Two-pulse ESEEM

Analytical expressions for the primary echo modulation function of an B = 1 /2, / = 1/2 system were worked out for some of the earliest ESEEM studies that appeared in the literature. Perhaps the most general of these theoretical treatments is that of Mims where the two-pulse ESEEM function is given by... 

The discussion of the two-pulse ESEEM experiment given above might cause one to conclude that the measurement is of little use. There are a few reasons why these data should be collected as part of the overall routine of an ESEEM... 

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. 

Two-pulse ESEEM of the multiline EPR signal from an l -Synechococcus PSII preparation... 

Since V/ is known, one can determine Vdd, and hence the distance between the electron and nuclear spin, even in the presence of small, unknown isotropic hyperfine couplings. The second-order shift with respect to twice the nuclear Zeeman frequency is small. Hence, two-pulse ESEEM with its inferior resolution is not well suited for measuring this shift. The sum combination frequency can be introduced into stimulated-echo ESEEM by inserting an mw tz pulse halfway through the evolution period of length T (sequence in Fig. 11 with fi = 2 = T/2). 

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... 

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 use of a remote-echo detector allows r values shorter flian the spectrometer deadtime to be employed [55]. This is important in two-pulse ESEEM experiments where the deadtime prevents the signal for times r < from being recorded. Also in the deadtime-free four-pulse experiments described in 3.3, a small T value is often needed to avoid blind spots. Bhnd spots are a particular concern for flie measurement of proton spectra at X-band, where flie signals typically extend from 5 to 25 MHz, and with a r = 100 ns blind spots occur at nh = 0, 10, 20,... MHz. 

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. 

In the case of V0(pic)2, ESEEM spectroscopy detected similar amine nitrogen coordination in the kidney and liver of treated rats (by i.p. injeetion), as with VOSO4, as well as weaker signals that were attributed to residual intaet V0(pic)2 in these organs [71]. This result was further supported by differenees in measured phase memory time for the two-pulse ESEEM spectra, where V0(pie)2 in kidney and liver was found to relax faster than kidney and liver samples derived from V0S04-treated rats [71]. For VO(ema)2, only signals due to equatorial " N amine coordination were detected, although it was not possible to deteet any residual VO(ema)2 eomplexes due to the ESEEM silence of the O4 ( 0, 99.76% abundant, 7=0) eoordination sphere [72]. 

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