Refocused echo

Figure 16.1 Pulse sequences for (A) three-pulse PELDOR and (B) four-pulse PELDOR (RE denotes the wanted refocused echo).

The four-Pulse PELDOR pulse sequence is in principle a pump-probe experiment that selects from all contributions to the EPR spectrum dominantly the dipolar coupling between the two unpaired electrons. The detection sequence 7i/2-T1-7i-T1-echo1-T2-7i (Fig. 16.IB) applied at a microwave frequency vA creates at time t2 after the last n-pulse a refocused echo (RE) for the spins being in resonance with vA. The position in time of... 

Fig. 14. (a) The two-pulse MQMAS sequence. The refocusing echo occurs at t2 = kt (solid line) and the anti-echo at t2 = —kt (dashed line), (b) The shifted-echo MQMAS sequence. An intermediate storage of the p-multiquantum coherence in the (+1) quantum coherence leads to a shift of the echo to t2 = kt + mtr. Fourier transformation of the whole echo gives a pure-absorption multiquantum spectrum, (c) z-Filter MQMAS sequence. Symmetrical pathways make the anti-echo and echo intensities equal. It allows a pure p-multiquantum spectrum. (Adapted from Charpentier el alP with permission.)... 

Fig. 7 Pulse sequence of the dead-time free four-pulse DEER experiment. The pulse sequence at frequency Vj (refocused spin echo) addresses the A spins, only, while the pulse at V2 flips the B spins. Applying the pump pulse at variable time T results in a modulation of the refocused echo intensity V (cf. Fig. 8a)...

Here nij is the transversal magnetization of the th spin at the time of the refocused echo and Xj is the inversion efficiency of the yth spin by the pump pulse. Rjcj and define the length and orientation with respect to the static magnetic field of the vector coimecting both electron spins, respectively. D is the dipolar interaction constant, given as (2ti x 52.18) MHz nm for two radicals. 

The QCPMG FID in the time domain is a continuous series of ca. 10—250 refocused echoes. Since the Fourier transform (FT) of this comb-like function is an inverse comb-fike function, performing an FT of the echo train in the time domain produces a SSNMR spectrum composed of a series of individual spikelets that trace out the manifold of the... 

The pulse sequence of the 4-pulse DEER experiment (Fig. 5) consists of a refocused echo sequence for the observer frequency and of an inversion pulse acting on the pumped frequency. The amplitude of the detected... 

The contribution of this effect depends on the strength of ZFS for a particular type of Gd(m) centres, because, depending on ZFS, a larger or smaller fraction of each transition is excited by the pump pulse and also because the strength of ZFS changes angular dependencies for the differences of resonance frequencies for pairs of Gd(iii) transitions with a level in common. For instance, at X and Q band the refocused echo amplitude gets reduced down to 30-40% of its initial amplitude for Gd(m)-DTPA complexes, while it is reduced down to 1-10% for Gd(m)-DOTA complexes, which have more symmetric structure and, thus, weaker ZFS. ... 

The reduction of the refocused echo leads to a loss of sensitivity for Gd(in)-nitroxide DEER. Still, available Q-band data suggest approximately... 

Another class of methods measures inter-spin dipolar interactions using pulses that selectively manipulate different spin populations. The representative of this class, which is widely used in SDSL, is double electron-electron resonance (DEER, also known as PELDOR, Fig. 6). In the dead-time free DEER scheme, a three-pulse sequence is applied to the observer spin (spin A) to generate a refocused echo at a specific... 

The resolution eidiancenient stems from the fact that the qiiadnipole frequencies for both transitions are correlated. At specific times the anisotropic parts of the qiiadnipole interaction are refocused and an echo fonns. The frequency of an (m, -m) transition is given by... 

Figure Bl.14.1. Spin warp spin-echo imaging pulse sequence. A spin echo is refocused by a non-selective 180° pulse. A slice is selected perpendicular to the z-direction. To frequency-encode the v-coordinate the echo SE is acquired in the presence of the readout gradient. Phase-encoding of the > -dimension is achieved by incrementmg the gradient pulse G...

Figure Bl.14.2. Gradient-recalled echo pulse sequence. The echo is generated by deliberately dephasing and refocusing transverse magnetization with the readout gradient. A slice is selected in the z-direction and v- and y-dimension are frequency and phase encoded, respectively.

In electron-spin-echo-detected EPR spectroscopy, spectral infomiation may, in principle, be obtained from a Fourier transfomiation of the second half of the echo shape, since it represents the FID of the refocused magnetizations, however, now recorded with much reduced deadtime problems. For the inhomogeneously broadened EPR lines considered here, however, the FID and therefore also the spin echo, show little structure. For this reason, the amplitude of tire echo is used as the main source of infomiation in ESE experiments. Recording the intensity of the two-pulse or tliree-pulse echo amplitude as a function of the external magnetic field defines electron-spm-echo- (ESE-)... 

The spin-echo experiment therefore leads to the refocusing not only of the individual nuclear resonances but also of the field inhomogeneity components lying in front or behind those resonances, a maximum negative amplitude being observed at time 2t after the initial 90° pulse. The frequency of rotation of each signal in the rotating frame will depend on its chemical shift and after the vector has been flipped by the 180° pulse, it... 

Figure 2.2 Effect of 180 pulse on phase imperfections resulting from magnetic field inhomogeneities. Spin-echo generated by 180 refocusing pulse removes the effects of magnetic field inhomogeneities.

Figure 2.3 Spin-echo experiment. The behavior of nucleus X in an AX spin system is shown. (A) Application of the second 180° pulse to nucleus X in the AX hetero-nuclear system results in a spin-flip of the two X vectors across the x -axis. But the direction of rotation of the two X vectors does not change, and the two vectors therefore refocus along the —y axis. The spin-echo at the end of the t period along the -y axis results in a negative signal. (B) When the 180° pulse is applied to nucleus A in the AX heteronuclear system, the spin-flip of the X vectors...

Will the vectors of a doublet be refocused at time 2t in a spin-echo experiment ... 

Nuclei resonating at different chemical shifts will also experience similar refocusing effects. This is illustrated by the accompanying diagram of a two-vector system (acetone and water), the nuclei of which have different chemical shifts but are refocused together by the spin-echo pulse (M, = magnetization vector of acetone methyl protons, M(v = magnetization vector of water protons). 

Spin-echo The refocusing of vectors in the xy-plane caused by a (t-180°-t) pulse sequence produces a spin-echo signal. It is used to remove field inhomogeneity effects or chemical shift precession effects. 

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