8.1 Radical Pairs Formed by Photolysis

8.1.1 Hydroquinone in Sulfuric Acid

Many important physicochemical processes form paramagnetic centers in pairs. For instance, the ultraviolet, or UV, photolysis of solids often produces an electron which becomes trapped by acceptors or the medium after travelling some distance. The holes resulting from loss of these electrons undergo analogous motion and trapping. Reactions of products with each other also occur. The distance between the pairs of paramagnetic products is described by a distance distribution function \(F(r)\) and can be studied by PELDOR. If \(F(r)\) is rather broad, the PELDOR signal has no visible oscillations. Nevertheless, information on the distribution of radical pairs can be obtained from analysis of the PELDOR time trace.

The pioneering PELDOR study [4] investigated radical pairs, composed of a hydrogen atom and a hydroquinone radical, trapped in frozen 8 M aqueous H2SO4 or D2SO4 glasses containing dissolved hydroquinone. The paramagnetic centers are formed by photoionization of the hydroquinone Ar(OH)2 by UV light at 77 K:

$$\frac{{\begin{array}{*{20}c} {{\text{Ar}}({\text{OH)}}_{2} \mathop \to \limits^{\text{UV}} {\text{Ar}}({{\text{OH)}}_{2}}^{\cdot + } + {\text{e}}^{\cdot - } } \\ {{\text{e}}^{\cdot - } + {{\text{H}}_{3}} {\text{O}}^{ + } \to {\text{H}}^{ \cdot } + {\text{H}}_{2} {\text{O}}} \\ \end{array} }}{{{\text{Ar}}({\text{OH}})_{2} + {\text{H}}_{3} {\text{O}}^{ + } \mathop \to \limits^{\text{UV}} {\text{Ar}}({{\text{OH)}}_{2}}^{\cdot + } + {\text{H}}^{ \cdot } + {\text{H}}_{2} {\text{O}}}}$$

The observed distance distribution is governed by two factors: (1) the free path length of an electron prior to trapping by \({\text{H}}_{3} {\text{O}}^{ + }\); and (2) the diffusion path length of hydrogen atoms before trapping in the matrix. In the PELDOR experiments, the hydrogen atoms were the A spins and produced the spin echo signals. The pump pulse was applied at the EPR frequency of the hydroquinone radical ions \({\text{Ar}}({{\text{OH)}}_{2}}^{\cdot + }\), which were the B spins, Fig. 8.1a. The PELDOR time trace \(V(T)\) from the hydrogen atoms depends on the concentration of hydroquinone radical ions. This means that each hydrogen atom has dipolar interactions not just with its partner, or geminate, hydroquinone radical, but also with other hydroquinone radicals.

Fig. 8.1
figure 1

Reprinted from Milov et al. [4]

UV-irradiated, frozen hydroquinone solutions in 8 M H2SO4, a EPR spectrum of paramagnetic centers formed in this system: 1 hydroquinone radicals, B spins and 2 hydrogen atoms, A spins; b the \(F(r)\) function calculated from the PELDOR data.

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The PELDOR time trace can be separated into \(V(T) = V_{INTER } V_{INTRA}\) because the hydroquinone radicals are distributed uniformly throughout the matrix, Eq. 1.13. The \(V_{INTRA}\) was determined from the dependence of \(V(T)\) on the concentration of hydroquinone radicals, and was then used to determine \(F(r)\), approximating \(\Phi (T)\), Eq. 1.11, in those early days of PELDOR, as a step function. The PELDOR data gave a distribution function with a maximum at 4.5 nm, Fig. 8.1. Integration of \(F(r)\) reveals that 63% of the radicals are within 8.5 nm of their geminate radical partner and nearly all are within 10 nm. The actual shape of \(F(r)\) is difficult to determine at the longer distances because the distant radical pairs have little impact on \(V(T)\).

8.1.2 Aromatic Molecules in Hydrocarbons

The UV photolysis of aromatic compounds in hydrocarbon solutions at 77 K produces trapped solvent radicals. The mechanism for their formation involves absorption of two photons by an aromatic molecule with subsequent transfer of energy or charge to a nearby hydrocarbon solvent molecule followed by radical decomposition [5].

UV photolysis of naphthalene in glassy decalin at 77 K by light with λ > 290 nm produces radicals whose EPR spectrum consists of six non-equidistant lines [6]. This spectrum belongs to radicals formed by abstraction of a hydrogen atom from a decalin molecule. The PELDOR time trace \(V(T)\), at low concentrations of decalin radicals, reaches a limiting value \(V_{p}\) rather quickly, by \(T\sim100\,{\text{ns}}\). Such behavior is characteristic of radicals distributed in clusters. The \(V(T)\) of nitroxyl biradicals 3-9 and 3-10 have the same shape.

The PELDOR measurements used a bimodal resonator Sect. 2.5 whose modes were independently tuned to different lines of the decalin radical for \(\omega_{A}\) and \(\omega_{B}\). This simplified the study of the \(V_{p}\) dependence on \(p_{B}\). Changing the \(B_{0}\) value moved the EPR spectrum relative to the pump and observe frequencies while the pulse amplitudes and durations remained constant. The \(V_{p}\) is a linear function of \(p_{B}\) with a slope that is independent of radical concentration or the extent of photolysis, Fig. 8.2. The relation \(V_{p} \approx 1 - (N - 1)p_{B}\), Eq. 1.26, was first derived for analysis of this data [6]. The slope of the experimental straight line gave the number of radicals per cluster as \(N = 1.85 \pm 0.2\). Thus, sensitized low-temperature photolysis of decalin produces stabilized, decalin radicals pairs. A limiting distance of 2.5 nm between radicals in the pair was estimated.

Fig. 8.2
figure 2

Reprinted from Milov et al. [6] with permission of Elsevier B.V., copyright 1984

Plots of the limiting \(V_{p}\) values versus \(p_{B}\): a biradical 3.9, b decalin radicals at 5.6 × 1017 cm−3 and c decalin radicals at 3 × 1017 cm−3.

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8.2 Radical Pairs in Photosynthetic Systems

Photosynthesis is one of the most important physicochemical processes. It converts solar light energy into electrochemical energy and is the basis for life on earth. The photosynthetic reactions involve energy, electron and proton transfers, with radical ions and free radicals as direct participants or by-products. Information on distances between these paramagnetic centers and their mutual orientation is of considerable importance in photosynthesis research since it provides a critical connection between structure and function. The vast majority of photosynthetic studies by PELDOR were carried out on Photosystem II (PSII) of green plants. The structural context for the photosynthetic reactions was known from X-ray diffraction studies [7] and a general outline of the reactions was known from extensive biophysical and spectroscopic studies. But the choreography of the movement of electrons, protons, molecules and proteins, as energy was captured and stored, was sometimes the focus of intense speculation. The overall scheme in PSII is roughly sketched below:

At the center of PSII is the primary electron donor P680, a chlorophyll a dimer with a distinctive optical absorption maximum at 680 nm. Light is absorbed by antenna pigments that funnel the excitation energy to P680, initiating a series of electron transfers in PSII. An electron from the excited P680 is relayed, via an intermediate acceptor pheophytin Phe, to the primary electron acceptor, quinone QA, and later on to the secondary acceptor, quinone QB. The electron vacancy or hole on P680 is rapidly filled by a sequence of redox reactions involving tyrosine radicals YZ and YD, and a cluster of manganese ions Mn4. The Mn4 carries out the crucial steps of water splitting and formation of oxygen. Each electron can be followed through the series of transient paramagnetic centers detected by EPR spectroscopy. These centers, along with systems that model various properties of the reaction center of PSII, has been studied extensively by magnetic resonance [8, 9].

8.2.1 Stable Radical Pairs

PELDOR and other pulsed dipolar methods were applied to several relatively-stable radical pairs in PSII. At room temperature, the oxidized \({{\text{Y}}_{\text{Z}}}^{{ \cdot }{ + }}\) has a short lifetime and can barely be detected by EPR spectroscopy. However, oxidized \({{\text{Y}}_{\text{D}}}^{{ \cdot { + }}}\) is stable in the dark and is readily detected. The EPR spectrum of \({{\text{Y}}_{\text{D}}}^{ \cdot { + }}\) is a single, narrow line with g ≈ 2. The Mn4 cluster has five states (S0–S4); each state has a different EPR spectrum. In addition, removal of a calcium ion (Ca) from the Mn4 cluster leaves it redox active but unable to release oxygen. A review of stable paramagnetic centers in PSII studied by PELDOR and other EPR methods can be found in [10].

The oxygen-evolving and the Ca-depleted PSII systems were studied [11]. The EPR spectra of the S2 and S3 states of Mn4 are quite different from those of \({{\text{Y}}_{\text{D}}}^{\cdot { + }}\) which made it possible to measure the dipolar coupling between these species by PELDOR. The pump pulse was applied to \({{\text{Y}}_{\text{D}}}^{\cdot { + }}\) and the spin echo signal was produced from Mn4 and shows clear modulation, Fig. 8.3. The distance between the unpaired electron spin in the S2 state and \({{\text{Y}}_{\text{D}}}^{\cdot { + }}\) is \(r = 2.7\,{\text{nm}}\) in oxygen-evolving and in Ca-depleted PSII, Table 8.1. The distance between the spins of the S3 state of Ca-depleted PSII and \({{\text{Y}}_{\text{D}}}^{\cdot { + }}\) is slightly larger at 3.0 nm, and even longer for the So state of the Mn4 cluster [11]. The distances between the \({{\text{Y}}_{\text{D}}}^{\cdot { + }}\) cation and the spin of Mn4 are different because the spin of Mn4 is localized on different ions of the cluster in its different S states.

Fig. 8.3
figure 3

Reproduced from Tsvetkov et al. [39]

The \(V(T)\) of pairs of paramagnetic centers in PSII: 1 oxygen-producing PSII with active Mn4 clusters in S2; 2 Ca-depleted PSII with Mn4 in S2; and 3 Ca-depleted PSII with Mn4 in S3; points denote experimental data and solid lines denote calculations.

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Table 8.1 Distances between paramagnetic centers in PSII determined by PELDOR
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PELDOR experiments with other stable radical pairs in PSII are difficult at X-band because their EPR spectra have strong overlap. It is often impossible to select \(\omega_{A}\) and \(\omega_{B}\) for selective mw excitation of individual centers. But X-band EPR experiments were possible between a number of centers, Table 8.1 [11,12,13,14,15,16].

The reaction centers of PSII are embedded in specific structures of the chloroplast membrane called thylakoids. The donor and acceptor regions of PSII are localized on opposite sides of the thylakoid membrane. Their orientation relative to the membrane surface was studied by the first PELDOR orientation measurements [17]. A Mylar sheet was coated with a layer of alligned PSII and the sheet was oriented relative to the external magnetic field \(B_{0}\). PELDOR time traces of the radical pair consisting of \({{\text{Y}}_{\text{D}}}^{\cdot { + }}\) and the S2 state of Mn4 were measured. The vector connecting the two centers makes a 20 ±2˚ angle with the normal to the thylakoid membrane surface.

Radical pairs have also been produced by spin labeling proteins of the photosynthetic apparatus. This approach was used to study the protein component of light-harvesting complex LHCIIb, which contains chlorophylls a and b and is present in both PSI and PSII. Spin labels were introduced pairwise into the protein and the distance distribution \(F(r)\) between pairs were determined [18]. The \(F(r)\) for all labels near the N-terminus of the protein appear to be bimodal, corresponding to two different conformations. The two conformers were assigned to LHCIIb in the two different photosystems, namely, PSI and PSII [18]. The N-terminal domain is involved in light flux regulation, suggesting a role for conformational changes.

8.2.2 Transient Radical Pairs

PELDOR studies on stable radical pairs in 8.2.1 were made at X-band. Higher EPR frequencies, where g-values can be resolved, provide additional opportunities to obtain the orientation of the donors, acceptors and cofactors in addition to distances. The most extensive high-frequency studies [19,20,21] focused on transient radical pairs of the reaction center (RC) of photosynthetic bacteria, Fig. 8.4.

Fig. 8.4
figure 4

Reproduced from Schnegg et al. [20], with permission Springer-Verlag, copyright 2007

X-ray structure of the cofactors in the reaction center of Rhodobacter sphaeroides; the cofactors P865 (bacteriochlorophyll a dimer), BChlA and BChlB (bacteriochlorophyll a), BPhA and BPhB (bacteriopheophytin a), QA and QB (ubiquinone-10), Fe (Fe2+ ion) are related by approximate C2 symmetry of the RC proteins; yet, the light-induced electron transfer (ET) proceeds almost exclusively along the A branch; Arrows indicate the ET steps with their time constants.

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A short-lived radical pair, \({{\text{P}}_{ 8 6 5}}^{ \cdot + } {{\text{Q}}_{\text{A}}}^{ \cdot - }\), Fig. 8.4, was produced by a laser pulse in frozen solutions of reaction centers from the photosynthetic bacteria Rb. sphaeroides and studied by W-band EPR spectroscopy at 95 GHz [19, 20]. Some of the reactions actually become faster at low temperature, so measurements were made near 150 K to reduce the radical pair lifetime. At W-band, the EPR spectra of these radical ions only partially overlap, which enables measurements at the gxx, gyy, gzz of \({{\text{Q}}_{\text{A}}}^{{{ \cdot } - }}\) and \({{\text{P}}_{ 8 6 5}}^{{{ \cdot } + }}\) [22], so that their orientation within the pair as well as their distance were determined. The orientation of g-axes within the radical pair is shown in Fig. 8.5.

Fig. 8.5
figure 5

Reproduced from Schnegg et al. [20] with permission Springer Nature, copyright 2007

a Geometry of the g-tensor frames \(R_{Q} (x_{Q} ,y_{Q} ,z_{Q} )\) and \(R_{P} (x_{P} ,y_{P} ,z_{P} )\) in terms of polar angles \(\eta_{Q} ,\phi_{Q}\) and \(\eta_{P} ,\phi_{P}\) and the dipolar vector \(r_{QP}\); the angle \(\zeta_{QP}\) is the relative tilt of the Q and P frames around the dipolar axis; b EPR absorption spectra of \({{\text{P}}_{865}}^{ \cdot + }\) and \({{\text{Q}}_{\text{A}}}^{ \cdot - }\) radicals at X-band (9.5 GHz) and W-band (95 GHz); the principal g-values of both radicals are indicated, with the maximum amplitude of each spectrum normalized.

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The RC radical pair produced by light is born in the singlet state. Therefore, the EPR spectrum is spin-polarized and has adsorptive and emissive components from the spin-correlated radical pair (SCRP) mechanism [23,24,25,26] and somewhat different selection rules [27, 28].

Figure 8.6a shows the mw pulse scheme used for 4pPELDOR on pulsed laser-generated SCRPs. The frequency \(\omega_{A}\) of the three observe π/2 pulses was adjusted to an EPR transition of the observed spins, either \({{\text{P}}_{ 8 6 5}}^{{{ \cdot } + }}\) or \({{\text{Q}}_{\text{A}}}^{ \cdot - }\). During the time period T, the mw π pump pulse at \(\omega_{B}\) was applied to flip the partner spins. The \(\omega_{A}\) and \(\omega_{B}\), Fig. 8.6a, correspond to the resonance conditions at constant field for the principal g-values in the normal field-swept EPR spectrum.

Fig. 8.6
figure 6

Reproduced from Savitsky et al. [19] with permission American Chemical Society, copyright 2007

Upper: Pulse sequence for the W-band PELDOR experiment on spin-correlated radical pairs generated by a laser flash in photosynthetic reaction centers: the thermally-equilibrated EPR spectra of both radicals, \({{\text{P}}_{865}}^{ \cdot + }\) and \({{\text{Q}}_{\text{A}}}^{ \cdot - }\), as well as the mw excitation bandwidths for typical mw pulse length settings are shown as a visual aid; lower: a representative example of a dipolar modulation echo-decay trace from the out-of-phase-detected echo versus τ is shown.

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The observed spins dephase during the time τ between the first and second π/2 observe pulses, in part from the dipolar field of the partner radical. But here, the dipolar field is reversed during τ following the third observe pulse when the A spins are refocused into a spin echo. Reversing the dipolar field modulates the spin echo with the frequency of the dipolar interaction.

The SCRP state produces two different echo signals, an in-phase signal S-y and an out-of-phase signal Sx [29]. Figure 8.6 shows a typical \(V(T)\) slice for Sx. The complete set of slices, measured by stepping the mw frequency \(\omega_{B}\) through the spectrum of the partner radical, contains modulation for the pump pulse at each position within the EPR spectrum of the partner radical. The PELDOR spectrum is detected only for those \({{\text{P}}_{ 8 6 5}}^{{{ \cdot } + }}\) or \({{\text{Q}}_{\text{A}}}^{ \cdot - }\) radicals in a SCRP which are coupled by a dipolar interaction.

Information about the full 3D geometry of the radical pair, Fig. 8.5, is encoded in the modulation of these PELDOR spectra. Geometrical parameters for the \({{\text{P}}_{ 8 6 5}}^{{{ \cdot } + }} {{\text{Q}}_{\text{A}}}^{ \cdot - }\) radical pair were extracted by newly-developed methods [19, 20] and are compared to the ground-state \({{\text{P}}_{ 8 6 5}}^{{{ \cdot } + }} {{\text{Q}}_{\text{A}}}^{ \cdot - }\) radical pair, Table 8.2. No significant differences were seen, meaning that no substantial reorientation of P865 and QA occurs during the light-driven charge separation that produces the \({{\text{P}}_{ 8 6 5}}^{{{ \cdot } + }}\) and \({{\text{Q}}_{\text{A}}}^{ \cdot - }\) radical ion pair [7, 30].

Table 8.2 Angles and distances describing the geometry of the \({{\text{P}}_{865}}^{ \cdot + } {{\text{Q}}_{\text{A}}}^{ \cdot - }\) pair
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The cofactor geometry in PSI was also studied by high-field PELDOR [31]. The short-lived ion-radical pair \({{\text{P}}_{ 7 0 0}}^{ \cdot + } {{\text{A}}_{ 1}}^{ \cdot - }\), where A1 is phylloquinone, is analogous to \({{\text{P}}_{ 8 6 5}}^{{{ \cdot } + }} {{\text{Q}}_{\text{A}}}^{ \cdot - }\). The position and orientation of the reduced \({{\text{A}}_{1}}^{\cdot -}\) coincide with those of its parent A1; again, no substantial orientation changes occur upon charge separation. On the other hand, several distinct orientations of the \({{\text{P}}_{ 7 0 0}}^{{{\cdot } + }}\) g-tensor axes were found and attributed to conformational substates of the \({{\text{P}}_{ 7 0 0}}^{{{\cdot } + }}\) radical ion with slightly different electron spin density distributions [31].

8.3 Spatial Distribution of Radicals from Radiolysis

The energy of hard radiation, e.g., α-, β- and γ-rays, and nuclear fission products, is deposited non-uniformly in liquids and solids, producing intermediates and reaction products, e.g., ions, electrons, atoms, and radicals, that are also spatially non-uniform. The regions containing products are known as tracks and spurs. These radical tracks and spurs were an early focus of pulse EPR and ESE in chemistry, e.g., see reviews [2, 3, 32].

Analysis of the PELDOR time trace \(V(T)\) characterizes the number of spins in a group much better than classic spin echo methods. Even if there is a distribution in the number of spins in a group, PELDOR can give a weighted average or effective number of spins, Sects. 1.2.6 and 1.2.7. Consequently, one early application of PELDOR was to characterize the radical clusters in γ-irradiated cyclohexane, polyethylene and a number of organic acids [33,34,35].

Cyclohexyl radicals in crystalline cyclohexane, γ-irradiated at 77 K, produce a \(V(T)\) similar to that of biradicals with a broad distance distribution [34]. There is an initial decay, in about 0.5 μs, to a limiting value \(V_{p}\). The dependence of \(V_{p}\) on \(p_{A}\) and \(p_{B}\) was different from that of biradicals or radical pairs produced by sensitized photolysis, Sect. 8.1. The parameter \(N_{eff}\) depends on \(p_{A}\), the probability or extent of excitation by observe pulses at \(\omega_{A}\) for the cyclohexyl radicals while a biradical control 8-1 gave \(N_{eff} = \sim2.2\) independent of \(p_{A}\), Fig. 8.7.

Fig. 8.7
figure 7

Reproduced from Tsvetkov et al. [39]

Effective number of radicals, \(N_{eff}\), versus excitation probability, \(p_{A}\), by the observe pulses at \(\omega_{A}\): 1 for cyclohexyl radicals and 2 for nitroxyl biradicals 8-1.

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The dependence of \(N_{eff}\) on \(p_{A}\) in γ-irradiated cyclohexane is due to groups containing different numbers of radicals. Analysis of the change of \(V_{p}\) with \(p_{A}\), Sects. 1.2.6, 1.2.7, and 1.5, gave some information about the number of radicals in a group. Most radicals, 75–90%, are distributed uniformly or in pairs, while the remaining 10–25% are in clusters containing three to several tens of radicals. The characteristic group size determined from the initial \(V(T)\) is \(r = \sim2.5\,{\text{nm}}\), which corresponds to a local radical density of ~1020 cm−3. High local concentrations like this are missed by two-pulse ESE because the dead time for ESE is greater than the short relaxation time at such radical densities. Thus, PELDOR gives much more detailed information about the spatial distribution of radicals in γ-irradiated systems than do ESE methods.

Alkyl radicals produced by γ-radiolysis of polyethylene and some organic acids gave similar results [35]. Irradiation and measurements were made at 77 K to minimize further radical reactions. Irradiated polyethylene, like irradiated cyclohexane, gave \(V(T)\) that decay rapidly at short times, reaching a limiting value \(V_{p}\), which depends on \(p_{A}\) and \(p_{B}\). Careful analysis, Sect. 1.2.7, determined \(N_{eff}\) and the first and second moments of the distribution of number of radicals in groups [35]. Low-temperature radiolysis of polyethylene produces alkyl radicals in groups with an average of 2.4 radicals, second moment ≤6, and a radius of ≤2.5 nm.

PELDOR was used to probe the spatial distribution of radicals in DNA irradiated at 77 K to doses of 1.7–50 kGy by heavy-ion beams of 100 meV per nucleon 40Ar ions having an LET of 300–400 keV/μm [36]. Such ions produce dense tracks of damage in their wake with extensive recombination of paramagnetic centers. At the doses used, the individual tracks are well separated and the samples had superimposable PELDOR spectra. The PELDOR time traces decayed smoothly over a range of \(p_{B}\) that varied by a factor of 12. At the smaller values of \(p_{B}\), the signal intensity reached a limiting value that allowed determination of the number N of radicals contributing to the PELDOR time trace. The rate of decay to that limiting value gave the local concentration of those paramagnetic centers. The \(p_{B}\) was underestimated, slightly overestimating N and local concentration. This error is partly offset when the track radius is calculated. A global fit of all samples and data gave Cloc~13.5 × 1019 radicals cm−3 and a track radius of 6.8 nm, consistent with the LET and radiation chemical yield.

Polycrystalline ammonium tartrate was studied by PELDOR after γ-, neutron- and 19.3 meV proton-irradiation [37] following initial spin echo measurements of instantaneous diffusion. This is the first reported case of PELDOR \(V(T)\) in irradiated materials with pronounced modulation not caused by nuclear modulation (ESEEM) artifacts [38]. The resolved modulation was attributed to radicals being trapped at multiples of the unit cell, but only along the crystal axes. The paper notes that this is the first report of radiation-generated radicals trapped preferentially only along the three crystallographic axes. Unfortunately, these remarkable \(V(T)\) were not shown. The \(F(r)\) extracted from the PELDOR data lies almost entirely between 2.0 and 5.5 nm with ripples at multiples of the unit cell dimension. This distribution was reproduced very closely by detailed simulations incorporating the crystal structure and anisotropic recombination. The observed and simulated differences in \(F(r)\) with different types of radiation were suggested as providing a way to determine LET of unknown radiation by the ammonium tartrate dosimeter.

These brief examples show the promise of PELDOR for future investigations of the spatial properties of paramagnetic particles participating in elementary acts of photo- and radiation chemistry. The success with photoexcited photosynthetic systems emphasizes that PELDOR is applicable to transient excited states as well as stabilized radicals. Applications of PELDOR to functioning conductive polymers and photoconversion devices appear to be feasible.