spectrum is too broad, or the FID decays too rapidly. In this case it is possible to detect an electron-spin echo after a two-pulse (p/2–p–echo) sequence. The spectrum of the flash-induced species is derived by repeating the measurement over a range of magnetic field strength. The lifetime (which should be a minimum of about 100 ns) is measured by repeating the electron-spin echo sequence, while the interval between the flash and the pulses is systematically incremented.
Electron-Spin Relaxation Rates The values of T1 and T2 are measured in different experiments which observe the decay of the electron-spin echo with time; T1 is measured with an inversion-recovery experiment as in NMR, while T2 is observed by a two-pulse echo sequence, as in Figure 8a. The amplitude of the echo decreases with increasing delay time t, owing to loss of ‘phase memory’. The spin–spin relaxation is affected by various factors, including molecular motion and spin–spin interactions between paramagnets.
hyperfine coupling frequencies cause dephasing of the electron spins, and so the echo amplitude is modulated with time (Figure 8c). This can be considered as being due to an interference between the frequencies of the allowed transitions, DmS¼1, with the ‘semi-forbidden’ transitions, DmS¼1, DmI¼1, which are allowed owing to quadrupolar interactions and anisotropy of the hyperfine interaction. Fourier transformation of the time-domain spectrum yields the spectrum of hyperfine frequencies (Figure 8d). Two-dimensional pulsed EPR experiments are also possible, such as HYSCORE (hyperfine sublevel correlation) spectroscopy. This uses a pulse sequence as in Figure 8b, separated by an inversion pulse into two variable time intervals. Fourier transformation in the two time-domains gives a 2D spectrum, in which the effects of multiple hyperfine couplings can be resolved. Pulsed ENDOR is an alternative technique, in which radiofrequency pulses at NMR frequencies are used to perturb the spin-echo sequence (Figure 9). Hyperfine interactions lead to loss of coherence of the electron spins during the mixing period, so the amplitude of the echo is decreased. A plot of echo amplitude against RF frequency yields a spectrum analogous to that of a CW ENDOR spectrometer.
Types of Material Studied Free Radicals Organic free radicals can be produced by one-electron oxidation or reduction reactions, by irradiation processes or by homolytic cleavage of a chemical bond. They may occur in the solid, liquid or gaseous states. Organic radicals in solution give complex EPR spectra. The hyperfine structure of their spectra provides information about the type of radical and the distribution of the unpaired electron in it. Free radicals tend to be unstable and to decay by recombination processes. However, some radicals, particularly those in the solid state, are stable. If they have a half-life of at least a few seconds, they can readily be examined by conventional EPR spectroscopy, using rapid-scan coils to sweep the B0 field. If they are more short-lived, the radical may be stabilized by cooling to low temperatures, or chemically trapped with a spin trap which reacts with the unstable species to produce a more stable radical.
Hyperfine Couplings Electron-spin echo envelope modulation (ESEEM) spectroscopy is a pulsed technique that detects weak hyperfine and quadrupolar couplings in the solid state. It is complementary to ENDOR in that it gives the best results in the intermediate regime of hyperfine couplings where A nN; in addition, it is particularly sensitive to couplings with quadrupolar nuclei such as 2H and 14N. The Mims three-pulse echo sequence is similar to the two-pulse sequence (Figure 8b) except that the p pulse is split into two p/2 pulses separated by time T. The decay of the echo is now determined by the slower spin–lattice relaxation time T1 allowing echoes to be detected over a longer period of time. During the evolution of the spin echo,
Spin Traps Ideally, a spin trap is a diamagnetic compound, which is introduced into a biological system without perturbing it and which reacts rapidly and specifically with a transient free radical to form a stable radical that can be identified from its EPR signal. These requirements are somewhat contradictory. The two most commonly used spin traps for organic radicals are nitroso compounds and nitrones (Table 4). These react with radicals to form nitroxides. The nitroso compounds give an adduct in which the radical added is bonded directly to the nitroxide nitrogen, so that the hyperfine splittings in the EPR signal are more diagnostic of the original radical; however, the
EPR, Methods
Figure 8 Pulsed EPR experiments. (a) flash photolysis, (b)–(d) ESEEM.
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Figure 9 Principle of Mims pulsed ENDOR.
Table 4
Types of spin traps
Type of spin trap
Structure
Suitable application
2-Methyl-2-nitrosopropane (MNP)
C,S-centred radicals
5,5-Dimethyl-1-pyrroline-N-oxide (DMPO)
C,S,O-centred radicals
N-tert-Butyl-a-phenylnitrone (PBN)
C,S,O-centred radicals
FeII(diethyldithiocarbamate)2
Nitric oxide
adducts are less stable and may decay within minutes. Nitrones tend to give more stable adducts which are more difficult to identify.
Spin Labels Spin labels are stable paramagnetic molecules that are introduced into a biological sample, and extend the use of EPR to situations where no endogenous radicals exist. The commonest type of spin labels are nitroxides (aminoxyl) radicals, though other types of radicals and transition metal ions have been used. The advantage of the specific labelling approach is that it makes it possible, through judicious labelling, to investigate the local environment and motion of defined parts of the system under study.
Transition Metals Transition metals are paramagnetic in certain oxidation states (Table 2). Although this paramagnetism is stable, the sample may have to be cooled to low temperatures for the EPR signal to be observed.
Defects in Solids Examples of defects are cation vacancies (V centres), anion vacancies (F centres) and impurities in crystals. Defects can be generated in various ways, such as irradiation with ultraviolet or ionizing radiation, or by imperfect crystallization. An example is a defect (latent image) generated in photographic emulsion by light irradiation. In addition, finely divided solid
EPR, Methods
materials commonly show radical centres due to homolytic cleavage of chemical bonds.
Information from EPR Spectroscopy Identification of the Paramagnet The type of paramagnetic species may be recognized from the characteristic features of its spectrum such as g factors and hyperfine splittings. For free radicals in solution, examination of the pattern of hyperfine splittings can provide information about the number of interacting nuclei and hence the structure of the radical. For example, in the benzoquinone radical (Figure 3a), the splitting by four equivalent protons gives rise to five lines with amplitudes in the ratio 1 : 4 : 6 : 4 : 1. A powerful technique is to substitute atoms in the molecule with nuclei having different nuclear spins, for example deuterium 2H (I¼1) for 1H or 13C (I ¼ 12) for 12C. Examples of nuclear spins and moments are given in Table 1. The observed change in the hyperfine splitting pattern is conclusive evidence of interaction with the nucleus.
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is conclusive, though in the case of semiquinones they may be anion radicals (formed by electron addition) or cation radicals (formed by removal of an electron). The EPR spectra of NiI and NiIII are similar. In these cases further oxidation–reduction experiments are needed to distinguish them. For transition ions such as FeIII, the EPR spectrum is a good indicator of spin state, in this case high spin (S ¼ 52) or low spin (S ¼ 12). The spectra of the high-spin states are influenced by zero-field splittings, in this case giving g factors of up to 10.
Distances The hyperfine coupling between an electron spin and a nucleus or between electron spins consists of two components: an exchange interaction (acting through chemical bonds, and generally isotropic), and a dipolar interaction. The dipolar component is anisotropic and its magnitude is inversely proportional to the (distance)3, and this can be used to estimate distances. In favourable cases, hyperfine couplings from ENDOR can be used to determine distances of protons up to 0.5 nm. Electron spin–spin interactions can be observed as splittings in the EPR spectrum over distances up to 1.5 nm, and relaxation effects at distances up to 4 nm.
Quantification The concentration of unpaired electrons can be determined from the integrated intensity of the EPR spectrum by double integration or by numerical simulation of the spectrum. For paramagnets with spin 12, measured under non-saturating conditions, the integrated intensity for a given concentration is the same, regardless of the nature of the paramagnetic species. Hence the concentration can be referred to a standard material such as CuII.
Spin Hamiltonian Parameters The parameters of the EPR spectrum are described formally by a spin Hamiltonian equation, which summarizes the energies of the different types of interaction. For example, the Hamiltonian for a spin S interacting with a nuclear spin I is
Orientation If the molecules of a paramagnet are orientated, as in a single crystal, the EPR signal consists of narrow lines, which shift as the crystal is rotated in the magnetic field. The angular dependence can be measured precisely using a goniometer. Some ordering is seen in fibres and layered materials, though less precisely than in crystals. From this orientation dependence it is possible to estimate the spin Hamiltonian parameters, yielding detailed information about the axes of the g and A matrices, and hence the orbital states.
Motion
where the operators g and A are shorthand notation for 33 matrices or tensors. The EPR spectrum may be interpreted by computer simulation of the energy of interaction with the magnetic field B0. This provides information about the electronic state of the paramagnet. For radicals, the information can be used in detailed molecular orbital calculations of electronic structure. For transition metal ions, EPR provides information about the coordination geometry, spin state and types of ligands.
The line width of the EPR spectrum of a radical such as a nitroxide in solution is sensitive to motion in the range of correlation times 107–1011 s. This is due to the anisotropy of the 14N hyperfine splitting. If the motion is rapid enough to average this anisotropy, the spectrum shows narrow lines. For slower motion the spectrum broadens out. The rate of motion is determined by simulation, or by comparison with labelled molecules of known correlation time. By means of an experimental technique known as saturation-transfer EPR the spectra may be made to be sensitive to correlation times up to 103 s, as found, for example, in membrane-bound proteins.
Redox and Spin States
EPR Dosimetry
Changes in oxidation states of paramagnets, by adding or removing unpaired electrons, cause the EPR signals to appear and disappear. This can be used to monitor oxidation–reduction reactions, and to measure reduction potentials. Generally the EPR spectrum is a useful indication of the oxidation–reduction state of the species observed. Often the presence of an EPR signal
The build-up of radicals in irradiated solids forms a method of estimating the absorbed dose of ionizing radiation. A standard used in EPR dosimeters is the amino acid alanine, in pellet form, which gives a linear relationship between radical signal amplitude and absorbed dose over several orders of magnitude. Where there has been accidental radiation exposure, the
H ¼ gmB B0 S þ AIS
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EPR of radicals in hydroxyapatite in tooth enamel has been used to estimate the absorbed dose. Irradiation of foods such as meat may be detected by radicals formed in bone.
EPR Dating Buried archaeological samples that contain crystalline materials show radical EPR signals due to the effects of the radiation in the soil. The time of burial can be estimated by taking measurements of the radioactive isotopes in the surrounding soil and observing the signal amplitude after applying an equivalent dose of radiation to the sample. The decay of the radical signal over time depends on the stability of the defects in the material. Dating works best for crystalline material such as silica; bone is unreliable because of recrystallization. The technique has been used for samples dated between 105 and 106 years, which is between the ranges possible for radiocarbon and potassium dating.
Medical Applications Oxygen radicals have been widely investigated in biomedical systems and are of great interest because of their cytotoxic effects and involvement in processes such as inflammation. They may be observed by spin traps (Table 4). Nitric oxide is also generated in conditions such as inflammation, and can be trapped by iron complexes such as iron diethyldithiocarbamate. Oximetry exploits another feature of the spectra of radicals in solution: that they are broadened by paramagnetic interactions with oxygen in solution. With narrow-line radicals it is possible to measure oxygen in human tissues at concentrations below 105 mol dm3.
See also: Chemical Applications of EPR; Chemical Shift and Relaxation Reagents in NMR; Electron Paramagnetic Resonance of
Membrane Proteins; EPR Imaging; EPR Spectroscopy, Theory; Laser Magnetic Resonance; Liquid Crystals and Liquid Crystal Solutions Studied by NMR; Muon Spin Resonance Spectroscopy, Applications; NMR of Paramagnetic Species; NMR Principles; Solid-State NMR of Membrane Proteins in Phospholipid Bilayers; Spin Trapping and Spin Labelling Studied Using EPR Spectroscopy.
Further Reading Abragam A and Bleaney B (1970) Electron Paramagnetic Resonance of Transition Ions. Oxford: Oxford University Press. Atherton NM (1993) Principles of Electron Spin Resonance. Chichester: Ellis Horwood. Bencini A and Gatteschi D (1989) EPR of Exchange Coupled Systems. Berlin: SpringerVerlag. Berliner LJ and Reuben J (1993) EMR of Paramagnetic Molecules: Biological Magnetic Resonance, vol. 13. New York: Plenum. Czoch R and Francik A (1989) Instrumental Effects in Homodyne Electron Paramagnetic Resonance Spectrometers. Chichester: Ellis Horwood. Dikanov SA and Tsvetkov YD (1992) Electron Spin Echo Envelope Modulation (ESEEM) Spectroscopy. Boca Raton, FL: CRC Press. Eaton GR, Eaton SS, and Ohno K (1991) ESR Imaging and In Vivo ESR. Boca Raton, FL: CRC Press. Eaton GR, Eaton SS, and Salikhov KM (1997) Foundations of Modern ESR. Singapore: World Scientific Publishing. Hoff AJ (ed.) (1989) Advanced ESR: Applications in Biology and Biochemistry. Amsterdam: Elsevier. Keijzers CP, Reijerse EJ, and Schmidt J (1989) Pulsed ESR – A New Field of Applications. Amsterdam: North Holland. Kurreck H, Kirste B, and Lubitz W (1988) Electron Nuclear Double Resonance Spectroscopy of Radicals in Solution. Weinheim: VCH Publishers. Lowe DJ (1995) ENDOR and ESR of Metalloproteins. Berlin: Springer. Mabbs FE and Collison D (1992) Electron Paramagnetic Resonance of d Transition Metal Compounds. Amsterdam: Elsevier. Pilbrow JR (1990) Transition Ion Electron Paramagnetic Resonance. Oxford: Oxford University Press. Poole CPJ (1983) Electron Spin Resonance, 2nd edn New York: Wiley. Specialist Periodical Reports on ESR Spectroscopy. Cambridge: Royal Society of Chemistry. Weil JA, Bolton JR, and Wertz JE (1994) Electron Paramagnetic Resonance: Elementary Theory and Practical Applications. New York: Wiley.
N, Nþ
Symbols A B0 B1 B2 g h H I k mI mS
hyperfine coupling constant static magnetic field microwave magnetic field radiofrequency magnetic field electron g factor Planck’s constant Hamiltonian operator nuclear spin operator Boltzmann constant nuclear spin angular momentum electron spin angular momentum
Q S T Tl T2 h l mB n nn t
Introduction Electron paramagnetic resonance (EPR) is also known as electron spin resonance (ESR) or electron magnetic resonance (EMR) spectroscopy; no single name has become generally accepted. It is a means of investigating materials that are paramagnetic, i.e. having unpaired electrons. These include organic free radicals, compounds of transition metal ions and defects in solids. Since the development of the X-band continuouswave spectrometer in the 1950s and 1960s, the basic design of the EPR spectrometer has remained relatively unchanged, while a wide variety of applications in physics, chemistry and biochemistry have been devised. Examples are the observation of radical intermediates in chemical reactions; the determination of electron density distributions on radicals; the observation of rapid motion of spin labels in solution; and the determination of coordination geometry of metal ion sites. Advances in solid-state microwave electronics have led to instrument extensions in many different ways, for specialist applications. Examples are ENDOR and TRIPLE and ESEEM, to measure hyperfine interactions, and low-frequency EPR imaging. The principles of typical applications will be described, with reference to the relevant equipment and sample requirements.
Characteristics of the EPR Spectrum EPR involves the interaction of electromagnetic radiation, usually in the microwave region, with the paramagnetic material in a magnetic field. Because paramagnetic centres are less common than nuclear spins, the method is more selective than the analogous technique of NMR. There are some differences in practice between NMR and EPR that result from the much This article is reproduced from the previous edition, Copyright 1999, Elsevier Ltd.
Encyclopedia of Spectroscopy and Spectrometry, Third Edition
populations of electron energy levels separated by a magnetic field quality factor of a resonator electron spin operator absolute temperature longitudinal (spin–lattice) relaxation time transverse (spin–spin) relaxation time filling factor of a resonator microwave wavelength Bohr magneton microwave frequency nuclear Larmor frequency delay in pulse sequence
greater magnetic moment of the electron compared to that of nuclear spins. The bandwidth of the spectrum is much greater than the parts-per-million scale of NMR. It is impossible to adjust the frequency over such a wide range, owing to the geometry of microwave waveguides, so it is the usual practice to observe the EPR spectrum at fixed frequency by sweeping the magnetic field. The relaxation rates of electron spins are faster than for nuclear spins, so that in some cases (particularly transition metals such as iron) it is necessary to cool the sample to cryogenic temperatures to observe the spectrum. The spectrum is characterized by a number of parameters which give information about the nature of the paramagnetic centres and their surroundings.
Zeeman Interaction The g factor defines the energy of the Zeeman interaction. This splits the energy levels of the paramagnet (Figure 1). At the resonance condition the energy DE required to reverse the direction of the electron spin in a magnetic field B0 is equal to the energy of the microwave quantum hn, given bym DE ¼ hv ¼ gmB B0 where h is Planck’s constant and mB the Bohr magneton. In an EPR spectrum the signals are obtained by increasing the B0 field. The g factor is inversely proportional to B0. For a free electron in a vacuum, g is a constant that is very precisely known (ge¼2.002 319 3044. . .). In a paramagnetic molecule, g varies from this, under the influence of spin–orbit interactions. These increase considerably with atomic number, and are particularly important for lanthanides. In the spin Hamiltonian formalism the effects of spin–orbit coupling are described by treating g as a spectroscopic variable, the ‘spectroscopic splitting factor’, which is characteristic of the paramagnetic centre. Therefore the EPR spectrum may be considered as a spectrum of g factors.
http://dx.doi.org/10.1016/B978-0-12-803224-4.00138-2
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EPR, Methods
Table 1 Isotope
% Natural abundance
Nuclear spin, I
mN
1
H
99.985
1 2
þ2.793
2
H
0.015
1
þ0.857
13
1.11
1 2
þ0.702
14
99.63
1
þ0.404
15
0.37
1 2 5 2 1 2 1 2 3 2 5 2 1 2 7 2 3 2 3 2 5 2 5 2
0.283
C N N
17
0.037
19
100
31
100
33
0.76
O F P S
55
100
57
2.19
59
100
63
69.09
65
30.91
95
15.72
97
9.46
Mn Fe Co Cu Cu Mo Mo
Figure 1 (a) Principle of electron paramagnetic resonance. (b) Effect of hyperfine splitting with a nucleus, l¼1/2.
Hyperfine Interaction The interaction between the magnetic moment of the electron and nuclear spins is a valuable feature of EPR spectra. It introduces splittings of the electron energy levels (Figure 1b). Each nuclear spin I induces a splitting into [2Iþ1] levels. The magnitude of the splitting is defined by the hyperfine coupling constant, A, which is expressed in energy units (usually MHz). Where there are several nuclei, for example protons in a radical, each level is further split by each nuclear hyperfine interaction. The hyperfine coupling can be observed as splitting of the EPR spectrum, if the coupling is greater than the line width. The magnitude of the splitting is given the symbol a, expressed in magnetic field units. The value of A depends on the nuclear moment, and the extent of interaction of the unpaired electron spin density with the nucleus; A has a sign as well as magnitude. If A > 0, the state in which electron and nuclear spins align antiparallel is of lower energy. Measurements of the magnitude and sign of hyperfine couplings provide some of the most detailed experimental evidence for electronic structures of molecules. They have been used to verify the results of molecular orbital calculations. In EPR spectra of transition ions, the hyperfine interaction gives rise to characteristic splittings, for example for copper
Some nuclei with magnetic moments
1.89 þ2.629 þ1.132 þ0.643 þ3.444 þ0.090 þ4.649 þ2.226 þ2.385 0.913 0.933
(I ¼ 32, 4 lines) and manganese (I ¼ 52, 6 lines) (Figure 2a). It can be used to identify paramagnetic centres and determine the electron density distribution over radicals. Isotopic substitution can be used (Table 1) to identify specific metals, for example 57Fe for natural iron. Interactions with nuclei of ligands, sometimes called superhyperfine splittings, allow the determination of the electron density distribution in transition metal complexes. Nuclei with spins greater than S ¼ 12 have a quadrupole moment and this gives rise to further splitting of the energy levels.
Interactions between Electrons (Fine Structure Interactions) The magnetic moment of the electron is 658 times that of the proton, so that interactions between electrons are of greater energy than those between nuclear spins, and are detectable over greater distances. This has a number of consequences. For example, when two or more electron spins are present in a paramagnetic centre such as a transition ion with spin S > 12 or an organic triplet state (S¼1), coupling of the electron spins gives rise to fine structure splittings (known as zero-field splittings) which strongly influence the apparent g factor. If the spin is an integral value, the splitting between the energy levels may be larger than the X-band microwave quantum, and no EPR signal is detected. However, for an odd number of electron spins there are always energy levels that can only be split by the magnetic field. As a consequence paramagnets with halfintegral spin, such as high-spin FeIII and CoII, are EPRdetectable (see Figure 2b). For the latter ions, with S ¼ 52, g factors may extend from 10 to 0. EPR spectra of transition ions are often measured in the solid state so that the spectrum is broadened by anisotropy of the g factor.
EPR, Methods
529
Figure 2 EPR spectra of transition ions; (a) manganese ions in aqueous solution; note the six-line hyperfine splitting owing to the 55Mn nucleus (I¼52); (b) high-spin FeIII in metmyoglobin, frozen at 77 K; note the g factors at 6.0 and 2.0.
Electron spin–spin interactions occur between paramagnetic centres in solution and in the solid state. This causes splitting or broadening of the EPR signal. For solid paramagnetic materials the broadening may be so great as to render the X-band EPR spectrum undetectable. For EPR spectra in the solid state, the material must usually be magnetically dilute, for example doped into a diamagnetic host material. Paramagnets in biological materials such as proteins are usually fixed within the protein matrix and are thus detectable. Spin–spin interactions give rise to characteristic changes in line shape, and enhancement of the electron-spin relaxation rate, from which it is possible to estimate distances between the paramagnetic centres.
Anisotropy The Zeeman, dipolar hyperfine and fine structure interactions are all anisotropic, meaning that the energy of interaction depends on the angle between the paramagnetic centre and the applied magnetic field. In solution spectra of small molecules, the anisotropy is averaged, and spectral lines are narrow. Note, however, that the isotropic hyperfine interaction does not average to zero and so there is still hyperfine splitting (e.g. Figure 2a and Figure 3a). For randomly oriented samples in the solid state (so-called powder spectra), the distribution of molecules in different orientations gives rise to characteristic broadening of the line shape (Figure 2b and Figure 3c).
Figure 3 EPR spectra of radicals; (a) benzoquinone anion radical in solution; (b) the nitroxide TEMPOL in solution and (c) in a photosynthetic reaction centre.
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EPR, Methods
Effects of Temperature, Electron-Spin Relaxation and Spectral Linewidths Temperature has a number of effects on the EPR spectrum. The populations of the electron energy levels N and Nþ (Figure 1a) differ by a small amount because of the Boltzmann distribution: Nþ DE gmB B0 ¼ exp ¼ exp N kB T kB T where kB is the Boltzmann constant and T the absolute temperature. At room temperature and a magnetic field of 0.32 T, the difference is about 0.07% of the unpaired electrons. It increases at higher microwave frequencies (hence higher fields), and at lower temperatures. The spin–lattice relaxation, with a characteristic time T1, is responsible for maintaining the population difference between levels N and Nþ. The spin–spin relaxation time T2 reflects the lifetime of the excited state and its effect on the line width. If the electron-spin relaxation rate is too rapid, the lifetime of the excited state is short and the EPR spectrum becomes broadened. At high temperatures the spectrum may become too broad for detection, hence the use of cryogenic temperatures for some transition ions. However, if the spin–lattice relaxation is too long, the population difference NNþ cannot be maintained, and the amplitude of the signal is attenuated, a situation known as microwave power saturation. Electron-spin relaxation times may be estimated by measuring the amplitude of the signal as a function of applied microwave power.
Figure 4 Outline of a typical continuous-wave EPR spectrometer.
Operation of the Spectrometer The outline of a conventional continuous-wave EPR spectrometer is shown in Figure 4. The term ‘continuous-wave (CW)’ refers to the fact that microwaves are applied throughout the measurement. It is designed to optimize the weak EPR signals originating from the sample, against a background of noise from the source. The microwave source is a reflex klystron (a type of thermionic valve) or a Gunn diode (a semiconductor device). The detector is a microwave diode. The operating frequency is typically in the X-band (9.5 GHz). This frequency is a compromise; higher frequencies increase the ratio N: Nþ (and hence sensitivity) but require smaller cavities and thus smaller sample size (and hence number of spins being measured). A typical sample volume is of the order of 0.1 cm3. The microwave circuit is known as the microwave bridge, to emphasize that it is a balanced circuit. The source is tuned to the resonant frequency of the cavity. Microwaves pass through waveguides to the cavity via a circulator, which ensures that signal arising from the sample in the cavity passes to the detector. The reference arm serves to balance the signal with the input microwave power. The circuit is optimally tuned by matching its impedance with the cavity using the iris, to a condition known as critical coupling. In this situation the intensity of the microwave field B1 at the sample is enhanced by the Q-factor of the cavity, typically several thousand-fold. When electron paramagnetic resonance occurs in the sample, a small amount of power is transmitted to the detector and is amplified and recorded.
EPR, Methods
The homogeneous B0 field is provided by an electromagnet. EPR spectra are obtained by modulation of the field by a small amount, at a frequency of 100 kHz. A lock-in amplifier detects the EPR signal in phase with the modulation. Modulation and phase-sensitive detection is a standard method of noise rejection and enhances the signal-to-noise ratio, and hence the sensitivity of the technique, by as much as 105. It gives rise to the characteristic first-harmonic (first-derivative) line shape. Although the absorption spectrum could be derived from this by integration, spectra are usually retained as the derivative form as it emphasizes narrow hyperfine splittings and other features.
Temperature Control The form of the paramagnetic material may be solid, liquid or gas, and so appropriate temperature control of the sample is needed. The temperature of the sample may be controlled by flowing gas through a quartz vacuum jacket. For low temperatures, helium is used. The sample may be held in a Dewar of liquid nitrogen or helium. For smaller resonator designs such as loop-gaps, the whole resonator is immersed in a cryostat containing helium or nitrogen.
531
example through a waveguide of length l which prevents microwave leakage. The applied magnetic field B0 is modulated with Helmholtz coils in the walls of the cavity. The B0 and Bl fields are oriented at right angles, which gives a maximum magnetic resonance interactions for S ¼ 12 paramagnets. For paramagnets with an integer spin, the resonant transition is forbidden in this geometry. Parallel mode cavities are used for this situation, in which Bl is parallel to B0. In the loop-gap resonator (Figure 5b), the coupling loop acts as an antenna to transmit microwave power to and from the bridge to the split-ring resonator element. The number of gaps is variable, depending on the sample size. The microwave magnetic field Bl circulates in the ring, while the electric component is mostly confined to the gaps. Magnetic field modulation is also by external coils (not shown). Loop-gap resonators have better filling factors than rectangular cavities, so that the resonator can be smaller and the sample tube larger. They are particularly effective for lossy samples such as aquesous solutions. Other designs of cavity are possible, including cylindrical resonators constructed of an inert dielectric material such as sapphire (alumina).
Computer Control and Data Acquisition
Resonators The quality, or Q factor, of the microwave cavity or resonator is a measure of its efficiency at concentrating microwave energy. For a resonant a.c. circuit it is given by Q¼
2pðEnergy storedÞ ðEnergy dissipated per cycleÞ
The filling factor is the fraction of the microwave magnetic field Bl which bisects the sample. Two examples of resonators used in EPR are illustrated in Figure 5. Rectangular cavities (Figure 5(a)) are of metal which is coated with silver and gold for high conductivity. The sample is positioned at the maximum of the microwave magnetic field, Bl. It may be irradiated with ultraviolet or visible light, in this
Most operations of the instrument are under computer control. The spectrum is recorded as a series of data points, along a linear axis of magnetic field. The signal-to-noise ratio can be improved by repetitive scanning and signal averaging. Fourier transform techniques are normally only used for analysis of pulsed EPR experiments. There is a range of different software for analysis of the spectroscopic data, in particular for simulation.
Sample Holders and Sample Preparation The holders for EPR samples are constructed of a diamagnetic, nonconductive material such as quartz. Electrically conductive
Figure 5 Resonators for EPR spectroscopy. (a) Rectangular cavity; (b) loop-gap resonator.
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EPR, Methods
materials such as metals cannot be used as they reflect microwaves and prevent penetration of microwaves into the sample. It is not possible to measure EPR spectra of large aqueous samples at frequencies above 1 GHz because of microwave power losses. For measurements in an X-band rectangular
cavity, specially constructed flat cells are used, with a thickness of about 0.3 mm (Figure 6). They are placed in the centre of the cavity, which is a nodal plane of the electric vector, hence minimizing dielectric losses. Oxidation–reduction reactions are used to generate organic or inorganic compounds in their paramagnetic oxidation states, for example quinones in their semiquinone states, or transition metal ions in their paramagnetic states (Table 2). Electrolytically generated radicals may be obtained by means of electrodes placed in the cell above and below the cavity. For kinetic measurements, paramagnets may be generated by mixing solutions and flowing them into a cell inside the cavity (Figure 6 (centre)). For short-lived states of transition metals in solution, samples may be obtained by rapid freezing, in which samples are mixed and squirted into a bath of isopentane at 140 K.
Multifrequency EPR
Figure 6 Sample holders for aqueous samples.
Table 2
Examples of paramagnetic transition ions
Metal ion
Paramagnetic oxidation states
Other states
Vanadium Chromium Manganese Iron Cobalt Nickel Copper Molybdenum
VIV CrIII, CrVI MnII, MNIV FeIII CoII NiI, NiIII CuII MoV
VV, VIII MnIII FeII CoI, CoIII NiII CuI MoIV, MoVI
Note – other oxidation states and isotopes exist for these elements.
Table 3
Although the majority of EPR spectra are still taken at X-band frequency, there are advantages for some applications to use lower or higher microwave frequencies, or a range of frequencies. To operate at each frequency it is usually necessary to use a different microwave bridge and cavity. These frequencies are identified by their frequency bands, as listed in Table 3. In high-frequency spectrometers, superconducting magnets are used. Up to 100 GHz, the microwaves may be obtained by mixing with lower-frequency radiation in a heterodyne arrangement. For higher frequencies, the radiation may be regarded as far infrared, and Fabry–Pe´rot resonators are used which consist of two parabolic mirrors to concentrate the radiation. In low-frequency spectrometers the magnetic field is produced by Helmholtz coils and the resonator is a coil similar to that used in NMR. Some features of the EPR spectrum increase with magnetic field, such as the separation between g factors. Others, such as the separation between hyperfine splittings, do not change, to first order. By altering the microwave frequency it is possible to resolve the effects of multiple electron–nuclear and electron–electron interactions. The EPR spectra of organic radicals at X-band (9 GHz) are dominated by hyperfine splittings by
Microwave wavebands and frequencies
Band
Frequency (GHz) (app.)
l (mm)
Field for g¼2 (mT)
Typical applications
Radiofrequency L S X K Q V W D G
0.25 1 4 9.5 24 35 65 96 140 250
1200 300 75 31.6 12.5 8.6 4.6 3.12 2.14 1.2
8.93 35.7 143 339 857 1250 2322 3430 5000 8931
EPR imaging Aqueous sample EPR Hyperfine splittings Routine spectroscopy
The definitions of bands follow EPR convention and the frequencies are approximate.
Electron spin–spin interactions g factor anisotropy in radicals Large zero-field splittings Even spin system
EPR, Methods
protons and other nuclei. At W-band (96 GHz) the spectra are dominated by the anisotropy of the g factor.
Electron–Nuclear Double Resonance (ENDOR) and TRIPLE Resonance The hyperfine interactions with nuclei adjacent to the paramagnetic centre are often too small to be observed because they are smaller than the EPR line width. Electron–nuclear double resonance is a technique which detects these interactions. In addition to the microwave field Bl a radiofrequency field, B2, is applied at right angles. A commercial design uses a coil wound around the sample tube in a special cavity. The energy levels and transitions relevant to the ENDOR measurement are illustrated in Figure 7. The microwave field, at the EPR resonant frequency, partially saturates the signal, equalizing the populations of the mS¼12 levels. The radiofrequency is swept, and when the latter is at the resonant frequency of the interacting nuclear spins this provides further pathways for electron spin relaxation and the EPR signal is enhanced. The resulting spectrum consists of a pair of lines. The positions of the lines depend on the relative magnitudes of the hyperfine coupling, A, and the nuclear Zeeman frequency,
533
nn (the NMR frequency of the nucleus) (Figure 7). In the case where nn > A/2, as for protons, which have a large nuclear moment, the lines will be centred at nn and separated by A. When A/2 > nn, as in the case of strong couplings to other nuclei, the ENDOR spectrum consists of two lines centred at A/2 and separated by 2nn. Hyperfine interactions of the order of a few megahertz can be resolved and provide information about nuclei at distances up to 0.5 nm. An additional advantage of ENDOR is that the number of lines is additive, rather than multiplicative. If there are numerous nuclear spins in the paramagnetic molecule, each type of hyperfine splitting will give just one pair of lines and so the ENDOR spectrum is simpler than the EPR spectrum. This feature is particularly useful in the interpretation of the complex spectra of radicals. TRIPLE resonance is another method which resolves further a spectrum containing multiple hyperfine couplings. It is analogous to the Overhauser effect in NMR. By continuously applying radiofrequency radiation at the resonant frequency of one line in the spectrum, other lines in the ENDOR spectrum are suppressed or enhanced if they are connected to the same transition. This method makes it possible to determine the sign of A, which is used in molecular orbital calculations.
Figure 7 Energy levels for an electron interacting with an I ¼ 12 nucleus, showing the transitions relevant to ENDOR and electron-spin echo envelope modulation (ESEEM), (dotted lines).
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EPR, Methods
Pulsed EPR Pulsed EPR spectrometers are now commercially available and have some of the same electronic features as NMR spectrometers. The layout of the microwave bridge is similar to that of Figure 4, but in addition a pulse programmer controls the microwave supply through diode switches. The microwave pulses, of duration 5–50 ns, are amplified by a travellingwave tube amplifier, to a power up to 1 kW. The cavity has a lower Q-factor than for CW EPR to allow the microwave field to build up more quickly. The main differences between pulsed EPR and pulsed NMR arise from the broad bandwidth of the EPR spectrum.
Flash Photolysis For the spectra of radicals that are dispersed over a narrow range of frequency, it is possible to detect a free-induction decay (FID). This makes it possible to derive a spectrum by Fourier transformation and observe the spectrum of a transient species induced, for example, by a laser flash which is synchronized with the microwave pulse programmer (Figure 8a). Normally, however, the spectrum is too broad, or the FID decays too rapidly. In this case it is possible to detect an electron-spin echo after a two-pulse (p/2–p–echo) sequence. The spectrum of the flash-induced species is derived by repeating the measurement over a range of magnetic field strength. The lifetime (which should be a minimum of about 100 ns) is measured by repeating the electron-spin echo sequence, while the interval between the flash and the pulses is systematically incremented.
Electron-Spin Relaxation Rates The values of T1 and T2 are measured in different experiments which observe the decay of the electron-spin echo with time; T1 is measured with an inversion-recovery experiment as in NMR, while T2 is observed by a two-pulse echo sequence, as in Figure 8a. The amplitude of the echo decreases with increasing delay time t, owing to loss of ‘phase memory’. The spin–spin relaxation is affected by various factors, including molecular motion and spin–spin interactions between paramagnets.
hyperfine coupling frequencies cause dephasing of the electron spins, and so the echo amplitude is modulated with time (Figure 8c). This can be considered as being due to an interference between the frequencies of the allowed transitions, DmS¼1, with the ‘semi-forbidden’ transitions, DmS¼1, DmI¼1, which are allowed owing to quadrupolar interactions and anisotropy of the hyperfine interaction. Fourier transformation of the time-domain spectrum yields the spectrum of hyperfine frequencies (Figure 8d). Two-dimensional pulsed EPR experiments are also possible, such as HYSCORE (hyperfine sublevel correlation) spectroscopy. This uses a pulse sequence as in Figure 8b, separated by an inversion pulse into two variable time intervals. Fourier transformation in the two time-domains gives a 2D spectrum, in which the effects of multiple hyperfine couplings can be resolved. Pulsed ENDOR is an alternative technique, in which radiofrequency pulses at NMR frequencies are used to perturb the spin-echo sequence (Figure 9). Hyperfine interactions lead to loss of coherence of the electron spins during the mixing period, so the amplitude of the echo is decreased. A plot of echo amplitude against RF frequency yields a spectrum analogous to that of a CW ENDOR spectrometer.
Types of Material Studied Free Radicals Organic free radicals can be produced by one-electron oxidation or reduction reactions, by irradiation processes or by homolytic cleavage of a chemical bond. They may occur in the solid, liquid or gaseous states. Organic radicals in solution give complex EPR spectra. The hyperfine structure of their spectra provides information about the type of radical and the distribution of the unpaired electron in it. Free radicals tend to be unstable and to decay by recombination processes. However, some radicals, particularly those in the solid state, are stable. If they have a half-life of at least a few seconds, they can readily be examined by conventional EPR spectroscopy, using rapid-scan coils to sweep the B0 field. If they are more short-lived, the radical may be stabilized by cooling to low temperatures, or chemically trapped with a spin trap which reacts with the unstable species to produce a more stable radical.
Hyperfine Couplings Electron-spin echo envelope modulation (ESEEM) spectroscopy is a pulsed technique that detects weak hyperfine and quadrupolar couplings in the solid state. It is complementary to ENDOR in that it gives the best results in the intermediate regime of hyperfine couplings where A nN; in addition, it is particularly sensitive to couplings with quadrupolar nuclei such as 2H and 14N. The Mims three-pulse echo sequence is similar to the two-pulse sequence (Figure 8b) except that the p pulse is split into two p/2 pulses separated by time T. The decay of the echo is now determined by the slower spin–lattice relaxation time T1 allowing echoes to be detected over a longer period of time. During the evolution of the spin echo,
Spin Traps Ideally, a spin trap is a diamagnetic compound, which is introduced into a biological system without perturbing it and which reacts rapidly and specifically with a transient free radical to form a stable radical that can be identified from its EPR signal. These requirements are somewhat contradictory. The two most commonly used spin traps for organic radicals are nitroso compounds and nitrones (Table 4). These react with radicals to form nitroxides. The nitroso compounds give an adduct in which the radical added is bonded directly to the nitroxide nitrogen, so that the hyperfine splittings in the EPR signal are more diagnostic of the original radical; however, the
EPR, Methods
Figure 8 Pulsed EPR experiments. (a) flash photolysis, (b)–(d) ESEEM.
535
536
EPR, Methods
Figure 9 Principle of Mims pulsed ENDOR.
Table 4
Types of spin traps
Type of spin trap
Structure
Suitable application
2-Methyl-2-nitrosopropane (MNP)
C,S-centred radicals
5,5-Dimethyl-1-pyrroline-N-oxide (DMPO)
C,S,O-centred radicals
N-tert-Butyl-a-phenylnitrone (PBN)
C,S,O-centred radicals
FeII(diethyldithiocarbamate)2
Nitric oxide
adducts are less stable and may decay within minutes. Nitrones tend to give more stable adducts which are more difficult to identify.
Spin Labels Spin labels are stable paramagnetic molecules that are introduced into a biological sample, and extend the use of EPR to situations where no endogenous radicals exist. The commonest type of spin labels are nitroxides (aminoxyl) radicals, though other types of radicals and transition metal ions have been used. The advantage of the specific labelling approach is that it makes it possible, through judicious labelling, to investigate the local environment and motion of defined parts of the system under study.
Transition Metals Transition metals are paramagnetic in certain oxidation states (Table 2). Although this paramagnetism is stable, the sample may have to be cooled to low temperatures for the EPR signal to be observed.
Defects in Solids Examples of defects are cation vacancies (V centres), anion vacancies (F centres) and impurities in crystals. Defects can be generated in various ways, such as irradiation with ultraviolet or ionizing radiation, or by imperfect crystallization. An example is a defect (latent image) generated in photographic emulsion by light irradiation. In addition, finely divided solid
EPR, Methods
materials commonly show radical centres due to homolytic cleavage of chemical bonds.
Information from EPR Spectroscopy Identification of the Paramagnet The type of paramagnetic species may be recognized from the characteristic features of its spectrum such as g factors and hyperfine splittings. For free radicals in solution, examination of the pattern of hyperfine splittings can provide information about the number of interacting nuclei and hence the structure of the radical. For example, in the benzoquinone radical (Figure 3a), the splitting by four equivalent protons gives rise to five lines with amplitudes in the ratio 1 : 4 : 6 : 4 : 1. A powerful technique is to substitute atoms in the molecule with nuclei having different nuclear spins, for example deuterium 2H (I¼1) for 1H or 13C (I ¼ 12) for 12C. Examples of nuclear spins and moments are given in Table 1. The observed change in the hyperfine splitting pattern is conclusive evidence of interaction with the nucleus.
537
is conclusive, though in the case of semiquinones they may be anion radicals (formed by electron addition) or cation radicals (formed by removal of an electron). The EPR spectra of NiI and NiIII are similar. In these cases further oxidation–reduction experiments are needed to distinguish them. For transition ions such as FeIII, the EPR spectrum is a good indicator of spin state, in this case high spin (S ¼ 52) or low spin (S ¼ 12). The spectra of the high-spin states are influenced by zero-field splittings, in this case giving g factors of up to 10.
Distances The hyperfine coupling between an electron spin and a nucleus or between electron spins consists of two components: an exchange interaction (acting through chemical bonds, and generally isotropic), and a dipolar interaction. The dipolar component is anisotropic and its magnitude is inversely proportional to the (distance)3, and this can be used to estimate distances. In favourable cases, hyperfine couplings from ENDOR can be used to determine distances of protons up to 0.5 nm. Electron spin–spin interactions can be observed as splittings in the EPR spectrum over distances up to 1.5 nm, and relaxation effects at distances up to 4 nm.
Quantification The concentration of unpaired electrons can be determined from the integrated intensity of the EPR spectrum by double integration or by numerical simulation of the spectrum. For paramagnets with spin 12, measured under non-saturating conditions, the integrated intensity for a given concentration is the same, regardless of the nature of the paramagnetic species. Hence the concentration can be referred to a standard material such as CuII.
Spin Hamiltonian Parameters The parameters of the EPR spectrum are described formally by a spin Hamiltonian equation, which summarizes the energies of the different types of interaction. For example, the Hamiltonian for a spin S interacting with a nuclear spin I is
Orientation If the molecules of a paramagnet are orientated, as in a single crystal, the EPR signal consists of narrow lines, which shift as the crystal is rotated in the magnetic field. The angular dependence can be measured precisely using a goniometer. Some ordering is seen in fibres and layered materials, though less precisely than in crystals. From this orientation dependence it is possible to estimate the spin Hamiltonian parameters, yielding detailed information about the axes of the g and A matrices, and hence the orbital states.
Motion
where the operators g and A are shorthand notation for 33 matrices or tensors. The EPR spectrum may be interpreted by computer simulation of the energy of interaction with the magnetic field B0. This provides information about the electronic state of the paramagnet. For radicals, the information can be used in detailed molecular orbital calculations of electronic structure. For transition metal ions, EPR provides information about the coordination geometry, spin state and types of ligands.
The line width of the EPR spectrum of a radical such as a nitroxide in solution is sensitive to motion in the range of correlation times 107–1011 s. This is due to the anisotropy of the 14N hyperfine splitting. If the motion is rapid enough to average this anisotropy, the spectrum shows narrow lines. For slower motion the spectrum broadens out. The rate of motion is determined by simulation, or by comparison with labelled molecules of known correlation time. By means of an experimental technique known as saturation-transfer EPR the spectra may be made to be sensitive to correlation times up to 103 s, as found, for example, in membrane-bound proteins.
Redox and Spin States
EPR Dosimetry
Changes in oxidation states of paramagnets, by adding or removing unpaired electrons, cause the EPR signals to appear and disappear. This can be used to monitor oxidation–reduction reactions, and to measure reduction potentials. Generally the EPR spectrum is a useful indication of the oxidation–reduction state of the species observed. Often the presence of an EPR signal
The build-up of radicals in irradiated solids forms a method of estimating the absorbed dose of ionizing radiation. A standard used in EPR dosimeters is the amino acid alanine, in pellet form, which gives a linear relationship between radical signal amplitude and absorbed dose over several orders of magnitude. Where there has been accidental radiation exposure, the
H ¼ gmB B0 S þ AIS
538
EPR, Methods
EPR of radicals in hydroxyapatite in tooth enamel has been used to estimate the absorbed dose. Irradiation of foods such as meat may be detected by radicals formed in bone.
EPR Dating Buried archaeological samples that contain crystalline materials show radical EPR signals due to the effects of the radiation in the soil. The time of burial can be estimated by taking measurements of the radioactive isotopes in the surrounding soil and observing the signal amplitude after applying an equivalent dose of radiation to the sample. The decay of the radical signal over time depends on the stability of the defects in the material. Dating works best for crystalline material such as silica; bone is unreliable because of recrystallization. The technique has been used for samples dated between 105 and 106 years, which is between the ranges possible for radiocarbon and potassium dating.
Medical Applications Oxygen radicals have been widely investigated in biomedical systems and are of great interest because of their cytotoxic effects and involvement in processes such as inflammation. They may be observed by spin traps (Table 4). Nitric oxide is also generated in conditions such as inflammation, and can be trapped by iron complexes such as iron diethyldithiocarbamate. Oximetry exploits another feature of the spectra of radicals in solution: that they are broadened by paramagnetic interactions with oxygen in solution. With narrow-line radicals it is possible to measure oxygen in human tissues at concentrations below 105 mol dm3.
See also: Chemical Applications of EPR; Chemical Shift and Relaxation Reagents in NMR; Electron Paramagnetic Resonance of
Membrane Proteins; EPR Imaging; EPR Spectroscopy, Theory; Laser Magnetic Resonance; Liquid Crystals and Liquid Crystal Solutions Studied by NMR; Muon Spin Resonance Spectroscopy, Applications; NMR of Paramagnetic Species; NMR Principles; Solid-State NMR of Membrane Proteins in Phospholipid Bilayers; Spin Trapping and Spin Labelling Studied Using EPR Spectroscopy.
Further Reading Abragam A and Bleaney B (1970) Electron Paramagnetic Resonance of Transition Ions. Oxford: Oxford University Press. Atherton NM (1993) Principles of Electron Spin Resonance. Chichester: Ellis Horwood. Bencini A and Gatteschi D (1989) EPR of Exchange Coupled Systems. Berlin: SpringerVerlag. Berliner LJ and Reuben J (1993) EMR of Paramagnetic Molecules: Biological Magnetic Resonance, vol. 13. New York: Plenum. Czoch R and Francik A (1989) Instrumental Effects in Homodyne Electron Paramagnetic Resonance Spectrometers. Chichester: Ellis Horwood. Dikanov SA and Tsvetkov YD (1992) Electron Spin Echo Envelope Modulation (ESEEM) Spectroscopy. Boca Raton, FL: CRC Press. Eaton GR, Eaton SS, and Ohno K (1991) ESR Imaging and In Vivo ESR. Boca Raton, FL: CRC Press. Eaton GR, Eaton SS, and Salikhov KM (1997) Foundations of Modern ESR. Singapore: World Scientific Publishing. Hoff AJ (ed.) (1989) Advanced ESR: Applications in Biology and Biochemistry. Amsterdam: Elsevier. Keijzers CP, Reijerse EJ, and Schmidt J (1989) Pulsed ESR – A New Field of Applications. Amsterdam: North Holland. Kurreck H, Kirste B, and Lubitz W (1988) Electron Nuclear Double Resonance Spectroscopy of Radicals in Solution. Weinheim: VCH Publishers. Lowe DJ (1995) ENDOR and ESR of Metalloproteins. Berlin: Springer. Mabbs FE and Collison D (1992) Electron Paramagnetic Resonance of d Transition Metal Compounds. Amsterdam: Elsevier. Pilbrow JR (1990) Transition Ion Electron Paramagnetic Resonance. Oxford: Oxford University Press. Poole CPJ (1983) Electron Spin Resonance, 2nd edn New York: Wiley. Specialist Periodical Reports on ESR Spectroscopy. Cambridge: Royal Society of Chemistry. Weil JA, Bolton JR, and Wertz JE (1994) Electron Paramagnetic Resonance: Elementary Theory and Practical Applications. New York: Wiley.