Time-domain ENDOR

Bennati M, Stubbe J, Griffin RG. 2001. High-frequency EPR and ENDOR time-domain spectroscopy of ribonucleotide reductase. Appl Magn Reson 21 389—410. 

Bar, G., M. Bennati et al. (2001). High-frequency (140-GHz) time domain EPR and ENDOR spectroscopy The tyrosyl radical-diiron cofactor in ribonucleotide reductase from yeast. J. Am. Chem. Soc. 123 3569-3576. 

A major limitation of CW double resonance methods is the sensitivity of the intensities of the transitions to the relative rates of spin relaxation processes. For that reason the peak intensities often convey little quantitative information about the numbers of spins involved and, in extreme cases, may be undetectable. This limitation can be especially severe for liquid samples where several relaxation pathways may have about the same rates. The situation is somewhat better in solids, especially at low temperatures, where some pathways are effectively frozen out. Fortunately, fewer limitations occur when pulsed radio and microwave fields are employed. In that case one can better adapt the excitation and detection timing to the rates of relaxation that are intrinsic to the sample.50 There are now several versions of pulsed ENDOR and other double resonance methods. Some of these methods also make it possible to separate in the time domain overlapping transitions that have different relaxation behavior, thereby improving the resolution of the spectrum. 

ESE envelope modulation. In the context of the present paper the nuclear modulation effect in ESE is of particular interest110, mi. Rowan et al.1 1) have shown that the amplitude of the two- and three-pulse echoes1081 does not always decay smoothly as a function of the pulse time interval r. Instead, an oscillation in the envelope of the echo associated with the hf frequencies of nuclei near the unpaired electron is observed. In systems with a large number of interacting nuclei the analysis of this modulated envelope by computer simulation has proved to be difficult in the time domain. However, it has been shown by Mims1121 that the Fourier transform of the modulation data of a three-pulse echo into the frequency domain yields a spectrum similar to that of an ENDOR spectrum. Merks and de Beer1131 have demonstrated that the display in the frequency domain has many advantages over the parameter estimation procedure in the time domain. 

ESEEM spectroscopy is a time-domain (i.e. pulsed) analog of EPR see Electron Spin Echo Envelope Modulation Spectroscopy). In principle, ESEEM contains the same information as is found in EPR and ENDOR, although in practice ESEEM is much more sensitive to weakly coupled nuclei that are not easily detected by ENDOR. On the other hand, strongly coupled nuclei can be undetectable by ESEEM, thus the combination of both techniques is often useful. 

To this list can be added various major specialized sub-systems that are required for some of the more sophisticated experiments. Some of the basic sub-systems also require modification for these experiments. (7) Pulse programmer for time domain ESR (8) programmable radio frequency source for electron-nuclear double resonance (ENDOR) (9) pump microwave source for electron-electron double resonance (ELDOR). 

The reader is referred to the book by Kevan and Kispert [19] for a thorough discussion of ENDOR and ELDOR, to the book by Kevan and Schwartz [20] for a discussion of time domain ESR, and to the review by Hyde and Froncisz [242] of multifrequency ESR. 

ENDOR and FT ESEEM spectra differ mainly in the intensities of the lines, which in ESEEM are given by a factor related to the ESR transition probabilities. A necessary prerequisite for modulations in the time domain spectrum is that the allowed Ami = 0 and forbidden Ami = 1 hyperfine lines have appreciable intensities in ESR. The zero ESEEM amplitude thus predicted with the field along the principal axes of the hyperfine coupling tensor is of relevance for the analysis of powder spectra. Analytical expressions describing the modulations have been obtained for nuclear spins I = V2 and / = 1 [54, 57] by quantum mechanical treatments that take into account the mixing of nuclear states under those conditions. Formulae are reproduced in Appendix A3.4. 

Fig. 5. Pulse sequences for basic time-domain ESR and pulsed ENDOR experiments, (a) Primary echo experiment, (b) Inversion recovery experiment (variation of T) or Davies ENDOR. (c) Stimulated echo experiment or Mims ENDOR. For ENDOR experiments, the horizontal bar in (b) and (c) indicates a radiofrequency pulse, whose frequency is varied while all interpulse delays are fixed.

The ID Mims ENDOR sequence can readily be extended to inelude a hyperfine dimension by inerementing, in addition to the r.f frequeney, the r value. Equation (27) shows that the ENDOR efficieney oseillates with eos(zlsr), and thus performing a FT of the time-domain traees reeorded as a funetion of r results in a hyperfme-correlated ENDOR speetrum. An example is shown in Figure 18 for the eomplex [Rh(tropp )2], whieh has rhodium (I = Vi) hyperfine couplings in the range 16-21 MHz [69]. 

In this section we describe selected time-domain ENDOR experiments where the free evolution of nuclear coherence is recorded. These experiments consist of at least three building blocks a nuclear coherence generator, a free evolution period for the nuclear coherence, and a nuclear coherence detector. 

Time-Domain ENDOR methods often employ a ehirp r.f pulse a pulse with a linearly swept frequency. This approach enables broadband excitation of the nuclear transitions that covers the entire frequency range of the ENDOR spectrum, often of the order of 30 MHz. Note that with the available r.f power this broad excitation range is not possible without the r.f frequency sweep (i.e., a n r.f pulse of around 10 ns would be required, whereas a length of around 10 ps is typically needed for protons). 

The pulse sequenees for a Davies-type, a Mims-type, and a Chirp-ENDOR-HYSCORE are shown in Figure 24 [82]. In the Davies-type sequence (a), the nuclear coherence generator consists of the first m.w. and r.f. chirp pulse, followed by a variable free evolution time T, and the nuclear coherence detector consisting of the second r.f chirp pulse and the m.w. primary echo sequence. The time-domain trace is thus measured by incrementing T and recording the echo intensity. FT gives the ENDOR spectrum. The Mims-type sequence, shown in Figure 24b, functions in a similar way. 

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