high-field EPR

Pulsed High-Frequency/ High-Field EPR T. F. P R I S N E R DEPARTMENT OF PHYSICS, FREE UNIVERSITY OF BERLIN, A R N I M A L L E E 14, D-14195 BERLIN

I. Introduction II. Technical Aspects: Spectrometer Design for Pulsed EPR A. Components for Millimeter-Wave EPR B. EPR Spectrometer Setup C. Resonators for Millimeter-Wave EPR Spectrometer D. Sensitivity of the EPR Spectrometer E. Time-Resolution/Dead Time of High-Frequency Pulsed EPR F. Pulsed E N D O R Setup G. Magnet Requirements for Millimeter-Wave EPR III. Theoretical Aspects: The Field Dependence of the Electron Spin Hamiltonian A. Zeeman Interaction with Anisotropic g Matrix B. Nuclear Hyperfine Interactions C. Dipolar Interactions D. Exchange Interaction E. Relaxation Processes and Mechanisms IV. Applications of Pulsed High-Field/High-Frequency EPR A. Measurements of Principal g Values on Disordered Samples B. Spin-Polarized Transient Spectra of Coupled Radical Pair Systems C. High-Field EPR on Mn 2+ Centers in Proteins D. High-Field ESEEM of Nitrogen Nuclei E. Libration of Molecules Studied by Pulse Echo Experiments V. Summary and Outlook References

I. Introduction During the past decade there has been increasing interest in highfield/high-frequency electron paramagnetic resonance (EPR), as can be seen by the number of publications in this area. This is an evolution very similar to that of nuclear magnetic resonance (NMR), where this trend has 245 ADVANCES IN MAGNETICAND OPTICAL RESONANCE, VOL. 20

Copyright 9 1997by Academic Press All rights of reproduction in any form reserved. 1057-2732/97 $25.00

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T. F. PRISNER

been obvious over the past two decades. For both types of magnetic resonance the reason is mainly the increased spectral resolution achievable at higher Zeeman field strengths. Another revolutionmmore than evolutionntook place in the field of high-resolution NMR spectroscopy about 20 years ago; that was the change from the continuous-wave (cw) experimental technique, where the spectrum is recorded by a slow adiabatic sweep of the external field B 0 through the resonance condition, to the pulsed or time domain experimental technique, where the signal is recorded after a pulsed excitation in the time domain [free induction decay (FID) signal] and the spectrum is obtained by a Fourier transform of the time domain signal. In the past few years pulsed Fourier transform methods have also come into use in the EPR field. The advantage of the pulsed method is again obvious: the increased sensitivity achieved by the multiplex advantage of the pulsed experiment compared to the cw experiment, as explained by Ernst and Anderson (1966). In addition, it was recognized very early in the field of NMR (Hahn, 1950) that the pulsed excitation allows much more versatile manipulation of the spin system. For complex spin systems, described by a highdimensional density matrix, this offers the possibility of unraveling this complex multidimensional spin space in a very elegant manner by separating the different matrix elements with especially tailored pulse sequences and then examining the individual matrix elements one by one, as described in detail by Ernst et al. (1987). Although both of these trends are taking place in modern EPR spectroscopy, the evolution to higher microwave frequencies is proceeding on a much slower pace than in NMR, and the introduction of pulsed methods is still far from being a revolution in the field of EPR spectroscopy. The reason for this discrepancy between the development in NMR and EPR is twofold. o

First, there are technical problems in converting the elegant experiments from the NMR to the EPR frequency region. The electron spin gyromagnetic ratio is a factor of 700 larger than for a proton nuclear spin. Not only the excitation frequency is scaled by this factor, which means working now at millimeter wave frequencies instead of easy-to-handle radio-frequencies below 1 GHz, but also the time scale of the experiment, the spectral width, and relaxation interactions scale by similar factors. So relaxation times often lie only in the nanosecond to microsecond range, and the linewidth easily exceeds 100 MHz. Therefore the technical realization of analogous pulsed experiments in the EPR field are much more demanding. This

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argument holds especially for the high-frequency (millimeter to submillimeter) range, where coherent microwave sources are getting more sophisticated. The other reason is the difference in the electron and nuclear spin Hamiltonians. Although theoretically there is nearly a one-to-one correspondence, the relative importance and amplitudes of specific parts of the Hamiltonian are very different for EPR and NMR applications. Therefore not all the experiments from the NMR field seem very promising in the EPR field. On the other hand, some experiments have already been created, just for EPR applications.

There are already several review articles on continuous-wave high-field EPR spectroscopy in the literature, by the pioneering groups of Moscow, Ithaca, and Berlin (Lebedev, 1990, 1994; Budil et al., 1989; Earle et al., 1996; M6bius, 1993) describing various technical aspects as well as field dependences of specific parts of the electron spin Hamiltonian. This chapter will therefore only review briefly some of these general ideas, where relevant, and concentrate on technical and theoretical aspects specific (or different) for pulsed high-field EPR. The number of contemporary cw high-field EPR spectrometers is still very small and this number is outrageously tiny for pulsed spectrometers. The pioneering work is pulsed high-field EPR was done in the group of Jan Schmidt in Leiden. Coming from their strong background with pulsed X-band (9-GHz) EPR, they started directly with a pulsed 95-GHz (W-band) EPR spectrometer as described in Weber et al. (1989) and Disselhorst et al. (1995). Most of the citations on pulsed high-field EPR spectroscopy will therefore come from their and our own group. Beside these two pulsed high-field/high-frequency EPR spectrometers there are only three other groups already exploring this field: There is the group of Robert G. Griffin at the Massachusetts Institute of Technology, where I started the first pulsed experiments at 140 GHz; the group of Yakob Lebedev in Moscov, pioneering cw high-frequency EPR at 140 GHz for almost two decades with some recent applications of pulsed high-field EPR; and the EPR group at the high magnetic field laboratory at Grenoble, which recently succeeded in performing a first demonstration of pulsed EPR at 600 GHz (for references see Prisner et al., 1992; Bresgunov et al., 1991; Kutter et al., 1995). Nevertheless, I believe that pulsed high-field EPR will soon gain importance, and it can easily be predicted that the number of groups and spectrometers working in this field will increase by a large factor soon. That is because there are some special features of the combination of high excitation frequency and pulsed excitation that might overcome some of

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the restrictions still limiting the applications of pulsed EPR at lower frequencies. In this chapter I will try to support and expend on this statement with some of the first applications done in our laboratory.

II. Technical Aspects: Spectrometer Design for Pulsed EPR A. COMPONENTS FOR MILLIMETER-WAVE E P R

Different from EPR spectrometers at usual X-band frequencies, the performance of EPR spectrometers working at frequencies above 90 GHz is strongly limited by the characteristics of the mm-wave components. This is true for both pulsed and cw high-field EPR spectrometers, but different mm-wave parts limit the spectrometer performance in both cases. In this frequency range the active solid-state mm-wave components are mostly working at their upper frequency limit, whereas for far-infrared devices the frequency is still somewhat too low. Therefore the technical specifications of some of the components hardly reach spectroscopic specifications and have to be chosen carefully. Where, for example, a typical pulsed X-band EPR spectrometer can easily be built with an overall noise figure below 5 dB, a typical noise figure for a 100-GHz spectrometer is at least 10 dB and can easily reach more than 30 dB, strongly limiting the application of this instrument. So characteristics of some of these microwave components will be summarized first, and general spectrometer designs will be discussed shortly. 1. Sources

The parameters describing the characteristics of the sources are the available microwave power and the noise and frequency characteristic of the source (see Table 1, specifications from commercial data sheets). Typical sources for spectroscopic requirements are Gunn diodes (GaAs or Si), Impatt diodes and klystrons for continuous-wave sources, and also more exotic high-power pulsed vacuum tube sources as gyrotrons, extended interaction oscillators (EIOs), backward wave oscillators (BWOs), or magnetrons. Pulsed sources can deliver huge amounts of power but are rather complicated and expensive. Their spectral characteristic can be very good (see Table 1), but they need highly stabilized high-voltage power supplies (10s!). Their applications are interesting for pulsed EPR experiments as for example described in Prisner et al. (1992) [or dynamic nuclear polarization (DNP) experiments as in Un et al. (1993), Becerra et al. (1995), and Gerfen et al. (1995)]. Gunn diodes have powers up to 20 dBm but not very good frequency stability. When they are phase locked to a

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TABLE 1 MILLIMETER-WAVE SOURCES

Source

Frequency (GHz)

Power (dBm)

Gunn diode (GaAs)

30-150

17

Gunn diode (InP) IMPATI' (GaAs) IMPATT (Si) Klystron

30-150 < 150 < 300 < 200

20 20 30 23

Gyrotron EIO

50-400 30-220

BWO (Carcinotron)

< 1000

90 (pulsed) 63 (pulsed) 47 (cw) 60-10

Magnetron

< 120

Far-infrared laser

> 150

a

64 (pulsed) 30 (cw) - 3 0 / + 20

Phase Noise (dBc/Hz) a (for 100-GHz Carrier Frequency) (Free-running source) 20 at 1 kHz/85 at 1 MHz (Phase-locked source) 90 at 1 kHz/100 at 1 MHz Same as above 100 at 10 kHz 120 at 1 kHz/145 at 1 MHz (heterodyne detection scheme) < 10 kHz linewidth at 140 GHz 110 at 50 kHz/140 at 1 MHz < 10 kHz linewidth at 300 GHz 80 dBc at 10 kHz

Amplitude noise problems

Often phase noise characteristics are calculated from spectrum analyzer output only.

low-frequency stable source like a quartz oscillator, their frequency stability is strongly improved, but they still have limited phase-noise characteristics for cw EPR applications. For pulsed EPR applications they suffer from the low initial power. Klystrons are very good with respect to their noise characteristic and deliver a medium amount of microwave power (up to 26 dBm). 2. Diodes

Schottky barrier diodes are still usable in this frequency range, but they are more fragile than at lower frequencies and are especially sensitive to static electricity and mechanical stress. The whisker contact junction is very small, so a few volts of static potential are enough to damage them. Beam lead diodes are more robust but also less sensitive. Diodes are used for mixers, harmonic mixers, up- and downconverters, and detectors. Their ability to handle power is rather limited, as is their conversion factor (Table 2). Used as mixers, their sensitivity (or noise figure) is strongly improved by choosing the intermediate frequency above some 100 KHz. In this case their noise figure drops approximately 20-30 dB. Therefore most of the sensitive high-frequency EPR spectrometers work with a heterodyne

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T . F . PRISNER

TABLE 2 MILLIMETER-WAVE DETECTION AND SWITCHING DEVICES

Function

Power detection

Noise Figure (dB)

Type

Schottkybarrier Whisker contact Phase detection Schottkybarrier Power detection Beamlead diodes Power detection InSbbolometer Power or phase SIS junction Phase detection Comer cube Power Switching PIN Phase modulation PIN

Bandwidth (MHz)

Bumout Power Isolation (dB) (dBm)

55

1000

20

6-10 60 35 (4 K) < 10 (4 K) 10 (RT)/6 (77 K) 5 (CL) 2 (CL)

1000

10 18 20 10 10 36 36

0.1-1 10 400-1000 1000 1000

20

30 20-30

detection scheme (see below). As spectrum analyzer mixers or harmonic mixers they have rather bad conversion factors, strongly limiting their use (for example, in measuring accurately the noise characteristic of highfrequency sources with a low-frequency spectrum analyzer). An alternative to a mixer, as a downconverter of the mm signal in the detection channel, is a hot-electron bolometer (GaAs or InSb). The noise figure of an He-cooled bolometer is superior to that of homodyne Schottky diode detection, but the small bandwidth of the bolometer limits its application to cw E P R experiments. PIN diodes are used up to 150 GHz for amplitude or phase modulation of the microwave in pulsed applications. For high-frequency EPR this is mostly done in a reflection mode configuration, with a circulator matching the diode. The switching speed is very good, because of the inherent broad bandwidth of this device (1 GHz, < 1 ns), but the losses are very high and the isolation is rather small, mostly limited by the circulator. They can handle car powers up to 36 dBm, sufficient for most of the cw sources. Still, because of the high losses, compromises with respect to the total isolation (pulses off) have to be made. Again a heterodyne scheme can offer some advantages, as will be described later.

3. Amplifiers There is a very limited number of high-frequency amplifiers with spectroscopic specifications and they are very expensive. Practically no easy-touse low noise detection amplifier exists. The noise figure of the available solid-state low-noise amplifiers just meets the conversion losses of good heterodyne mm-wave mixers, so there is no advantage in using them.

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Several medium- to high-power amplifiers exist that can be used for powering up low-power mm-wave excitation pulses. All of them are again rather expensive and induce additional source noise. They are listed with some specifications in Table 3. An important characterization of these active detector and amplifier devices is the noise figure F, defined by: F = 10log ~T

(1)

where Pn is the noise power at the output of the device and PT is the thermal noise for the device bandwidth at room temperature. Some other definitions describing the noise characteristic of the devices are also in use, such as the noise equivalent power ( N E P ) ( W / H z for coherent detectors or W / U z 1/2 for incoherent detectors), the tangential sensitivity or responsivity R (V/W), the noise temperature Tn (K), the dynamic range (dB), or the noise floor (W). They can easily be converted to a noise figure if all the parameters are given (i.e., pre- and postdetection bandwidth, resistance, gain, modulation frequency, conversion loss), which is not always the case! 4. Circulators

As passive components, the circulators play an important role in a high-frequency spectrometer. Their directionality and therefore isolation is rather limited ( ~ 2 0 - 3 5 dB), which can lead to problematic leakage pathways in the setup. This is crucial for a pulsed EPR setup with reflection cavity design, because the leakage of the circulator, connecting the excitation pathway, cavity and detection mixer, limits the maximum usable power of the microwave excitation pulses. This is different for a transmission setup, where the cavity performance determines the trans-

TABLE 3 MILLIMETER-WAVE AMPLIFIERS

Function Power amplifier Power amplifier Power amplifier Detection amplifier

Type LOPILA Pulsed IMPATT Extended interaction amplifier Schottky barrier

Frequency Range (GHz)

Noise Figure (dB)

< 200 GHz <200 GHz 50-200 < 150

6

Gain (dB)

Output Power (dBm)

20 20

25 26

40 15

60 8

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T . F . PRISNER

mitted pulse power. By using a bimodal design, with orthogonal excitation and detection modes, the isolation can be as high as 60 dB, as described by Prisner et al. (1992). The circulators are also used for avoiding back reflection and interference, for impedance matching of active devices and for fast phase switching of the mm-wave. 5. Waveguides

The fundamental modes (TEl0) for rectangular waveguides are rather lossy for mm waves (see Table 4). Therefore oversized waveguides are normally used to transport the microwaves with much smaller attenuation. Unfortunately, the oversized waveguides can also support higher than fundamental modes, so care has to be taken in using them. In front of all discontinuities the waveguide has to be tapered back to the fundamental waveguide, which strongly damps all higher modes. The noise of the oversized waveguide is enhanced by the number of supported modes for the given frequency band. Progressive pyramidal tapered transitions or mode converters match different waveguides; their conversion loss strongly depends (as does the attenuation of the fundamental waveguide) on the quality of fabrication (surface quality, surface material, and slope profile accuracy). Circular waveguides are much less lossy and very handy, but can usually not be directly used for coupling to a cavity or semiconductor devices, which normally support linearly polarized waves. The formula that describes the theoretical attenuation a for a given frequency f is given by (K~is and Pauli, 1991): 0.023Rs ( b ) b/-,------)2~/l_(fc/f 1 + 2 a ( f c / f ) 2 (dB/m)

(2)

TABLE 4 WAVEGUIDES FOR MILLIMETER WAVES

Band

Waveguide

Frequency (GHz)

Loss (dB/m)

Q Q W F W Q W-Q W-W

WR22 (rectangular) WR22 (oversized) WR08 (TEl0 fundamental mode) WR06 Cylindrical--TEM 11 Cylindrical--oversized ZE01-TEo1 TE01-TEMll

33-50 95 75-110 90-140 75-110 95 W W

2 1 5 8 2 0.5 0.2 0.2

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253

for rectangular waveguides (TE01 mode), with a, b the inner waveguide dimensions (m), fc the cutoff frequency (GHz), and R~ the waveguide impedance (I~), with the cutoff frequency fc given by: f~ = 0.15/a (GHz) and the resistivity R s for an electroformed copper waveguide by: R s = 0.00825 X/if (f~) For a cylindrical waveguide (TEM~ mode) the attenuation is given by (K~is and Pauli, 1991): a = 0.023 ~/t/'l -

Rs

((L/f)

2

+ 0.418)(dB/m)

(3)

(L/f) The real values for the attenuation are, depending on the machining, worse than these theoretical losses! Table 4 gives some more realistic values for the attenuation. B. EPR SPECTROMETER SETUP High-field/high-frequency EPR spectrometer setups can be distinguished between homodyne and heterodyne detection schemes. Pulsed high-frequency spectrometers use nearly exclusively heterodyne detection schemes, as described by Weber et al. (1989), Prisner et al. (1992, 1994), and Kutter et al. (1995). Only one pulses mm setup at 125 GHz is described with a homodyne detection scheme by Bresgunov et al. (1991). For pulsed purposes a high bandwidth is needed, so only Schottky diode mixers can be used for the downconversion of the mm-wave signal. The Schottky diodes are much more sensitive at high intermediate frequencies (IFs), as stated above, so heterodyne detection schemes are preferred. The heterodyne scheme can be realized by two phase-locked or flee-running mm-wave sources or an upconversion of the mm-wave source in one branch of the spectrometer. The upconversion can be done either in the excitation or in the local biasing branch. The advantage of doing the upconversion in the excitation branch is the possibility of doing most phase and amplitude manipulation of the excitation pulses very conveniently at the IF frequency (for example, 3 GHz in Weber et al., 1989). This offers the possibility of performing all the advanced pulsed EPR experiments (1D and 2D) that require CYCLOPS phase cycling for their best performance (Gemperle et al., 1990). Additional switching of the IF frequency shifts and attenuates the mm wave, so better isolation performance can be achieved without further loss in mm-wave power. On the other hand, upconverters in this frequency band

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T.F. PRISNER

have very limited output power, so further expensive amplifiers are needed to achieve the necessary mm-wave power for pulsed experiments. Furthermore, for this setup, the frequency and phase noise characteristic of the IF source also enter into the noise figure of the spectrometer (see below). Upconversion in the local biasing branch (just for biasing the detection mm-wave mixer at the LO port) is also possible as described by Prisner et al. (1994). In this scheme, the power in the excitation branch is delivered by the mm-wave source alone and is not limited by the upconverter power handling capability. In addition, by carefully balancing the physical branch lengths, the phase noise characteristic of the IF source does not enter into the noise figure of the spectrometer. Thus there is no need in phase locking (PLL) of the local oscillator source, avoiding additional noise of the PLL. This design can achieve the best noise performance with a low-noise mm-wave tube source, such as a klystron. As a disadvantage, all phase and amplitude switching of the mm wave has to be performed with ferrites and PIN diodes directly at the mm-wave frequency. Our heterodyne pulsed 95-GHz EPR setup operating with this scheme is shown in Fig. 1. C. RESONATORS FOR MILLIMETER-WAVE EPR SPECTROSCOPY Typically used cavities for mm-wave EPR are cylindrical cavities with a TE011 mode and Fabry-Perot (FP) resonators with TEM00 m modes (m 3 . . . 7). The FP resonator can be used in a confocal or semiconfocal configuration, both in reflection or transmission mode. Some very highfrequency experiments have also been done without a cavity but with much reduced sensitivity. Typical parameters describing the performance of these two types of cavities are given in Table 5. The mechanical specifications of cavities for mm waves are demanding; cavity surfaces and dimensions and iris thickness, and dimensions are critical. For example, a typical FP, critically coupled with a Q of 10,000, is sensitive to displacements of the mirrors by as little as 0.1 /xm. Also, the mechanical isolation of the cavity from the modulation coils has to be improved compared to lower frequency designs because of the larger modulation amplitudes and increased interaction forces with the larger static field. D. SENSITIVITY OF THE E P R SPECTROMETER

For a comparison of the different setups, the sensitivity of the spectrometer has to be specified. Technically, this can be done by defining the overall noise figure F of the spectrometer setup. This is a satisfactory characterization if the spectrometer noise power is white within the spectrometer bandwidth. For pulsed EPR experiments, this is the noise

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255

superconducting magnet power supply

-] transient

Pulser up-

4 GHz DRO ..,

95 GHz klystron

FIG. 1. Block diagram of the Berlin pulsed heterodyne detection EPR spectrometer working at W-band frequency (95 GHz, 3.4 T). The spectrometer consists of a solenoid superconducting magnet (<6 T), with additional sweep coil (approximately 0.2 T sweep range) that can also be set into superconducting mode. The microwave board sources are a high-frequency (95 GHz) klystron tube source and a 4-GHz dielectric resonator oscillator (DRO) for the intermediate frequency.

floor when the mm-wave excitation pulses are switched off. Even in this case, F is very often still affected by the source phase noise characteristic, because of limited isolation of the switches, other leakage problems, and the LO noise of the detection mixer. This overall noise figure is determined mostly by the noise of the mm-wave and IF sources, by the conversion loss of the waveguides in the detection channel, and by the noise figure of the mm-wave diode mixer and the first IF amplifier. The phase-noise characteristic of the mm-wave sources is essentially for many experiments in cw as well as pulsed high-frequency EPR applications. For phase-locked sources, the phase noise of the mm-wave source is, within the locking bandwidth, determined by the phase-noise characteristic

256

T.F. PRISNER TABLE 5 CHARACTERISTICS OF MILLIMETER-WAVECAVITIES

Cavity FP a FP ~ FP c' ~' FP a FP e FP f Cylindricalg CYlindricalh CYlindrical/ CylindricalJ

Mode

Frequency (GHz)

Quality Factor Q

Conversion Factor (txT/v/W)

140

1000-5000

5-10

140

1000

5

250 604 95

100-200 40*m 2000

2.5

95 95 95 140 140

1000-3000 1000-5000 2000

4.7 50 47 43 36

Semiconfocal (reflection) Confocal 90~bimodal (transmission) Semi-confocal (transmission) Confocal (transmission) Confocal (reflection) Semiconfocal (reflection) TE011 TE011 TE011 TE011

1000

700-1000

3.3

aprisner et al. (1993) bprisner et al. (1992) CBudil et al. (1989) dKutter et al. (1995) eBurghaus et al. (1992) fvan der Meer et al. (1990) gPrisner et al. (1994) hpoluektov et al. (1993) iBresgunov et al. (1991) JBecerra et al, (1995) kEarle et al. (1996)

of the lock source multiplied by the frequency ratio" P n mm =

(mm)

20 log ~

Pnl~

(4)

This can be unfortunate, even with a good lock source, if the frequency ratio becomes large. In addition, the noise is often further increased by residual phase lock noise from the lock circuit itself. This is a real problem at high frequencies, especially for cw E P R applications, where the signal is typically probed at the first sideband frequency of the field modulation. This is normally only at an offset of 1-100 kHz from the carrier frequency, where the phase-noise contributions of the source are still dominant. In contrast, the pulsed E P R experiments are sensitive only to phase-noise contributions that are on the time scale of typical coherent pulsed experi-

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ments( ~ 1/zs). The phase noise of the sources at an offset frequency of 1 MHz from the carrier frequency is already strongly reduced and may be hidden below other noise contributions, as shown, for example, in Prisner et al. (1994). Therefore pulsed EPR experiments suffer less from the bad noise characteristics of mm-wave sources than cw EPR experiments do. This is different for lower frequency EPR, where the noise figure of the source is not the sensitivity-limiting factor in standard designs. Unfortunately, it is not easy to estimate the phase-noise characteristic of mm-wave sources with typical low-frequency spectrum analyzers (< 48 GHz), because of the limited dynamic range with external harmonic mixers and the substantial noise floor of the LO sources for these measurements. The other important contribution to the overall noise figure arises from the detection mixer because of the lack of low-noise mm-wave detection amplifiers (see above). Noise figures of different detectors are listed in Table 2. Here, a compromise between noise figure, cost, reliability, and handling has to be made. Also, the noise figure can be deteriorated by standing waves, interference, reflection, and leakage in the waveguides, all of which are more crucial at higher frequencies. Instead of this technical description of the spectrometer performance, a more magnetic resonance-related parameter is the spectrometer sensitivity E (spins/mT), describing the minimum number of spins necessary to get (for an assumed linewidth of 1 mT and a lock-in detection bandwidth of 1 Hz) a signal-to-noise ratio ( S / N ) of 1. Experimentally this parameter can be easily obtained by

N E =

( S / N ) ( 2 m I + 1) An1~ 2

(s)

with N the total number of spins in the sample, m~ the nuclear quantum number for hyperfine resolved spectrum, and AB1/2 the linewidth of the hyperfine line (mT). The theoretical formula describing the sensitivity E for a cw EPR experiment is given by (Feher, 1957):

N*=

Cl(kT)3/2V s Q "qB o

Af -~o v/ff

(6)

where N* is given in spins/mT, Vs is the sample volume, Af the detector bandwidth, P0 the excitation power, Q the quality factor, r/ the filling factor of the cavity, F the noise figure of the spectrometer, k the Boltzmann constant, B 0 the external magnetic field in mT, T the absolute

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T.F. PRISNER

temperature of the sample, and c1 is given by 1 Cl =

og

e S(S +

1)

(7)

For a t00-GHz cw EPR spectrometer this leads to a typical performance of about 108 spins/roT, which has been achieved experimentally in several laboratories (Grinberg et al., 1983; Weber et al., 1989; Burghaus et al., 1992; Prisner et al., 1994). For a pulsed EPR experiment there is no unique description of sensitivity as in the cw EPR case, because the ram-wave pulse power o r ~ b e t t e r ~ t h e effective field strength B~ of the excitation pulses, the detection bandwidth, the time resolution, and the experimental repetition time enter additionally or differently into the overall spectrometer sensitivity. An alternative descriptions of experimental pulsed EPR spectrometer sensitivity could be the single-shot S / N of a two-pulse-echo signal. The test sample should have the following properties: 1. A broad inhomogeneous linewidth (broader than typical pulse excitation widths, ~ 10 roT) with a fiat amplitude distribution and without dominant field-dependent inhomogeneous linewidth contributions. 2. Room temperature echos, without any electron spin-echo envelope modulation (ESEEM) effects. 3. An easy and reproducible way to get the absolute spin number of the sample. 4. An electronic spin 1/2 with Boltzmann distribution of spin level populations. For such a sample a pulsed sensitivity E' can be defined as: E' =

N

e -(2r/T2)

(8)

AB1/2S/N

Again, N is the number of spins in the test sample, A B e l 2 the inhomogeneous linewidth of the sample, r the pulse separation, and T2 the transverse relaxation time. The S I N for the pulse experiment would be best defined as the peak echo amplitude compared to the noise rootmean-square (rms)value (with the detection bandwidth matched to the echo shape). In this definition, the noise figure of the spectrometer as well as the microwave excitation field strength B~ contributes to E' (by the spectral width of the excitation), so that this number could be a good characterization of a pulsed spectrometer.

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259

The signal-to-noise ratio for a time domain free induction decay signal can be calculated (Shaw, 1976) from: ~)FID ~noise

(X

r

CVcFA f ( kT )

(9)

with Vc the cavity volume. Formula (9) leads to the same result as formula (7), assuming a single homogeneous line and optimum microwave power for the cw excitation. An experimental comparison of the sensitivity for pulsed and cw EPR applications is interesting. While it is known from NMR that the pulsed Fourier transform method is superior to the slow adiabatic passage method because of the multiplex advantage of the FT method, this is not always true for pulsed EPR applications. One reason is that the electron spin lattice relaxation rate is so high. Thus the technically available averaging rate of the FID signal is not fast enough for optimal duty cycle of the pulsed experiment. Another reason is that for pulsed EPR experiments at X-band frequencies, the quality factor Q of the cavity has to be lowered compared to the cw EPR experiment in order to match the bandwidth of the cavity to the very short excitation pulses. Inevitably this leads to decreased sensitivity of the spectrometer. Again, in the high-frequency pulsed EPR experiment the situation is improved compared to the X-band frequency range. The Q does not have to be lowered, even for pulsed and time-resolved applications, because of the larger cavity bandwidth at higher frequencies. Also, for many samples, the relaxation times are longer at higher fields, as will be discussed in the next section. Therefore the duty factor for usual data averaging digitizers is increased. Experimentally, both methods are compared for a solid sample with a narrow line for our pulsed/cw W-band EPR spectrometer. With the same cavity and optimal parameters for both experiments the gain in S/N for a 500-point spectrum is 45 with the FT EPR method. This is actually more than the theoretical value of 27 calculated from the repetition rate and the 7'1 relaxation time. This additionally improved value for the pulsed experiment is contributed to the reduced sensitivity of the pulsed experiment to source noise. The sensitivity of FT EPR and echo-detected EPR experiments of high-frequency EPR (at 95 and 140 GHz) was measured and found to be a factor of about 50 better than for commercial available X-band spectrometers under favorable conditions (small sample, narrow, and not field-dependent linewidth). Comparing the sensitivity of an echo experiment with time-resolved transient nutation experiments and cw EPR experiments for samples for which the spectral linewidth strongly exceeds the available excitation field

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T . F . PRISNER

strengths of our spectrometer leads to the following results: The multiplex advantage is lost for the pulsed experiment, because the spectral information is lost and the width of the echo signal is comparable to the pulse lengths (40-100 ns). Because the data acquisition is effective only for this time interval, the duty factor of the echo-detected experiment is strongly reduced. On the other hand, the pulsed experiment excites a larger spin packet than the cw or transient nutation method. In addition, the pulsed experiment detects the signal against a black background without any microwave excitation, whereas for the other two methods the microwave excitation is on for the time period of the detection. Because of the low quality of the noise characteristic of mm-wave sources stated above, this is often the limiting factor for high-frequency EPR sensitivity. Experimentally, the relative signal-to-noise ratios are 1, 4, and 24 for the transient nutation spectra, the pulsed two-pulse echo-detected field-swept spectra, and the cw-detected EPR spectra, respectively. E. TIME RESOLUTION/DEAD TIME OF HIGH-FREQUENCY PULSED E P R

Another characteristic of the pulsed EPR spectrometer which has not yet been discussed is the dead time of the spectrometer after strong excitation pulses. For a T 2 longer than 1 /xs, this characteristic does not enter into E', but it could be included by taking a sample with a short T2 ( < 50 ns) and recording the echo with the experimentally shortest possible pulse separation. Because this would be more strongly dependent on the individual procedure in treating the data, this seems less applicable. Instead, it seems better to cite the dead time of the spectrometer independently. This time is defined differently in the literature; the most useful definition seems to be the following: The dead time of the spectrometer is the time interval from the beginning of the excitation pulses (with the maximum available excitation power) to the time at which a signal can be recorded without any distortions (after subtraction of the off-resonance ringing signal, with full detection amplification for highest signal sensitivity).

This time is the one most relevant for practical applications. It is different from the ringing time of the pulse power down to the noise floor of the spectrometer (or to the thermal noise floor level); this time is longer than the dead time defined above. Through the lack of a low-noise mm-wave amplifier (which is a disadvantage with respect to noise figure), it is possible by careful design to avoid saturation of the detection channel even for the time interval in which the excitation pulses are on. In this case

PULSED HIGH-FREQUENCY / HIGH-FIELD EPR

261

no real dead time appears in the pulsed high-frequency EPR spectrometer. The Rabi oscillations can be seen on top of the pulse and the FID signal directly after the end of the pulse. Thus the FID signals can be recorded even for linewidths much broader than the excitation bandwidth. Still, the usual distortions from the radiofrequency spikes at the sharp pulse edges limit the observation of the FID directly after the pulse. In addition, any reflections of the mm-wave pulses within the spectrometer lead to strong signal distortions after the pulses. Avoiding this reflection in the whole excitation branch can be a cumbersome task. All these parameters~sensitivity, excitation pulse power, and dead time after the pulses~are a characteristic of the mm-wave EPR spectrometer including the loaded cavity. Whereas the conversion factor c of the mm-wave cavity affects the pulse excitation field strength B1 by (10)

B 1 = c v/QPmw

the conversion factor c is itself a function of the microwave frequency:

ccL

~/ ~0

rc v o

~~0

v~

(11)

Therefore high B 1 field strengths can be reached more easily at higher microwave frequencies because the field is concentrated in a smaller cavity volume. Also, the Q of the cavity can be chosen higher for the same pulse lengths, again enhancing the conversion from excitation power to magnetic field strength. The increased conversion factor of mm-wave cavities can be seen in Table 5. For example, the conversion factor of a cylindrical TE011 cavity at 100 GHz is much higher than the conversion factor for a rectangular cavity at X-band frequencies (9 GHz, c - 2 /.LT/W1/2). On the other hand, it can be seen that it does not further increase from 95 to 140 GHz, most probably because of technical difficulties of effective coupling to the cavity at these frequencies. Also, specialized cavities with improved conversion factors for pulsed EPR applications exist at X-band frequencies, for example, dielectric cavities, slotted tube cavities (Mehring and Freysoldt, 1980), loop gaps (Froncisz and Hyde, 1982), and the bridged-loop gap cavity as designed by Pfenninger et al. (1988), with conversion factor up to 14 ~ T / W 1/2. Unfortunately, none of these efficient structures could be converted to mm-wave frequencies yet, because of too small sizes. The ringing time constant after the mm-wave pulses is determined by the bandwidth of the loaded cavity. This bandwidth is~despite the high Q of the cavitymstill larger than typical pulsed X-band values. The ringing of

262

T . F . PRISNER

the cavity after the pulses is described by: t r

.

.

.

Q In (nose) .

,o

P0

(12)

For our setup (Q = 1000, e e x - - 3 mW, r e = 3 ns) the ringing power directly after the pulse is too low to saturate the heterodyne mm-wave mixer. With a noise figure F of 13 dB, the noise power in a detection bandwidth of 500 MHz at room temperature is -98 dBm or 0.16 pW. The time needed for the ringing power to fall below this threshold is 40 ns. Even this time constant, which is not the dead time, as mentioned above, is exceedingly short for pulsed EPR. Also, for a heterodyne detection scheme most of the ringing signal is dumped in 90 ~ out-of-phase branch of the mixer and does not disturb an in-phase echo detection. Both these features together, high conversion factor and short ringing time, give high-frequency pulsed EPR the potential of extremely high time resolution. This potential cannot be fulfilled yet, because typical 7r/2 pulse lengths are still a factor of 10 longer than the times achievable by state-of-the-art pulsed X-band spectrometers (50 ns versus 5 ns). F. PULSED E N D O R SETUP The electron spin/nuclear spin double-resonance (ENDOR)version is also very attractive for high-field EPR setups. Not only are the nuclear resonance frequencies for most nuclei in a very convenient frequency range, but also, because of the high spectral resolution of mm-wave EPR, orientation-selective or site-specific E N D O R data can be obtained, with enhanced information content compared to X-band E N D O R applications. This was first demonstrated in Berlin in the group of K. M6bius by Burghaus et al. (1988) and subsequently by Rohrer et al. (1995) and in Leiden in the group of J. Schmidt by Bennebrock et al. (1995) and Coremans et al. (1995). For the pulsed mm-wave EPR spectrometer the typical pulsed E N D O R versions (Mims and Davies ENDOR) are implemented. Because, as stated above, an FID signal can be recorded with a pulsed mm-wave EPR spectrometer even for very broad inhomogeneous spectral widths, the Davies sequence can be used with a simple "n'mw-'B'rf7r/2mw-FID detected version, instead of the usual two-pulse echo-detected version. Thus this experiment is now limited only by the electronic T 1 time and no longer by the electronic T2 relaxation time. The realization of an E N D O R probe head is shown in Fig. 2. A cylindrical cavity (TE011) is used together with a saddle coil for the rf excitation. The mm-wave frequency is 95 GHz and the rf circuit is tuned and matched to 140 MHz (with 40 MHz bandwidth), corresponding to the

263

PULSED HIGH-FREQUENCY / HIGH-FIELD EPR oll

/9

cavity

NMR

coil

tuning

,'lit

R F - ci I"cui t

47

? /

piston

laZ B1 M

, ,-

(~

/

- bridge

t B0

10 mrn

FIG. 2. W-band cylindrical TE011 ENSOR cavity. The cavity has a quality factor Q of 3500; the microwave B 1 field strength is 0.2 mT (95 GHz) and the radiofrequency B E field strength is 3 mT (140 MHz). The filling factor is r / < 0.2. The cavity is equipped with an optical quartz fiber of 800-/zm diameter for light excitation of the sample.

proton Zeeman splitting frequency (3.4 T static magnetic field). The pulse lengths for this setup are 40-100 ns for the mm-wave 7r/2 pulse and 2-5 /zs for the rf 7r-pulse. The respective excitation powers are 10 mW for the 95-GHz microwave and 1 kW for the 140-MHz radiofrequency (Rohrer, 1995). To demonstrate the performance of our pulsed high-frequency/highfield setup some of our typical pulsed experiments are shown in Fig. 3. The sample is a photoexcited triplet state of a pentacene molecule in a p-terphenyl crystal. The triplet state is populated with an electron polarization of almost 1 by selective intersystem crossing. The relaxation times T 1 and T2 of this system are, even at room temperature, long enough to observe the spin-polarized echo signals. Shown are a transient nutation

264

T . F . PRISNER

.,..,

r~

0

5

15

l0

0

ms--0

0

z

1

2

3

time [~s]

.j 145

155 radio frequency [MHz]

165

FIG. 3. Transient nutation, two-pulse echo, and pulsed Davies-ENDOR high-frequency experiments on a photoexcited triplet state of pentacene in a p-terphenyl crystal at room temperature.

experiment, a pulsed two-pulse echo experiment, and a pulsed Davies E N D O R experiment. The signal-to-noise ratio is very high for all these measurements. Remarkably the two-pulse echo sequence shows a series of multiple echos, because of nonlinear effects of the strong echo signal (see next section). The E N D O R experiment is performed on the m s = +1 to m s = 0 electronic transition. Whereas the m s ---0 electronic state contributes only to the free proton line (Zeeman splitting 139.5 MHz, no hyperfine coupling), the m s -- +1 electronic state shows the proton hyperfine shifted E N D O R lines.

PULSED HIGH-FREQUENCY / HIGH-FIELD EPR

265

G. ]VIAGNET REQUIREMENTS FOR MILLIMETER=WAVE E P R

For mm-wave EPR applications with microwave frequencies above 90 GHz a superconducting magnet is normally required (field strength > 3 T). The demands on the magnet for typical EPR applications are still moderate, compared to NMR standards. A homogeneity of the magnetic field of 10 ppm over a 1-cm cube, as for solid-state NMR magnets, is totally sufficient for EPR applications. This is because of the intrinsic linewidth of the EPR spectra (typically on the order of > 1 G) and the small sample sizes. Thus no additional shimming of the magnet is required. The bore of the magnet should be not too small (70-110 mm), otherwise the construction of the probe heads degenerates into filigree. Because the excitation width of the microwave pulses often does not cover the whole spectral range, EPR spectra are normally taken by sweeping the magnetic field, even for pulsed EPR applications. Sweeping of the main coil of the superconducting magnet is slow, inaccurate, and expensive (because of liquid helium boil-off). Thus an additional sweep coil with a sufficient range to cover typical EPR spectra (some fractions of a tesla) is needed. This coil can be an additional superconducting coil in the magnet Dewar, which has the advantage that it can be set to persistent mode for pulsed EPR experiments at a fixed field position. Or it can be an additional coil in the room temperature bore of the magnet. Care has to be taken to minimize the cross-talk between the sweep coil and the main coil of the magnet, to get reproducible and linear field sweeps. For accurate measurements or locking of the magnetic field a NMR teslameter can be used, as described by Un et al. (1993). With a careful =alibration, such a lock system gives very high accuracy for measuring the resonance field values of the sample. The g factor accuracy and resolution for such a high-frequency EPR spectrometer can be 10 -6 for the absolute and 10 -7 for the relative values.

III. Theoretical Aspects: The Field Dependence of the Electron Spin Hamiltonian The use of high-field/high-frequency EPR can be understood best by an examination of the field dependence of the electron spin Hamiltonian H. H = H'(Bo)

+ H"

(13)

Parts of this Hamiltonian are field dependent (H'(B0)) and parts are not (H"). Performing EPR experiments at different Zeeman fields allows

266

T.F. PRISNER

these two parts to be distinguished. Moreover, different contributions have distinguishable functional field dependences, so they can be separated easily. This has already been discussed in several review articles on high-field/high-frequency EPR by Budil et al. (1989), M6bius (1993), and Lebedev (1994). Here, only a short review of some of the aspects will be given, with special emphasis on the consequences for pulsed applications. The electron spin Hamiltonian examined is of the form: H = H 0 + H(t)

(14)

where H 0 is the stationary part: H 0 = OzSe + Hdi p + Hex + O~e + Hhf i A- Hquad

(15)

with H s the electron Zeeman Hamiltonian, HI~ the nuclear Zeeman Hamiltonian, Odi p the electron dipole spin-spin Hamiltonian, Hex the exchange Hamiltonian, Hhn the electron-nuclear hyperfine Hamiltonian, and Oquad the nuclear quadrupole Hamiltonian. H(t) is the timedependent part of the Hamiltonian, responsible for the dynamics and relaxation of the time domain EPR signal. The contributions to H(t) examined and demonstrated here in more detail are chemical reactions and kinetics of light-induced transient radical states, molecular rotations resulting in a time-dependent variation of the g-value~g(t)~for anisotropic g matrices, and modulation of the exchange interaction J of coupled radical pair s y s t e m s ~ J ( t ) ~ for geometrically flexible systems. There are further classical processes for the spin relaxation in solids, all of them with specific dependences on the external magnetic field (or the energy separation). Experiments at different fields allow the spectral density function of these fluctuations to be probed at different Larmor frequencies and help to identify their mechanisms. A. ZEEMAN INTERACTION WITH /~kNISOTROPIC g MATRIX

The field dependence of the electron spin Zeeman interaction is most obvious for EPR spectra. The electron spin Zeeman Hamiltonian is given as usual by: Hze = h/3eSgB 0

(16)

with h the Planck constant divided by 27r, /3~ the Bohr magneton, B 0 the external magnetic field vector, ~ the 3 x 3 g matrix and S the spin operator vector given by:

PULSED HIGH-FREQUENCY / HIGH-FIELD EPR

267

The energy separation increases linearly with the external magnetic field. This leads to a larger Boltzmann population difference at mm-wave frequencies. The absolute spin polarization at 100 GHz is still only 1.6% at room temperature; therefore it scales almost linearly with the external field. The temperature that corresponds to the Zeeman splitting is about 4.8 K; therefore at liquid helium temperatures the upper level is already depleted, which has effects on some relaxation mechanisms as demonstrated by Kutter et al. (1995) and helps to examine the sign of dipolar couplings D, as demonstrated by Lebedev (1994). A more striking effect is that radicals with different g values are better separated at mm-wave frequencies. If A g is the difference in g values of two radicals, the separation of the two resonance field values, A B, is again proportional to the microwave frequency and a factor of 10 larger at W-band EPR (compared to X-band EPR). This can lead to increased spectral resolution if the separation of the lines overtakes the intrinsic linewidth of the individual spectral lines. Even for a single radical the spectral resolution can be enhanced for disordered solid samples. Here, the anisotropic part of the g matrix competes with other linewidth contributions, such as hyperfine interactions. Whereas the hyperfine line broadening is not field dependent, the anisotropic g matrix contribution scales linearly with the external field B 0 . Thus, if the external field is large enough, the powder spectrum is dominated by the anisotropic g matrix. In this case orientation selection can be achieved for some spectral positions. For these specific orientations single crystal-like information can be obtained, for example, by pulsed EPR or E N D O R experiments. Typical linewidths of EPR lines for organic radicals--mostly dominated by unresolved hyperfine couplings--are about 10-30 MHz. The anisotropy of the g matrix for such radicals is typically on the order of 10-3-10 -4. Therefore microwave frequencies of more than 70 GHz are needed, so that the g anisotropy dominates the spectral shape. This can be used for a definition of high-frequency EPR. As can be seen, this definition is related to the sample properties and not of universal use. Ag giso

//hfi Bo > A-'-'l/2

(18)

B. NUCLEAR HYPERFINE INTERACTIONS

The hyperfine interaction between the electron spin and the nuclear spin is defined by: Hhf i = hS/t[

(19)

268

T . F . PRISNER

This part of the Hamiltonian is not dependent on the external field; the hyperfine splitting stays the same for most of the field values B 0 (high-field approximation for the nuclear spin). But even if the spectral hyperfine line splitting does not change, the nuclear energy levels do, by the nuclear Zeeman interaction. Therefore the mixing of the nuclear spin states can change for the different electronic spin states, depending on the sign of the hyperfine coupling A. This can lead to "forbidden" transitions because the nuclear selection rule for allowed EPR transitions, Am~ = 0, is no longer a strict selection rule for the mixed nuclear spin eigenstates. Therefore, depending on the size of the hyperfine coupling with respect to the nuclear Zeeman splitting, the spectrum will change with the external magnetic field by enhancing or suppressing the forbidden transition intensities. So, by performing EPR experiments at different field values, additional information on the nuclear sublevel wavefunctions can be obtained. In solids these transitions are normally not resolved but hidden under a broad powder spectrum. Pulsed EPR experiments at X-band frequencies have proved to be very efficient in probing the nuclear wavefunctions. Electron spin-echo envelope modulation (ESEEM) of the echo decay function occurs if the nuclear sublevels are mixed differently by the hyperfine interactions for the two electronic spin states involved. While the frequencies of the ESEEM effect are directly given by the energy splitting of the nuclear spin states, the modulation intensities are related to the mixing coefficients of the nuclear spin states. The condition for strong ESEEM intensity in disordered samples is examined in detail, for example, by Flanagan and Singel (1987). Maximum ESEEM intensity is given for a situation in which the quantization axis of the nuclear spin state differs strongly for the two electron spin states m~ = + 1 / 2 and m s = - 1 / 2 . It is easy to imagine that this condition will be fulfilled if the external field B 0 has the same magnitude as the isotropic part of the hyperfine field at the nucleus. In this case for one of the electronic spin states, the external magnetic field B 0 (assumed in the z direction)will almost cancel. The quantization axis will be given by the main axis of the anisotropic part of the hyperfine interaction tensor and may point in any direction. For the other electronic spin state, the isotropic hyperfine field will add to the external magnetic field. In this case the quantization axis will be the z direction if the anisotropic part of the hyperfine field is not very large. The cancellation condition is thus given by: a = YI B0 (20) Therefore, for a given nucleus, with a hyperfine coupling a (given in s -1) and gyromagnetic ratio y~ (given in s -~/T), a specific field has to be

269

PULSED H I G H - F R E Q U E N C Y / H I G H - F I E L D EPR

chosen to satisfy the condition of Eq. (20). For nuclei such as protons, deuterons, and weakly bound nitrogens this situation is closely fulfilled at X-band frequencies. On the other hand, for nuclei with strong couplings and small nuclear gyromagnetic ratios, higher fields are needed to get to the cancellation condition. A nice example of this is given by Coremans et al. (1995). They examined a blue copper protein azurin with pulsed EPR at X-band and W-band frequencies. Whereas the remote nitrogen, with a small nitrogen coupling, dominates the modulation intensity at X-band frequencies, the situation is totally different at W-band frequencies; there the strongly bound nitrogen gives rise to strong ESEEM intensities. Table 6 gives a comparison for proton and nitrogen nuclei. Typical hyperfine couplings together with the corresponding gyromagnetic ratios allow the range of external magnetic field values to be calculated, where strong ESEEM effects can be expected. As can be seen from Table 6, different nuclei will match the requirements of cancellation at different microwave frequencies. But even for a nucleus where the Zeeman splitting is too high at W-band frequencies to fulfill the cancellation condition, the additional information of highfrequency ESEEM might be very useful. If the hyperfine coupling is small compared to the Zeeman splitting, the effect of the (unknown) hyperfine and quadrupole interactions is only a small perturbation to the high-field nuclear spin eigenfunctions, so calculations are rather simplified. This is especially important for nuclear spins I > 1/2, with additional quadrupole interactions.

C. DI P O LAR INTERACTIONS

In the case of an electron spin S > 1/2 the electron spin Hamiltonian and spectrum are further complicated by an additional term Hdip" ^.,,

^

Hai p = h S D S

(21)

TABLE 6 HYPERFINE AND ZEEMAN SPLITI'ING FOR SEVERAL NUCLEI

Nucleus 1H 2H 14N 15N

Hyperfine Coupling a (MHz)

Gyromagnetic Ratio Yx ( M H z / T )

Magnetic Field B 0 for ESEEM (T)

1-20 1-5 3-30 3-30

43 6.5 3.1 4.3

0.01-0.23 0.07-0.38 0.48-4.8 0.35-3.5

.

.

.

.

.

.

270

T.F. PRISNER

The second-rank tensor D describes the self-interaction of the electronic high-spin system and leads to additional splittings of the different Am s = 1 transitions (also called zero-field splitting, ZFS). Again, as for the case of the hyperfine interaction, the ZFS is not field dependent but leads, in combination with the electronic Zeeman Hamiltonian, to a fielddependent mixing of the electron spin eigenfunctions. While the electron spin eigenfunctions for a spin S = 1 are described in zero field by the eigenfunctions T x, Ty, T z, the eigenfunctions at high field are the spin functions T+, T_, and T0. For external fields, where the electron spin Zeeman splitting is comparable with the zero-field splitting D, the electron spin functions are mixed functions with both bases. Also in this region the energy eigenvalues of the different electron wavefunctions are not linearly related to the external magnetic field strength B 0. Again, this leads to more complicated calculations of spectral and dynamic properties, because more complex electron spin wavefunctions have to be taken into account. If the dipole coupling strength D exceeds the microwave frequency Wmw, some of the transitions cannot be excited for any value of B 0 . Here, higher frequency experiments are essential for recording the whole spectrum of the high-spin system. In addition, the high-frequency/high-field EPR experiment at low temperatures allows the sign of the zero-field splitting constant D to be distinguished (Lebedev, 1994), which is normally not assigned by low-frequency EPR spectroscopy. D. EXCHANGE INTERACTION For systems with more than one unpaired electron spin, such as radical pairs or biradicals, there is a further term describing the interaction of the two spins, normally written as: nex = - J ( 1

-k- 2g1,~2)

(22)

For a system of two spin 1 / 2 electronic spins (S 1 = 1 / 2 and $2 = 1/2), this leads to a four-level system which can be described, for example, in a basis of the four spin functions S, T+, TO, and T_. The energy separation between the S and TO wavefunctions is determined by the exchange coupling 2J. If other parts of the Hamiltonian (such as dipole coupling between the two electron spins S 1 and $2 and their Zeeman interactions with the external magnetic field) are also involved, the electron wavefunctions in the basis above are again mixed. This can affect the dynamics and polarization behavior of the four-level spin system, as examined in great detail for photoexcited transient paramagnetic radical pair systems, where the radical pair is created by a fast electron transfer reaction (ClDEP: chemically induced dynamic electron polarization).

PULSED HIGH-FREQUENCY/ HIGH-FIELD EPR

271

By changing the external magnetic field, the mixing properties of some of the four spin eigenstates are altered because of different energy separation of the levels. Again, this can be used to examine the value, distribution, and dynamics of the exchange interaction J in more detail and more accurately. This can often be done by optical techniques, because for these chemical reactions the rate constants and yields are spin dependent and therefore strongly affected by the external magnetic field. Performing EPR experiments at different magnetic field values on these systems probes more directly the properties of the electronic spin states, responsible for the rate constants of the electron transfer reactions. E. RELAXATION PROCESSES AND MECHANISMS Relaxation processes for transverse and longitudinal relaxation, T2 and T1, of the electronic spin depend on the spectral density function J(to) of the stochastic process. The spectral density function of the stochastic process is probed at different frequencies (such as to = 0, 1 too, 2to0). If the spectral density of the process is not "white," the frequency dependence can be used to identify the relaxation process. For the solid state three main relaxation processes can be distinguished, the direct process, the Raman process, and the Orbach process. In the direct process, phonons with the electron spin transition energy couple to the electronic spin system. Usually the electron spin energy separation is given by the Zeeman splitting and therefore the phonons that couple to the relaxation process can be tuned by the microwave frequency. The longitudinal relaxation time 7"1 for the direct process is given by Bowman and Kevan (1979):

1 (OH)2(htomw) --Or, 3 I]/1 ~ 62 coth T1 tomw

kT

2 kT (I tomw

(

I]/1

0H

r

)2

(23)

where $1 and $2 are the two electron spin wavefunctions, and 3 H / 3 e is the derivative of the spin Hamiltonian H with respect to the modulation by the phonon process. The approximation is valid for the hightemperature limit, where kT is much larger than the energy difference of the two electronic spin states. Thus, the longitudinal relaxation rate 1 / T 1 of the direct process is proportional to the square of the microwave frequency. There is an additional dependence by the term

2

(~//1 ~0. I//2)1 which describes the relaxation mechanism responsible for the relaxation process. This term can have an additional dependence on the microwave

272

T.F. PRISNER

frequency, which will be investigated below. By measuring the frequency and temperature dependence of the longitudinal relaxation rate, the responsible mechanism and process can be determined. Whereas the direct process is a first-order effect in perturbation theory, the Raman and Orbach processes are second-order processes in the modulation of the spin Hamiltonian, where another virtual or real excited state is involved. Therefore for these processes the dependence of the microwave frequency is less obvious and mostly very weak. Only in cases in which the phonon lifetime approaches the inverse of the microwave frequency, an inverse dependence on the microwave frequency allows for the Orbach process, as described in detail by Bowman and Kevan (1979). The longitudinal relaxation rate in this case is given by:

T1

at _.-L--T-csc h - ~ OJmw

(24)

where E is the energy difference between two phonon modulated states. Somewhat different dependences are obtained for Kramer's salts of rare earth ions (Poole and Farach, 1971). In this case the longitudinal relaxation rate 1 / T ~ is given for the direct process by: 1 ct TB 4

(25)

L and for a two-phonon Orbach process by: 1 ct BZ T 7

(26)

L In the past mostly the temperature dependence of these processes has been examined and used to distinguish them. Pulsed EPR at different microwave frequencies offers a new way to examine and discriminate them. The theoretical models for the relaxation processes stated above suggest an increase in the relaxation rate and therefore a decrease in the longitudinal relaxation time by going to higher microwave frequencies. On the other hand, the experimental results of most of the pulsed high-field experiments performed show an opposite effect. For most reported applications on solid-state samples the relaxation times T1 and T2 tend to increase. Some examples are listed in Table 7. As mentioned earlier, the relaxation mechanisms which are responsible for the modulation of the spin Hamiltonian and the coupling of the lattice to the spin system also have different frequency dependences. Here, only some of the possible mechanisms will be mentioned, which have strong frequency dependences and of which applications will be shown in the next section.

273

PULSED HIGH-FREQUENCY / HIGH-FIELD EPR TABLE 7 RELAXATION TIMES AT X-BAND AND MILLIMETER-WAVE FREQUENCIES OF SEVERAL TEST SAMPLES TI

(X-band/W-Band) Sample DANO (nitroxide, crystalline) TEMPO (frozen solution, 120 K)

Malonic acid (y-irr., crystallineY Calcium formeat (powder) Quarz (y-irr. crystalline)b Pentacene (in p-terphenyl, photoexcited triplet, RT) c PT~0.(plant reaction center, 110 K)d P~65.(bact. reaction center, 150 K) e C60 (photoexcited triplet, toluene, RT) / C70 (photoexcited triplet, toluene, RT) f H 2 TPP (photoexcited triplet, toluene, 110 K)g (FA) 2PF6 (organic conductor) h

(p-s) 5/4 4/10 20-100/30 30i/35i-180

200/300

50/30 < 1/36 5/100-300 0.45/0.45 ?/0.15 60/100 12/1.4

T2 (X-Band/W-Band) (p.s) 0.2/0.7 0.5/0.2 1-5/3 0.6/2 24/26

3/5 0.5-1/0.8 1-2/2 0.425/0.45 0.05/0.01 <0.01/<0.01 12/1.4

X-band experiments: H6fer et al. (1986) ~Lee et al. (1993) bGhim et al. (1995) CSloop et al. (1981) dKothe et al. (1994) eDzuba et al. (1995) eKothe et al. (1994a) a

fDinse (in prep.) gJaegermann et al. (1993) hMaresch et al. (1984) /stimulated echo decay ( < T1)

One of the important mechanisms for relaxations of the electronic spin system is the modulation of orientation-dependent parts of the Hamiltonian by motion of the radical itself. Where the rotational process itself is not dependent on the microwave frequency, the orientation-dependent anisotropic parts of the Hamiltonian might be as stated above. The anisotropy of the g matrix, for example, leads to a direct proportionality of the strength of the modulation with the microwave frequency. So for a disordered sample, where the spectrum is dominated by the g anisotropy, pulsed high-frequency EPR is a powerful tool for examining the libration or rotational motion of the radical. The relaxation effect by the modulation of the g anisotropy is enhanced at high frequencies, so it can more easily dominate other relaxation mechanisms. In addition, be-

274

T.F.

PRISNER

cause of the orientation selection mentioned above for this case, highly informative anisotropic relaxation data can be obtained over the spectral range which will give detailed information on the motional process of the radical in its environment. Examples of the utility of this method for pulsed high-frequency EPR will be given in the next section. For liquids the change to higher frequencies may result in a transition from the fast motion limit, where ~'c A to << 1, to the slow motion limit, where the broadening mechanism is much more pronounced and informative. In this limit:, rotational motion can be examined in much greater detail as demonstrated with impressive accuracy and resolution by the group of J. Freed in numerous publications (for example, see Budil et al., 1993), Earle et al., 1993, and references therein). The situation is different for a modulation of the zero-field coupling, such as by a libration motion of a high-spin transition metal ion in a biological enzyme. Going from a Zeeman splitting where D > tomw to a microwave frequency where D < tomw leads to a different modulation depth of the energy eigenvalues and therefore transition frequencies. This is shown in Fig. 4, where energy eigenvalues for the most simple spin S = 1 case are shown as a function of the external field. Where a modulation of the zero-field splitting D at low frequencies leads to a nonlinear modulation of the energy separation (and therefore the resonance field strength Bres) , the dependence in the high-field region is linear.

FIG. 4. S = 1 energy level diagram with zero-field splitting, as a function of external magnetic field B 0 . T h e p a r a m e t e r s for the zero-field splitting are D - 8 G H z , E = 0 G H z . T h e variation of the splitting is 6D/D - _+20%. T h e energy eigenfunctions are calculated for a molecular orientation x parallel to B 0 .

PULSED HIGH-FREQUENCY / HIGH-FIELD EPR

275

This leads to a reduced change in the resonance frequency for a modulation of the D value at higher frequencies and therefore a smaller linewidth. The same effect can be observed on a static inhomogeneous linewidth, if a distribution of D values occurs, such as by a heterogeneity in the sample. This list is far from covering all field/frequency-dependent relaxation effects in EPR. A close look at most of the applications will show such contributions. Rather specific examples will also be shown in the next section for samples with high conductivity, such as one- or two-dimensional organic conductors. For such samples with a high conductivity the lineshape of the observed resonance is distorted by phase changes due to the induced eddy currents in the sample, as described by Dyson (1955). This leads to an admixture of dispersive parts of the complex magnetic susceptibility ( g ' ) to the usual observed absorptive part (g"), depending on the size and the shape of the sample. Maximum admixture and therefore distortion of the lineshape is given for sample sizes comparable to the skin depth 6s of the sample. The EPR experiment probes the conductivity ~r(to) of the sample at the microwave excitation frequency. Therefore high-frequency EPR extends the frequency range of the conductivity data measurable by EPR methods. In addition, because the skin depth 3s is also a function of the frequency: r

6s

=

v/2rrtr (to) w

(27)

the high-frequency EPR is much more sensitive to these effects for small samples. This is shown for a two-dimensional organic conductor /3~(BEDT-TTF)2I s sample in Fig. 5. The thickness is between 150 and 2 5 0 / , m for the two crystalline flat plates. Whereas the small sample is still nearly purely absorptive, the lineshape of the thicker sample is already Dysonian. Thus, the skin depth and therefore the high-frequency conductivity can be derived. A somewhat similar effect, called radiation damping and first described by Bloembergen and Pound (1954) and by Bloom (1957), is observed if the sample has a strong magnetic susceptibility. In this case, a back interaction of the oscillating magnetic field is induced by the strong signal with the spin magnetic moment. Therefore the Bloch equations, describing the interaction of the magnetic moment with the external magnetic field, have to be coupled with the cavity equation, describing the interaction of the induced signal with the cavity. The possible effects on the dynamics of the spin system are discussed in detail by Warren et al. (1989). The induced signal is described by: B x ct M o Q r t

(28)

276

T.F. PRISNER 150 lam thickness

reference

250 ~tm > .,..~

reference

20 mT magnetic field B0 FIG. 5. Dysonian lineshape effects on cw EPR spectra by high-frequency (140 GHz) conductivity of the two-dimensional conductor /3--(BEDT-TTF)2I3 for two flat plates of different thicknesses: (a) 150/.~m; (b) 250/xm.

where M 0 is the Boltzmann magnetization of the sample, Q is the quality factor, and r/ is the filling factor of the cavity. The effect is more pronounced at high frequencies, because M 0 becomes larger (proportional to the excitation frequency) and often Q and 77 may also be increased. This leads to distortions and nonlinearities in the system response. An example of such nonlinearities for a two-pulse excitation was already shown in Fig. 3. The same effect was also observed on cw and FT E P R spectra of small crystallites of a one-dimensional organic conductor fluoranthenyl hexafluorophosphate, as reported by Prisner et al. (1992). Due to anisotropy of the g matrix different crystallites are dispersed in the frequency range and can be distinguished by their spectral position. The cw and pulsed experiments both show different lineshapes for large and small crystallites, but to a different extent. This is expected because in the cw experiment, there is only a self-interaction of each crystallite with its own signal, whereas in the pulsed experiment all signals interact with all different crystallites at the same time, because of the broadband excitation, which may lead to more complex interference effects.

PULSED HIGH-FREQUENCY / HIGH-FIELD EPR

277

For a single line the FID signal is given approximately by (Bloembergen and Pound, 1954): ~bFiD(t) = sec h(27rXoBoQrWt)

(29)

With the reported value for the susceptibility of 3 x 10 -5 cm4/mol (Maresch et al., 1984), the damping of the FID signal is almost the measured T2 time of 1.4 /xs. Therefore at high frequencies this effect cannot be neglected any more. At X-band frequencies the Te time is substantially longer (Table 7).

IV. Applications of High-Field/High-Frequency EPR A. MEASUREMENTS OF PRINCIPAL G VALUES ON DISORDERED SAMPLES

As already explained in the preceding section, one of the main advantages of high-field EPR is the potential to resolve small g tensor anisotropies for organic radicals. This additional spectral resolution shows up in most of the high-field EPR applications. Whereas it is the main argument for cw EPR applications, this increased spectral resolution is very often also the main advantage of pulsed high-frequency EPR applications. Therefore this argument will follow as a central theme throughout the applications shown here. We will start will a classical example of g tensor resolution in cw EPR spectra. For many systems the anisotropic g matrix powder pattern is not resolvable at X-band EPR frequencies, because it is obscured by inhomogeneous linewidth contributions from unresolved hyperfine couplings. This can be overcome at high frequencies, if this other inhomogeneous broadening mechanism is not field dependent. This not only offers the possibility of performing orientation-selective work, but also the g anisotropy contains direct information about the symmetry and elongation of the electronic wavefunction. The principal values of the g matrix are difficult to calculate with high accuracy for organic radicals with extended electronic wavefunctions. Nevertheless, conclusions about the symmetry and surrounding of the molecule can often be drawn by the change of the experimental main g matrix values under various conditions of the sample. This is demonstrated with a small sample of galvynoxyl radical in a polystyrene matrix in Fig. 6. EPR spectra at 140 GHz (F-band) and at 9 GHz (X-band) for the same sample are shown for comparison. While the X-band spectrum is a complicated superposition of anisotropic hyperfine and anisotropic g tensor contributions, the F-band spectrum directly shows the main values of the g tensor in the spectrum. In addition, this

278

T . F . PRISNER

F-band (140 GHz)

5 mT X-band (9 GHz)

m

!

i

m

5mT FIG. 6. EPR spectra of galvynoxyl radical in polystyrene, measured at F-band (140 GHz) and X-band (9 GHz) frequencies for comparison. The small sample contains approximately 3 x 1015 spins. Microwave power was 10 ~W at 140 GHz and 100 /~W at 9 GHz. Detection bandwidth was 1 Hz.

comparison with the same sample demonstrates the increased sensitivity of the high-field experiment for small sample sizes. Bresgunov et al. (1992) also used high-field (140 GHz) EPR to analyze quantitatively the g tensor of the galvynoxyl radical in frozen solutions and obtained structural information on the nonplanar geometry of the two phenyl rings of the radical. There are numerous publications demonstrating the resolution enhancements of g tensor anisotropies by high-frequency cw EPR. Here a pulsed application, which measures and relies on the g tensor main values and their orientations, will be shown. Spin-polarized spectra of photoexcited transient states of photosynthetic reaction centers will be discussed in more detail in the next paragraph. Figure 7 shows such spectra for transient radical pairs of plant and bacterial reaction centers, measured by

PULSED HIGH-FREQUENCY / HIGH-FIELD EPR Zn-bRC's

279

PS I

,~ W-BAND A

W-BAND

A t

...

3381'.0

3387'.0

B0/mT

3393'.0

~ X-BAND

/•

338110

3387'.0 B0/mT

~ X-BAND

/• . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

i

. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .

33710

34310

3393'.0

. . . . . . . . . . . . . . . . . . . . . . . . .

. . . . . . . . . . . . . . . . . . . . . . . . . . . . .

B0/mT

34910

31570

32110

B0/mT

32710

FIG. 7. Spin-polarized spectra of the photoinduced charge-separated radical pair in photosynthetic reaction centers. (a) Radical pair Ps~5"-QA" of zinc-substituted bacterial reaction center of Rhodobacter sphaereoides R-26. (b) Radical pair P~00"-Af" of photosystem I of cyanobacteria. In both cases the high-frequency (W-band) spectra are for protonated samples, and the low-frequency (X-band) spectra are for fully deuterated samples. The W-band spectra are recorded by field-swept two-pulse echo spectroscopy, and the X-band spectra are recorded via transient EPR spectroscopy as described in Stehlik et al. (1989), Fiichsle et al. (1993), and van der Estet al. (1993).

pulsed high-frequency EPR at 95 GHz. More information than just the g matrices of the two radicals enters in the description of this spin-polarized spectrum, as will be explained in the next paragraph. Here we will concentrate on the g matrix values and their orientations that can be deduced from this transient spectrum. For the radical pair (P~0b-Al") spectrum of photosystem I, the low-field part of the spectrum is solely described by the gxx and gyy g tensor contributions of the vitamin K 1 anion radical A1-. The analysis of the high-frequency spectrum clearly shows a shift of the gxx value of this g matrix compared to in vitro measurements (Burghaus et al., 1993) of the same anion radical in a frozen solution of isopropanol. Thus this g matrix value is strongly affected by the surrounding of the molecule and this can be probed sensitively by the pulsed high-frequency technique. The high-field part of the spin-polarized spectrum is dominated by the donor chlorophyll dimer molecule (P8~5" and PT~0"). For an accurate simulation of the spin-polarized spectrum the main g matrix values of these tensors also have to be known. Unfortunately, their g anisotropy is too small to be determined from these measurements at 95 GHz without ambiguity. The main values of these g tensors were

280

T.F. PRISNER

determined independently, with high-field cw EPR at 140 GHz by Prisner et al. (1993) for PT00" and with cw high-field EPR experiments at 95 GHz on single crystals by Klette et al. (1993) for P~65"- With the single-crystal measurements not only could the main g matrix values be determined, but also information on the orientation of the g tensor within the chlorophyll dimer molecular axis system could be obtained. Because of four magnetic inequivalent sites in the crystal unit cell, four different orientations of the g matrix within the molecular frame are possible. In this case, the spin-polarized high-field spectrum of the correlated radical pair, together with the X-ray data, could solve this ambiguity, because the g tensor orientation was now related to the molecular as well as the dipolar axis of the coupled spin pair (Prisner et al., 1995). Thus, highly specific information on the orientation and surrounding of radicals, their electronic wavefunction, and chemical identity can be obtained by various high-field EPR methods. The dependence of the main g values on the specific surrounding of the molecule is explored with cw high-field EPR for stable nitroxide radicals by Tsvetkov et al. (1987) and Gulin et al. (1991) and for chemically created semiquinone radicals by Burghaus et al. (1992). B. SPIN-POLARIZED TRANSIENT SPECTRA OF COUPLED RADICAL PAIR SYSTEMS

Spin-polarized spectra of coupled radical pair systems are widely studied by EPR. For reviews on the subject see, for example, Hore (1989), Snyder and Thurnauer (1993), and Salikov et al. (1984) and references therein. Photoexcitation leads to a fast charge separation and the creation of a paramagnetic radical pair state. Under most of the experimental conditions this radical pair recombines within milliseconds back to a neutral species, so time-resolved or pulsed methods are usually used to study the kinetics and polarized spectra of the coupled radical pair. The spin Hamiltonian of such a couple radical pair is described by the dipolar and exchange interactions, g matrices, and hyperfine couplings of the two radicals. This Hamiltonian can be explicitly time dependent on the time scale of the lifetime of the transient state, if the two radical are mobile in a liquid. In this case, the Hamiltonian is controlled by the diffusive motion of the two radicals in the liquid, which may be a very complex process. The examples described here are for systems where the radical pair system is more or less rigid. This can be achieved by embedding the two radicals in a protein environment, as in the photosynthetic reaction center case, or by a covalently bound donor-accepted system, as for linked porphyrin-quinones.

PULSED HIGH-FREQUENCY / HIGH-FIELD EPR

281

Nevertheless, the radicals are not really frozen in their relative orientation and distance, which might lead to additional dynamic contributions to the spectrum. Already in the static case, the Hamiltonian of such a two-spin system has more free parameters than can be assigned without ambiguity from the spin-polarized EPR spectrum at one fixed microwave frequency alone. Therefore independent knowledge of some of the parameters is normally mandatory. This can be achieved, for example, by EPR measurements on the single radicals, to get their g matrices. Again, this will be preferentially done by high-frequency EPR, with its increased resolution and accuracy for these values. Hyperfine couplings can be obtained independently by ENDOR experiments and the relative orientation and distance of the coupled radical pair can be extracted from X-ray experiments on single crystals (if available) or from calculations. These values are very helpful as a starting point for the simulations of the spin-polarized spectrum but need not necessarily be identical for the coupled radical pair system! This is because several of these parameters are measured under different conditions, such as the diamagnetic ground state, oxidized or reduced samples, different temperatures, or different environments. For an unambiguous assignment of the parameters describing the coupled radical pair system, it is important to increase the information content of the transient EPR experiment. Therefore experiments with additional information content have to be performed, adding a new dimension to the experiment. This can be either a time dimension, where additional information about the coherences of the coupled radical pair is contained, or the microwave excitation frequency dimension, separating contributions by their different frequency dependences. Figure 7 shows spin-polarized spectra of two different correlated radical pair systems. The spectra on the left are for the photoexcited radical pair Ps~5"-QA" of a Zn-substituted bacterial reaction center of Rhodobacter sphaeroides R-26, and the spectra on the right are for the photoexcited radical pair P7-00"-A{" of plant photosystem I. Two spectra are depicted for each system, at 9 GHz (X-band) and 95 GHz (W-band) microwave frequencies, corresponding to magnetic field values of 0.3 and 3.4 T. As can be seen, there is a strong change in the spectral characteristic on going from X-band to W-band frequencies. This is because the high-frequency spectra are dominated by the anisotropies and differences of the two g tensors, whereas the X-band spectra are strongly influenced by the hyperfine couplings of the two radicals to their nuclear spins, although the X-band experiments are performed for deuterated samples with reduced hyperfine couplings.

282

T . F . PRISNER

Close inspection of these spectra allows a very detailed stereogeometry of the two radicals in their protein environment in the photoexcited active state to be obtained, as described by Prisner et al. (1995) and references therein in detail. Here, only the high-frequency aspects will be briefly mentioned: The two high-field radical pair spectra in the two different reaction centers are very different. Immediately, a different structural arrangement of the two radicals with respect to each other can be inferred for the two photosystems. This was already concluded from the K-band experiments as described by Fiichsle et al. (1993) but cannot be obtained easily from the X-band comparison. Therefore the high-frequency experiments demonstrate the increased sensitivity to the relative geometry of the correlated radical pair for these systems. Nevertheless, spectra at different microwave frequencies are clearly necessary to assign all the parameters describing the spin system. For example, the dipole coupling tensor, mostly responsible for the spin polarization pattern, can be assigned with more significance by simultaneous fitting of the spectra at various frequencies. Covalently bound porphyrin-quinone (P-Q) molecules also create a correlated charge-separated radical pair system (P+.-Q--) under specific conditions, as described by Schliipmann et al. (1993). The radical pair state observable on the time scale of EPR experiments is created in this case via a triplet precursor state of the porphyrin (pT_Q),, in contrast to the photosynthetic reaction centers. Whereas the spin-polarized spectra and the time-resolved kinetics at X-band frequency alone can be successfully analyzed by a static Hamiltonian for the coupled radical pair, the multifrequency experiments in this case show that the Hamiltonian has to be dynamically modulated on the time scale of the EPR experiments, to explain all of the results with one set of parameter values. Figure 8 shows kinetic traces at different Zeeman frequencies for a zinctetraphenylporphyrin covalently bound with a cyclohexylene bridge to a benzoquinone molecule (ZnTFP-BQ). The benzoquinone molecule is still flexible around the bridge axis, under the experimental conditions (temperatures of 150 K, ethanol solution), therefore some of the spin Hamiltonian interactions (as g a n d / o r J values) will be modulated and time dependent. Again, the analysis of the spectra and kinetics at different Zeeman frequencies sets much more stringent restrictions on the parameters of the spin Hamiltonian and on the proposed dynamical model. C. HIGH-FIELD E P R

ON M n 2+ CENTERS IN PROTEINS

In the examples shown so far, the spectral resolution was increased by stretching the powder pattern by anisotropic g tensor contributions. An opposite effect can be observed for high-spin systems in disordered solids,

i

i

i

'

i

optical detection

Zero-Field I

,

I

,

I

I

,

0

10

20

30

1

i

'

i

'

I

~

'

,

,

t [us]

i

'

ta

X-Band l

,

0

10

I

20

30

,

t [us]

t,!ai,,,,,, / e /

~, ,,y~,~-, ,#~,e~t '';', ,,~,t......

4, ~

%~/;f '

,

0

I

,

10

!

K-Band ~

20

I

30

;

t[us]

*eL I

0

i

,

10

w

20

I

I

30

l

t [us]

FIG. 8. Transient signal of the photoinduced radical pair P + - Q - of a zinctetraphenylporphyrin covalently linked with a cyclohexylene bridge to a benzoquinone molecule. Shown are the reaction kinetics of the transient triplet radical pair state at 150 K in ethanol solution. The zero-field experiments provide transient optical data and have therefore no spin polarization effects (fast rise) (for details see Fuchs et al., 1996). The X-band, K-band, and W-band experiments are transient EPR experiments; the buildup is given by spin polarization effects. X-band experiments were performed by SchliJpmann et al. (1993). The K-band data were provided by A. van der Est. The signal-to-noise ratio is worse at higher frequencies, because the sample size has to be reduced strongly because of the highly polar solvent.

284

T.F.

PRISNER

for example, a n M n 2+ ion (S = 5/2). In this case, the transitions are broadened by contributions from the zero-field splitting tensor D, as explained in the previous chapter. Normally, only the m s = - 1 / 2 to + 1 / 2 transition is observed, because of severe broadening of the other transitions. The linewidth of the hyperfine split lines (I = 5 / 2 for Mn 2§ ) of this transition are influenced only by second-order contributions from the ZFS coupling: D

AO)I/2 (X D - -

(30)

to 0

This leads to a reduction of this linewidth contribution for each of the individual hyperfine lines at high frequencies. In addition, the spectrum is simplified at higher frequencies, because of the intensities of forbidden transitions Am~ = _+1 are strongly reduced. The frequency dependence of the relative intensity of the forbidden transitions is given by: /forbidden

Ial,owe

cx

D2

(31)

Therefore the high-frequency spectrum of this transition is more sensitive to other line-broadening mechanisms. One other contribution to the linewidth is the modulation of the anisotropic Hamiltonian (D) by motional dynamics of the molecule; this effect is also decreased as described in the preceding section. The second contribution is a line broadening by hyperfine coupling to nearby nuclei. In Fig. 9 such an effect is shown for a p21-ras GDP protein, where an Mg 2+ is replaced by a n M n 2+ ion in the active site of the enzyme. The Mn 2§ center is located close to the guanosine diphosphate (GDP) complex, as can be seen from the hyperfine broadening of the Mn 2§ hyperfine lines by ~70 labeling of the GDP at the /3-phosphor position (the first hyperfine line m I = - 5 / 2 of the m s = - 1 / 2 to + 1 / 2 transition is shown). The hydration number of the Mn 2§ in the active site by water molecules can be proved similarly by replacing the water by l a b e l e d H2170. This analysis was already done for this system by Smithers et al. (1990) and Latwesen et al. (1992) with Q-band EPR work, but the accuracy and significance of the analysis are strongly improved by going to higher microwave frequencies [Bellew et al. (1996)]. Whereas at Q-band frequencies deconvolution and difference methods still have to be used to see the effect of the 170 labeling in the spectrum, this can be seen at W-band frequencies directly without further manipulation of the spectrum. For other proteins even higher magnetic field values will be necessary to resolve specific hyperfine couplings.

PULSED HIGH-FREQUENCY / HIGH-FIELD EPR

285

experimental

-1

1

3

field (mT) simulation i

-3

-1

1

3

field (mT)

FIG. 9. W-band EPR spectra of Mn 2+ in a p21-ras GDP complex protein. Shown is only one manganese hyperfine line (m I = -5/2) of the m s = - 1 / 2 to +1/2 transition. The spectra correspond to the native system, the system with the GDP labeled with an 170 at the B-position of the phosphor, and the native sample exchanged with 50% H2170. The simulations are powder averages with D = 100 G, E = 0 G, a residual linewidth of 8.4 G, Mn hyperfine splitting of 94 G, and an isotropic 170 coupling constant of 2.4 G. The H2170 sample is simulated with a coordination of the Mn 2+ to four water molecules and the simulation of the /3-1TO-labeled sample with a 50% labeling efficiency. The measurements were all performed at room temperature with a 0.2-mm-diameter capillary, corresponding to a sample size of approximately 10 nl.

T h e p u l s e d m e t h o d s offer t h e a d d i t i o n a l possibility of m e a s u r i n g t h e r e l a x a t i o n times. W i t h t h e high t i m e r e s o l u t i o n of t h e p u l s e d high-field E P R setup, /'1 a n d T 2 r e l a x a t i o n t i m e s w e r e m e a s u r e d for the p r o t e i n f r o m r o o m t e m p e r a t u r e d o w n to 100 K. E v e n at 100 K t h e T 1 a n d T 2 r e l a x a t i o n t i m e s are short (300 ns), b u t still l o n g e r t h a n t h e m e a s u r e d linewidth of a b o u t 0.5 to 1 m T . W i t h t h e s e a d d i t i o n a l m e a s u r e m e n t s m o t i o n a l c o n t r i b u t i o n s to t h e l i n e w i d t h can easily be d i s t i n g u i s h e d f r o m static i n h o m o g e n e o u s b r o a d e n i n g by h y p e r f i n e couplings.

286

T . F . PRISNER

Because of the narrowing of the linewidth with increasing microwave frequency, these signals are very strong at high frequencies and can easily be observed, even if the signal is not observable by highly sensitive X-band experiments.. The amount of sample used for the W-band experiments shown in Fig. 9 is only 10 nl. With this small amount of sample (0.2-mm capillary), the cavity could be coupled with this aqueous sample even at room temperature, allowing experiments under physiological conditions. This high sensitivity can also be a disadvantage, because natural Mn 2§ of the protein may obscure the observation of other radicals at high frequencies (for example, in photosynthetic reaction centers). High-field EPR is therefore a very sensitive method for studying the surrounding, coordination, and occurrence of Mn 2§ even in very dilute protein systems. D. HIGH-FIELD ESEEM NITROGEN NUCLEI For a nitrogen nucleus 14N with I - 1, coupled to an electron spin S = 1/2, three parts of the spin Hamiltonian determine the intensity and frequencies of the ESEEM modulation. These are the nuclear Zeeman interaction with the external field, the quadrupole interaction of the nitrogen nucleus, and the hyperfine coupling to the electron spin. Whereas the quadrupole and hyperfine interaction are not field dependent, the nuclear Zeeman interaction is. The ESEEM frequencies have a rather simple frequency dependence for the high-field case (where the nuclear Zeeman splitting to~ is larger than the hyperfine and quadrupole splitting). On the other hand, it is well known that the ESEEM intensities contain additional information on the wavefunctions and therefore on the spin Hamiltonian. The ESEEM intensities have a strong nonlinear field dependence, especially for the cancellation region, where ESEEM intensities blow up, as demonstrated for disordered samples by Singel (1989). The ESEEM intensities are given by the change of nuclear eigenfunctions by the hyperfine coupling tensor A. Whereas it is well known that the quadrupole interaction can change the ESEEM intensities, it cannot create ESEEM by itself. Therefore a hyperfine induced field Bhfi given by: l Bhfi =

"Ye

m S "Ye

is necessary to change the quantization axis for the nuclear spin depending on the m s state and therefore the composition of the nuclear wavefunctions. This induced field has to compete with the external field B 0 and a pseudofield Bq, describing the quantization of the nuclear spin in the combined Hamiltonian of the nuclear Zeeman and quadrupole interaction. Whereas only the Zeemand field is frequency dependent, the other two

PULSED HIGH-FREQUENCY/ HIGH-FIELD EPR

287

interaction tensors A and Q are orientation dependent. For many cases, ESEEM experiments at X-band frequencies alone failed to determine quantitatively and without ambiguity both of these tensors with their relative orientation. This is even more true for complicated systems with more than one nitrogen coupled to the electron spin, that is, for the primary donor in photosynthetic reaction centers mentioned above. Therefore a measurement at high fields, where the g tensor anisotropy allows an orientation selection, again considerably increases the information content for disordered samples. Performing these measurements at different external field values, together with the orientation-selective information of high-field EPR, should, in principle, allow a separation and full determination of the hyperfine tensor A and quadrupole tensor Q. In practice, the information content is limited by a small modulation depth (at least for some orientations) and by broad ESEEM linewidths for disordered samples. Figure 10 shows an experimental high-frequency (95-GHz) ESEEM spectrum for a DANO single crystal. The high-pass filtered stimulated echo decay time domain signal and the Fourier-transformed ESEEM frequency spectrum are shown. The observed ESEEM frequencies are nitrogen couplings of the m s = - 1 / 2 manifold. The stimulated echo modulations are very narrow and can easily be observed even with a small modulation depth of below 10% of the echo signal intensity. The situation becomes more complicated for powder samples, as mentioned above. Figure 11 shows the two-pulse ESEEM spectrum of the DANO nitroxide for a disordered powder sample. Still ESEEM lines can be observed by pulsed W-band EPR experiments, but only for the "low-field" part of the powder spectrum (external magnetic field parallel to gxx and gyy axis of the molecule). For the "high-field" part of the modulation depth is too small and the spread in ESEEM frequencies too broad to be observable. Further experiments, especially well suited for powder spectra ESEEM, such as HYSCORE experiment introduced by H6fer et al. (1986) or the DEFENCE experiment by Ponti and Schweiger (1995), are under progress in our laboratory and may help to increase the information content of high-field powder ESEEM spectra. E. LIBRATION OF MOLECULES STUDIED BY PULSE ECHO EXPERIMENTS The high sensitivity of EPR spectroscopy for motional processes is well known (see, for example, Budil et al., 1989). This sensitivity can be improved further with pulsed echo methods, as demonstrated by Millhauser and Freed (1984) and a series of other publications from Freed's group at Cornell. The echo experiments are blind for static line

288

T.F. PRISNER

1

0

3 5 pulse separation [Ixs]

10 frequency [MHz]

7

20

FIG. 10. High-frequency (95-GHz) two-pulse ESEEM experiment on DANO crystal. Shown are a time domain echo decay function (highpass filtered with 5% of the Nyquist frequency) of a stimulated echo and its corresponding Fourier-transformed spectrum. The nitrogen splittings for the m s = -1/2 manifold for different sites in the crystal can be distinguished in the Fourier spectrum.

broadening mechanisms, such as hyperfine broadening. Thus dynamic line broadening contributions can be observed which are normally hidden under broad static contributions and therefore not observable with cw E P R spectroscopy. For many organic radicals, the low-frequency (X-band) E P R powder spectrum is dominated by inhomogeneous line broadening of unresolved hyperfine interactions. In these cases, there is barely any spectral information (despite the g factor value and linewidth). The two-pulse echo experiment can still detect slow dynamic contributions to

PULSED HIGH-FREQUENCY / HIGH-FIELD EPR

289

EPR powder spectra

magnetic field B0

2-pulse ESEEM of DANO powder N 10 -r" ._._,

>, o c. a o

~

50

I _ O

l

_!

field [G]

_l

..... l

l

100

F[o. 11. High-frequency (95-GHz) two-pulse ESE E M experiment on a powder sample of DANO. The Fourier-transformed E S E E M frequencies are shown as a function of the spectral position in the powder E P R spectrum. E S E E M intensities are seen only for the gxx and gyy range of the powder spectrum. For the g~z orientation the hyperfine coupling is too large to mix the nuclear sublevels efficiently.

the linewidth but is in this case a purely one-dimensional experiment in the time domain. Therefore, hardly any detailed information on the motional process can be obtained from the echo decay function. The situation is different, if there is an orientation resolution in the spectral range by anisotropic interactions. In this case two-dimensional experiments allow a much more detailed analysis of the motional process. At X-band frequencies, this is mostly demonstrated for nitroxides, where a large g anisotropy and the large anisotropic hyperfine tensor of the nitrogen allow this partial orientation selection (see, for example,

290

T . F . PRISNER

Gorcester and Freed, 1986). At high fields, this can also be achieved for molecules with small g anisotropies and hyperfine couplings. Figure 12 shows such a two-dimensional experiment for a semiquinone anion radical. The sample is a ubiquinone U-10 measured in a frozen solution of isopropanol at 120 K. The echo decay exhibits a strong T2 relaxation anisotropy over the spectral range. This can be seen easily in Fig. 13a, where field-swept, echo-detected spectra are shown for different pulse separation values ~'. They can be simulated by small-angle libration of the molecule. Assuming a libration about the three main axes of the g tensor, the simulation gives a nearly isotropic motion of the molecule, about 20 ~ for an isotropic correlation time of ~'c = 5 ns. The anisotropy of the echo decay function is totally different for the same semiquinone embedded in a protein environment, as can be seen in Fig. 13b. The ubiquinone is created as a transient radical in the photosynthetic electron transfer reaction of bacterial reaction center Rhodobacter sphaeroides R-26, as explained in the example of Section IV.B. In this case the anisotropy of the two-pulse echo can be simulated with an anisotropic motion of the molecule about its g tensor x axis ( C B O axis). This is also expected for the molecule from X-ray studies (Ermler et al., 1994), where two H-bridge bonds from nearby protein molecules (His M219 and Ala M260) to the oxygen are proposed. Therefore these measurements clearly allow us to probe the geometry and chemistry of the radical close sur-

=

%

% r

magnetic field Bo

FIG. 12. Two-pulse echo signal intensity of a chemically reduced ubiquinone radical in a frozen isopropanol solution at 120 K. One dimension is the magnetic field value B0; the other dimension is the pulse separation ~'. The echo decay function is anisotropic with respect to the spectral position. For each data point 200 echos are averaged. The field range is 10 mT; the pulse separation is varied between 150 and 4150 ns.

PULSED H I G H - F R E Q U E N C Y / H I G H - F I E L D EPR

in isopropanol

small (O 0 (D

5

large field position BO in reaction center R-26

o~

~D 0 ~D

large field position B0 FIG. 13. Two-pulse echo-detected spectra for different pulse separations ~-. The spectra are arbitrarily normalized to have the same maximum intensity for better comparison. The upper diagram is for the frozen isopropanol solution (from Fig. 12), the lower one for the ubiquinone in a bacterial reaction center Rhodobacter sphaeroides R-26. The anisotropies of the two-pulse echo are very different in the two cases, expressing the different molecular mobilities of the radical in the two environments.

291

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T.F. PRISNER

roundings. A more detailed analysis of the librational motion of the ubiquinone in isotropic solution and the protein environment of the bacterial reaction center is given in Rohrer et al. (1996). Two further things are worth pointing out for this application: First, the absolute decay rate does not change very dramatically between the two experiments. This means that the information on the anisotropy of the motion could be obtained only by the spectral highly resolved high-field experiment and not by one-dimensional low-field echo decay functions. Second, the effect of the motion on the two-pulse echo decay is increased by a factor of 100 for this experiment performed at 95 GHz (W-band) compared to an experiment at 9.5 GHz (X-band). The T2 relaxation time is given in the Redfield approximation by: 1

r2

= A to2rc

(33)

where A 0) 2 is the mean square value of the electron spin Zeeman splitting modulation by the motional dynamics. In the case of g anisotropy this is directly proportional to B 2 . Because there is also an isotropic contribution to the echo decay, not related to the motion, this would most probably make the motional effect unobservable at X-band frequencies. This demonstrates clearly the increased sensitivity of the high-field two-pulse echo experiments for slow dynamics that modulate the energy splitting (T 2 processes), especially if the modulation intensity is also proportional to the Zeeman splitting, as for this case. This is different for T~ processes. The longitudinal relaxation rate 1 / T 1 , for example, probed by an inversion recovery experiment, is for a fast limit approximation given by:

1

2

re

--( *1 Iv(t)l *2) 1 + r2to 2

(34)

In this case the relaxation rate 1 / T 1 is smaller for higher frequencies, because of the reduced spectral density of Marcov processes at higher frequencies too. On the other hand, if the matrix element V ( t ) , inducing transitions from the electronic state qq to ~2, is proportional to B o, this first effect may be compensated. So contributions to T 1 that are not field dependent are reduced at higher frequencies. The highly spectrally resolved two-pulse echo decay anisotropies allow an unambiguous identification of motional anisotropies, but the separation of the rate of the motion from the amplitude of the motion still depends on the model used. This is because both the amplitude and the rate may have angular dependences which are not known a priori. To get a more

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model-free description of the motional process, another pulsed experiment is very useful, namely the stimulated echo experiment. This is already a two-dimensional experiment in the time domain. Together with the spectral dimension of pulsed high-field EPR this three-dimensional experiment can give very detailed information on the motional process. If the dynamic process occurs on the time scale of the pulsed EPR experiment (10 ns-100 /xs), and if the magnitude of the spectral diffusion process is in the range of the inverse pulse separations (100 kHz-10 MHz), then this experiment allows to unravel in detail the motional process, separating the correlation time information (in the T dimension) from the libration angle information (~- dimension), as explained in detail by Mims (1972). Thus the probability function P(Sto, T), describing the probability of finding a spin originally on resonance at a frequency offset of 8to after a time T, can be directly depicted with this three-pulse experiment. The high-frequency version adds another dimension, namely the magnetic field B 0 . Thus the probability function P(Sto, B 0 , T) describes this probability for a resonance condition given by the magnetic field B 0 . Because the resonance condition here is directly related to a specific orientation, this again allows for more detailed information on the three-dimensional motion of the molecule. An example of such an experiment is shown in Fig. 14. There a two-dimensional spectrum of the spectral diffusion integral kernel is shown for a discorded sample of a galvynoxyl radical in a polystyrene matrix. Clearly the spreading out of the Larmor frequencies of the spin packets in time can be seen, thus separating the amplitude of the libration (information in the frequency dimension to) from the rate of the motion (information in the T dimension).

V. Summary and Outlook

All of the examples above take advantage of the increased spectral resolution of high-frequency EPR. This advantage in the spectral dimension is shared by both cw and pulsed high-field EPR. The timeresolved/pulsed experiments add more dimensions to the spectral dimension, given by the pulse separation times t i. This adds information to the one-dimensional spectrum and may also lead to increased spectral resolution, for example, by separating two different species by their different relaxation behaviors, as shown by Sebbach and Schweiger (1993). This is similar to ENDOR or other multidimensional experiments, in which another frequency is used to further separate spectral information.

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6O O3 0

FIG. 14. Time evolution of the spectral diffusion integral kernel P(oJ, T) measured by a stimulated echo experiment on a disordered galvynoxyl sample (measured at the gyy position). The broadening of the distribution of the Larmor frequencies of the excited spin packets with the time T can easily be observed. Therefore information on the rate r c and on the spectral width A ~o of the motional

process can be obtained independently.

While all this is true for pulsed EPR in general, the u s e of these methods strongly depends on the system investigated and the microwave frequency. Very often the EPR spectrum at usual X-band frequencies is dominated by inhomogeneous line broadening mechanisms that are not well defined or specific. This may be unresolved hyperfine couplings to many nuclei, distributions and distortions in surrounding, crystal strains, and so on. In many cases, these contributions are not well known and too

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complex to be unraveled; therefore the spectral dimension obtains very little specific information about the system on an analytical level. Thus, the pulsed experiments at these frequencies can rely on only the onedimensional time domain information content to unravel and assign the responsible mechanism and processes. Fortunately, this is not true for all samples, but it holds for many biological samples with less well-defined surroundings, multiple radical states or species, and large molecules. In these cases, high-frequency EPR strongly enhances the information content, by adding a meaningful further dimensionmthe spectral dimensionmto the experiments. This allows us to get detailed information on the relevant processes and allows unambiguous assignments. In this sense mulidimensional experiments, as in NMR, will become much more attractive and useful. One example is the coupled radical pair of the photosynthetic charge separation process, as shown above. With the possibility of separating the two radicals partially in the spectral dimension by high-field ERP, two-dimensional FT EPR experiments on this system should give strongly enhanced information on the structural properties of the radical pair. This is totally analogous to a dipolar coupled nuclear spin system with chemical shift anisotropy for solid-state NMR. With these multidimensional experiments unambiguous structure determination may be accessible, otherwise obtainable only by single-crystal work. Still, the realization of these multidimensional experiments at high microwave frequencies is not trivial. EPR linewidths tend to be broad; further spreading them in the spectral dimension does not simplify a pulse excitation of the whole spectrum. Therefore, instead of multiplex excitation of the whole spectrum, often time-consuming selective excitation with serial scanning of the multidimensional space will be necessary. Also pulse manipulations such as power attenuation, phase switching, and frequency switching have to be explored in high-frequency work, which is still on the level of early-1960s pulsed X-band EPR work. Fortunately, there are no real technical constraints in their realization. On the contrary, pulsed high-field EPR seems to possess some real advantages compared to both pulsed X-band EPR and cw high-field EPR applications, as already mentioned in the technical section. They include arguments such as high intrinsic time resolution, short ringing time, high conversion factor, low sensitivity to source noise, and high sensitivity. Most of them are not optimized yet, but in principle pulsed high-frequency EPR offers the opportunity of getting pulses and time resolution into the subnanosecond time range. This would open up a new field of dynamic processes and systems that could be studied by EPR techniques. All this neither makes X-band EPR unnecessary nor means that pulsed high-frequency EPR is a magic key for solving all EPR problems. It should

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be realized that the effort and the real total measurement time are also a function of the microwave frequency; one reason for this is often just the handling of the rather small samples for high-frequency EPR work. If the sample size is restricted, as for small single crystals, this leads to strong sensitivity and spectral resolution enhancement for high-field EPR, as impressively demonstrated by Groenen et al. (1992) on a single crystal of C60. If these restrictions in sample size do not apply naturally, it leads to a decrease in sensitivity, only increasing the problems in sample preparation and handling. For these kinds of samples, pulsed X-band EPR will still be the much more versatile and elaborate choice of frequency. On the other hand, if there is a field dependence of the spin Hamiltonian, performing the experiments at different microwave frequencies will give additional information and constraints on the analysis. Thus performing pulsed EPR experiments over decades of microwave frequencies gives a further independent dimension to the experiment, the microwave frequency. Therefore I believe that pulsed high-frequency EPR will capture an important position for a broad range of applications--of course, for the analysis of dynamic effects and transient paramagnetic states, but even for the analysis of static interactions in the spectral range.

Acknowledgments I am pleased to thank all my co-workers on the high-frequency/high-field EPR work reported here. They are first of all Sun Un at MIT in Cambridge and Martin Rohrer and Jens Ttirring at the FU in Berlin, who helped in the building of the high-frequency spectrometers and were involved in most of the measurements reviewed here. Jeffry Bryant (MIT) and Joachim Claus (FUB) are both thanked for their technical support. The high-frequency work on photosynthetic reaction centers was done with different collaborators. The work at MIT on cyanobacteria was done together with Ann E. McDermott (Columbia University, New York) and the group of James Norris in Argonne. The experiments in Berlin on the coupled radical pair of photosynthetic reaction centers were done together with Art van der Est, Robert Bittl, Dietmar Stehlik, Wolfgang Lubitz, and Klaus M6bius. Reaction center samples for the libration measurement of the semiquinone acceptor radical were from Peter Gast of Arnold J. Hoff's laboratory in Leiden. The experiments on the p21-ras proteins are a joint project with Thomas Schweins and Andreas Wittinghofer from the Max-Planck Institute on Molecular Physiology in Dortmund and Hans-Robert Kalbitzer from the Max-Planck Institute for Medical Research in Heidelberg. The twodimensional organic conductors /3-(BEDT-TI'F) 2I3 are from Dieter Schweitzer (University of Stuttgart) and the one-dimensional organic conductor flouranthenyl radical cation salt from Michael Mehring (University of Stuttgart). Measurements on the fullerene triplet states are done together with Klaus-Peter Dinse (Technische Hochschule Darmstadt). The covalently linked porphyrin-quinone samples were synthesized by J6rg von Gersdorff from the group of Harry Kurreck (Free University Berlin). The high-field EPR measurements on these samples are performed together with Jacobine Vrieze, the K-band EPR experiments are from

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Art van der Erst, the X-band EPR experiments from Jenny Schliipmann, and the optical transient absorption experiments at zero field from Martin Fuchs. The high-field ESEEM experiments were performed together with Andreas Bloess. Pulsed and FI' EPR comparison experiments at X-band frequencies were performed by Hans van Willingen (University of Massachusetts, Boston) and Hanno K~il3(Technical University Berlin). I would also like to mention the very efficient and open information exchange and discussions with members of the various pulsed high-frequency EPR groups: Gary Gerfen and Lino Becerra from MIT, Yacob Lebedev from Moscow, Edgar Groenen, Oleg Poluektov, and Jan Schmidt from Leiden, Alexander Dubinskii (Free University Berlin), Jack Freed (Cornell University) and Louis-Claude Brunel (HFNML Tallahassee). Special thanks go to Robert Griffin and Klaus M6bius, who gave me the opportunity to perform this work in their laboratories and supported it with stimulating and encouraging interest, and, last but not least, for their financial support. This work was supported by a postdoctoral research fellowship from the Deutsche Forschungsgemeinschaft, by NIH grants, a European Human Capability and Mobility program, and the Sonderforschungsbereich SFB 337 of the Deutsche Forschungsgemeinschaft.

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