Two- and Three-Pulse ESEEM

In the two-pulse ESEEM experiment (Fig. 5a), the intensity of the primary echo is recorded as a function of the time interval r between the Jt/2 and it pulses. The modulation formula for an 4 = A, I = A spin system is given by 

For the ease of an isotropic hyperfine interaction A=aisoI, or if Bo is oriented along one of the principal axes of the hyperfine tensor (0 = 0 or 0 = nil), the echo modulation disappears, since in either of these cases the quantity B in Eq. (15) becomes zero. 

Equation 14 consists of an unmodulated part with amplitude 1 - U2, the basic frequencies and cop with amplitudes kJl, and the combination frequencies and w+ with amplitudes k 4, and inverted phase. To compute the frequency-domain spectram, first the unmodulated part is subtracted, as it gives a dominant peak at zero frequency for the usual case of small k values. A cosine Fourier transform (FT) of the time trace results in a spectrum that contains the two nuclear frequencies, w and cop, with positive intensity, and their sum and difference frequencies, a + and m, with negative intensity. If the initial part of the time-domain trace is missing, then the spectrum can be severely distorted by frequency-dependent phase shifts and it may be best to FT the time-domain trace and compute the magnitude spectrum. 

In multinuclear spin systems the echo modulation is given by the product rule 

The main shortcoming of the two-pulse experiment is that the primary echo decays within the phase memory time, 7m, which is often very short. This can prevent the observation of low-frequency modulations, and thus the estimation of the magnetic parameters can become uncertain. Another important limitation arises from the spectrometer deadtime u (typically 100-150 ns at X-band frequencies), which restricts the observation of the signal to times t ti. The loss of the initial part of the time trace can cause severe distortions in the frequency-domain spectrum, especially in disordered systems where destructive interference from differ- 

---

Overlap of lines can make analysis difficult when several nuclei contribute in the one-dimensional (ID) two- and three-pulse ESEEM spectra. Eollowing the development in NMR, methods to simplify the analysis involving two-dimensional (2D) techniques have therefore been designed. The Hyperfine Sublevel Correlation Spectroscopy, or HYSCORE method proposed in 1986 [14] is at present the most commonly used 2D ESEEM technique. The HYSCORE experiment has been applied successfully to study single crystals, but is more often applied to orienta-tionally disordered systems. It is a four-pulse experiment (Fig. 2.23(a)) with a k pulse inserted between the second and the third k/2 pulse of the three-pulse stimulated echo sequence. This causes a mixing of the signals due to the two nuclear transitions with m.s = Vi of an 5 = Vi species. For a particular nucleus two lines appear at (v , V ) and (V ", v ) in the 2D spectrum as shown most clearly in the contour map (d) of Fig. 2.23. The lines of a nucleus with a nuclear Zeeman frequency... 

Hung and co-workers have performed two- and three-pulse ESEEM on succinate ubiquinone reductase from Paracoccus denitrificansJ° They were able to obtain structural information about the environment of the reduced [2Fe-2S] + cluster, the oxidized [3Fe-4S] cluster and the anionic FAD radical. The flavin radical was centred a.tg = 2.005 in agreement with previous work by Ohnishi and co-workers. From analysis of the ESEEM spectra hfcs from two nitrogens could be obtained. These were assigned to N1 and N3 of the isoal-loxazine ring. It was noted that the nuclear quadrupole coupling parameters were very similar to those obtained from cholesterol oxidase. ... 

Fig. 8. Illustration of microwave pulse schemes for two-pulse and three-pulse ESEEM (adapted from Kevan and Bowman ). In the two-pulse experiment, the interpulse time t is varied and the amplitude modulation of the resulting electron spin echo is recorded. In the three-pulse experiment, t is fixed and the electron spin echo amplitude is recorded as a function of the interpulse time T.

The electron-spm echo envelope modulation (ESEEM) phenomenon [37, 38] is of primary interest in pulsed EPR of solids, where anisotropic hyperfme and nuclear quadnipole interactions persist. The effect can be observed as modulations of the echo intensity in two-pulse and three-pulse experiments in which x or J is varied. In liquids the modulations are averaged to zero by rapid molecular tumbling. The physical origin of ESEEM can be understood in tenns of the four-level spin energy diagram for the S = I = model system... 

Muns ENDOR mvolves observation of the stimulated echo intensity as a fimction of the frequency of an RE Ti-pulse applied between tlie second and third MW pulse. In contrast to the Davies ENDOR experiment, the Mims-ENDOR sequence does not require selective MW pulses. For a detailed description of the polarization transfer in a Mims-type experiment the reader is referred to the literature [43]. Just as with three-pulse ESEEM, blind spots can occur in ENDOR spectra measured using Muns method. To avoid the possibility of missing lines it is therefore essential to repeat the experiment with different values of the pulse spacing Detection of the echo intensity as a fimction of the RE frequency and x yields a real two-dimensional experiment. An FT of the x-domain will yield cross-peaks in the 2D-FT-ENDOR spectrum which correlate different ENDOR transitions belonging to the same nucleus. One advantage of Mims ENDOR over Davies ENDOR is its larger echo intensity because more spins due to the nonselective excitation are involved in the fomiation of the echo. 

Fig. 16. Three-pulse ESEEM spectrum of the Rieske cluster in hovine heart submit-ochondrial particles at gy = 1.89 and 3.7 K. The pairs of trEmsitions belonging to the two nitrogen atoms are indicated. Conditions of measurement EU-e as stated in (87).

Figures 1 and 3 show that although the modulations of the three-pulse, or stimulated echo are less intense than those of its two-pulse counterpart, the resolution is much higher and the spectrum is simplified because combination peaks only enter into the data through the presence of multiple ESEEM-active nuclei. Equation (8) shows that for an S = 1 /2, 7 = 1/2 spin system, judicious selection of the r-value can control the ESEEM amplitudes of the hyperfine frequencies from a and electron spin manifolds allowing them to be optimized or suppressed. For weakly coupled protons, where the modulation frequencies from both electron spin manifolds are centered at the proton Larmor frequency, x can be set at an integer multiple of the proton Earmor frequency to suppress the contributions of this family of coupled nuclei from the three-pulse ESEEM spectrum. It is common for three-pulse ESEEM data to be collected at several r-values, including integer multiples of the proton Larmor period, to accentuate the other low frequency modulations present in the data and to make sure that ESEEM components were not missed because of T-suppression.

ESEEM studies require microwave pulse widths that are short in comparison with the period of the highest frequency modulation to be studied. 90° pulse widths of 16-20ns are typical for X-band ESEEM studies where the period of the proton Larmor frequency is about 70 ns at g = 2. One typically adjusts the sample probe s microwave coupling to the maximum overcoupling position, sets up a two- or three-pulse ESE sequence, and optimizes the echo amplitude as observed on an oscilloscope or transient recorder display by adjusting the pulse power and reference arm phase. If sensitivity is low, the probe coupling can be adjusted some to increase the probe Q without giving up too much in terms of the instrument s dead-time. 

Left two-pulse [(a) primary ESEEM] and three-pulse [(b) stimulated echo ESEEM] sequences t is the (fixed) delay time between pulses one and two and T is a variable delay time. Right frequency domain and time domain (inset) of the two-pulse EESEM spectrum of VO - vanabin, recorded at the m = — 1 /2 line, at 77 K and a pulse width of 20 ns.P l The superhyperfine coupling constant = 4.5 MHz (obtained from the N double-quantum lines at 3.9 and 7.1 MHz) is in accord with amine nitrogen provided by lysines of the vanadium-binding protein. The spin echo due to proton coupling, at 13.7 MHz, was also observed. Reproduced from K. Eukui et al., J. Am. Chem. Soc. 125, 6352-6353. Copyright (2003), with permission from the American Chemical Society. 

Altliougli EPR is very sensitive to tlie surroundings of the paramagnetic cation, it cannot provide directly infonnation concerning the fine interactions with the framework. Such interactions can, however, be measured by ESEEM. This teclmique is particularly useful for the measurement of weak hyperfine interactions. The modulation frequencies are the NMR frequencies of the coupled nuclei. In disordered systems, the modulation frequencies are essentially the Lannor frequencies of the coupled nuclei, which serve to identify the coupled nuclei. The modulation depth can be related to the distance between the electron spin and the coupled nuclei, and to their number. The ESEEM measurements described here were carried out at 4 K using an operating frequency of 9.1 GHz. Both two-pulse and three-pulse sequences were employed. 

In a three-pulse ESEEM experiment the time T between the second and the third pulse is increased while the time x between the first and second pulse is kept constant. In contrast to the two-pulse ESEEM experiment, the three-pulse ESEEM spectra do not contain sum and difference frequencies as illustrated schematically in Fig. 2.21 for an S = Vi species with anisotropic hyperfine coupling due to a proton. Both spectra contain lines with nuclear frequencies and v expected for = /2. The combination lines at v v seen as satellites in the two-pulse spectrum do not appear in the corresponding 3-pulse spectrum. On the other hand lines can escape detection in the 3-pulse spectrum for certain values of the time x between the first and second pulse at so called blind spots. It is therefore customary to record several 3-pulse specfra with different values of x. 

The disadvantage of the fast echo decay in two-pulse ESEEM can be circumvented with the three-pulse ESEEM experiment shown in Figure 5b. In this pulse sequence the first two nil pulses create nuclear coherence that develops during the evolution time T and decays with the transverse nuclear relaxation time 72n which is usually much longer than the corresponding relaxation time 7m of the electrons. The third nJl pulse transfers the nuclear coherence back to observable electron coherence. The modulation of the stimulated echo is given by... 

When T is varied the echo envelope is modulated only by the two basic frequencies CDa and (Up, the sum and difference frequencies do not appear, in contrast to the two-pulse ESEEM experiment. This is usually advantageous, as it simplifies spectra, but it may also be a disadvantage for disordered systems where the sum-combination line is often the only narrow feature in the ESEEM spectrum. Another important difference is the dependence of the three-pulse ESEEM amplitudes on r, as is apparent from Eq. (17) by the factors 1 - cos(copr) and 1 - cos(cOcir). Due to this suppression effect, individual peaks in the spectrum can disappear completely. These blind spots occur for the a(P) peak when r = 2n /(Up(a) (k = 1, 2,. ..). In principle they can be avoided by using r < Inlco, where (Umax is the maximum nuclear frequency however, this is usually precluded by the spectrometer deadtime. Consequently, the three-pulse ESEEM experiment has to be performed at several r values to avoid misinterpretation of the spectra due to blind-spot artifacts. 

The remote-echo detector is shown in Figure 11. In this method the electron spin echo at the end of the pulse sequence, which uses Vi < rnuclear coherence generator, is not recorded. Instead, at the time of echo formation an additional nil pulse transfers the electron coherence to longitudinal magnetization. The echo amplitude information can thus be stored for a time interval up to the order of T. After a fixed time delay h < T l, the z-magnetization is read out using a two-pulse echo sequence with a fixed time interval X2 > r. Remote echo detection can be applied to many experiments, including three-pulse ESEEM and HYSCORE, and thus can eliminate blind spots with an appropriate choice of small ri. Note, however, that it may suffer from reduced sensitivity due to the increased sequence time. 

Figure 1. Scheme of the pulse EPR sequences mentioned in this chapter, (a) Two-pulse ESEEM. (b) Three-pulse ESEEM. (c) Four-pulse ESEEM. When times fi and ti are stepped under the constraint of ti= ti= T, combination-peak experiment is performed. Two-dimensional HYSCORE spectroscopy is done using the same sequence, whereby t and are stepped independently. The second and third nil pulse are replaced by high-tuming-angle (HTA) pulses in a matched HYSCORE experiment, (d) SMART-HYSCORE. The first and third pulses are HTA pulses, (e) Davies ENDOR. (f) Mims ENDOR. (g) ELDOR-detected NMR. 

Resolvable modulation is detected on a three-pulse echo decay spectrum of predeuterated 3-carotene radical (Gao et al. 2005) as a function of delay time, T. The resulting modulation is known as ESEEM. Resolvable modulation will not be detected for nondeuterated P-carotene radical since the proton frequency is six times larger. The modulation signal intensity is proportional to the square root of phase sensitive detection and interfering two-pulse echoes and suppressed by phase-cycling technique (Gao et al. 2005). Analysis of the ESEEM spectrum yields the distance from the radical to the D nucleus, a the deuterium coupling constant, and the number of equivalent interacting nuclei (D). The details related to the analysis of the ESEEM spectrum are presented in Gao et al. 2005. 

The three-pulse electron spin-echo envelope modulation (ESEEM) technique is particularly sensitive for detecting hyperfine couplings to nuclei with a weak nuclear moment, such as 14N. It has been used to probe the coordination state of nickel in two hydrogenases from M. tkermoautotrophicum, strain AH (56). One of these enzymes contains FAD and catalyzes the reduction of F420 (7,8-dimethyl-8-hydroxy-5-deazaflavin), while the other contains no FAD and has so far only been shown to reduce artificial redox agents such as methyl viologen. 

---