ESEEM stimulated echo

The main advantage of tlie tln-ee-pulse ESEEM experiment as compared to the two-pulse approach lies m the slow decay of the stimulated echo intensity detemiined by T, which is usually much longer than the phase memory time Ty that limits the observation of the two-pulse ESE. 

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. 

Rapid stepping of the magnetic field, instead of using a second microwave frequency, has been used to measure interspin distances of the order of 20 A at X-band.28 A microwave pulse, called the pump pulse, is synchronized with the field step and occurs between the second and third pulses of a stimulated echo sequence. The effects of nuclear ESEEM were removed by dividing data obtained with a pump pulse (at the stepped magnetic field) by data obtained without a pump pulse. 

Fig. 6. ESEEM spectra of Ni in the F4j0-reducing and methyl viologen (MV)-reducing hydrogenases from M. thermoautotrophicum (A/f strain). Spectra (a) were obtained using a three-pulse stimulated-echo sequence, the time T between the second and third pulses being varied, (b) Fourier transform of FH2ase data (c) simulated spectra. Spectra are the average of recordings from g = 2.0 to 2.34. Reproduced, with permission, from Ref. 56.

Figure 3 Three-pufse or stimulated echo ESEEM data (a) and associated FFT spectrum for the type-1 Cu(II) site of the Fet3p protein (b). Data were collected under the same conditions as those of Figure 1, except r-value, 120 ns starting T, 40 ns and time increment, 16ns...

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.

In a paper that appeared in 1979, R.P.J. Merks and R. DeBeer pointed out that the sinusoidal dependence of the stimulated echo ESEEM experiment on x and T (equation 8), presented the opportunity to collect ESEEM data in both time dimensions and then apply a two-dimensional EFT to derive two important benefits. The first benefit was that suppression-free spectra should be obtained along the zero-frequency axis for each dimension while the second benefit would be the appearance of cross-peaks at (tUo, cofs) and (tw, co ) that would allow one to identify peaks that belonged to the same hyperfine interaction. This ESEEM version of the NMR COSY experiment (see Nuclear Magnetic Resonance (NMR) Spectroscopy of Metallobiomolecules) would prove invaluable for ESEEM analysis of complex spin systems. However, the disparity in spin relaxation times in the x and T time dimensions precluded the general application of this method. 

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. 

Hyperfine spectroscopy methods, such as ID ESEEM, 2D HYSCORE, and ENDOR, have been employed to determine the coordination sphere of Mn " ions bound to the HHRz or to the Diels-Alder ribozyme. The HHRz was first investigated by X-band stimulated echo ESEEM by Britt and coworkers [102]. The ESEEM data revealed nitrogen hyperfine coupling of 2.3 MHz,... 

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... 

Considering the resolution of the nuclear frequency spectrum, this two-pulse echo experiment is not optimal. The nuclear frequencies are here measured as differences of frequencies of the ESR transitions, so that the line widths correspond to those of ESR transitions. The nuclear transitions have longer transverse relaxation times Tin and thus smaller line widths. In fact, if the second mw pulse is changed from a n pulse to a Ji/2 pulse, coherence is transferred to nuclear transitions instead of forbidden electron transitions. This coherence then evolves for a variable time T and thus acquires phase v r or vpT. Nuclear coherence cannot be detected directly, but can be transferred back to allowed and forbidden electron coherence by another nil pulse. The sequence (jt/2)-x-(Jt/2)-r-(jt/2)-x generates a stimulated echo, whose envelope as a function of T is modulated with the two nuclear frequencies v and vp. The combination frequencies v+ and v are not observed. The modulation depth is also 8 211. The lack of combination lines simplifies the spectrum and the narrower lines lead to better resolution. There is also, however, a disadvantage of this three-pnlse ESEEM experiment. Depending on interpulse delay x the experiment features blind spots. Thus it needs to be repeated at several x values. 

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). 

The stated aim of this review is to demonstrate that elassical analyses of physieal organie ehemistry are feasible with respect to complex systems such as supported metal catalysts through the application of advanced EMR spectroscopic techniques and determining the relevant spin Hamiltonian parameters via the Zeeman-dependent hyperfine spectrum. The principles of analysis were outlined in the preceding section and entail replicate collection of ESEEM or ENDOR spectra by incremental steps and mapping the trajectory of peak positions. Deconvolution of peaks may be made either by traditional tau-suppression in the stimulated echo pulse sequence or via advanced pulse sequences such as HYSCORE (2-D ESEEM, Hofer, 1994). Mapping of spectral peak position as it varies depending on the Zeeman field is very important to the accurate determination of hyperfine terms. 

Figure 5. Pulse sequences making use of the ESEEM effect, (a) Two-pulse sequence and the primary echo, (b) Three-pulse sequence and the stimulated echo, (c) Four-pulse sequence for the HYSCORE experiment.

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... 

The ESEEM spectrum is substantially better resolved for stimulated echoes than for the two-pulse echo, because it does not contain combination frequencies (sums and differences of the basic resonance frequencies), and the lines are not broadened by fast transverse spin relaxation. Thus stimulated ESEEM is the more preferable for studying electron-nuclear interactions. 

The stimulated ESEEM experiment is performed at X-band ( 9.5 GHz), which is optimal for echo modulation induced by deuterium nuclei. The stimulated echo is observed after application of three microwave pulses, with the sequence nl2-r-nl2-T-nl2-r-echo. Pulse durations typically are 8 or 16 ns. To maximize the deuterium modulation, the interval r between the first and second pulses is set to t = 1/2vd, where is the deuterium nuclear Larmor frequency. Because is close to 2.2 MHz at X-band, r is close to 220 ns. ESEEM is recorded by scanning the second time delay T. The upper limit for this decay time T ax is determined by echo decay from spin-lattice relaxation typically it is around 10 ps in... 

Analysis of the ESEEM signal can be performed either directly in the time domain, by measuring the amplitude of echo modulation, or in the frequency domain, after numerical Fourier transformation of V T). Because theoretical descriptions of ESEEM " predict that the stimulated echo is modulated according to a cosine function, with t=x + T sls time variable, the real Fourier transform must be used to get the frequency spectra ... 

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