ENDOR Davies

In Davies ENDOR the first selective m.w. n pulse inverts the polarization of a particular EPR transition (Fig. 15a). During the miKing period a selective r.f. a pulse is applied. If the r.f pulse is resonant with one of the nuclear frequencies (Fig. 15b), the polarization of this transition is inverted, which also alters the polarization of the electron spin echo observer transition (1,3) detected via a primary echo, a/2 - T - % - X - echo. The ENDOR spectrum is thus recorded by monitoring the primary echo intensity as the r.f frequency is incremented stepwise over the desired frequency range. 

JEFFREY HARMER, GEORGE MITRIKAS, and ARTHUR SCHWEIGER 

Mims ENDOR is based on the stimulated echo sequence with three nonselec-tive m.w. n/2 pulses (Fig. 14b). The preparation part, nil - r - nil, creates a r-dependent grated polarization pattern. During the mixing period, the polarization is changed by a selective r.f. pulse if it is on-resonance with a nuclear frequency. The electron polarization is then detected via a stimulated echo created at time r after the last nil m.w. pulse. The ENDOR efficiency is given by [64] 

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The Davies-ENDOR teclmique is based on an inversion recovery sequence (see figure B1.15.13(A ). The experiment starts by interchanging the populations of levels 1 and 3 of one of the EPR transitions of the. S-/=i... 

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. 

Figure Bl.15.13. Pulsed ENDOR spectroscopy. (A) Top energy level diagram of an. S-/=i spin system (see also figure Bl,15,8(A)). The size of the filled circles represents the relative population of the four levels at different times during the (3+1) Davies ENDOR sequence (bottom). (B) The Mims ENDOR sequence.

The other major form of pulsed ENDOR spectroscopy is known as Davies ENDOR, after its discoverer, E. R. Davies at the Clarendon Laboratory, Oxford, UK. Davies ENDOR is in many ways complementary to Mims ENDOR in that the former is more suited for larger couplings and the latter for smaller couplings, as described earlier (Section 3.3.4). 

Figure 7 Davies ENDOR pulse sequence. The upper level indicates the microwave pulses and immediately helow delay times are indicated. The lowest level indicates the rf pulse. Typical times are given based on a 35 GHz spectrometer. The timing of the microwave and rf pulses is less commonly altered, hut the delay time T and the repetition time need significant adjustment to optimize spectral appearance of a given sample. Microwave phase cycling is also employed, hut is not indicated in the figure...

Fig. 7. Pulse sequences for (A) Mims ENDOR and (B) Davies ENDOR. The top line in each sequence indicates pulses at microwave frequencies, whereas the lower line indicates pulses at rf frequencies. In both cases the microwave pulse sequence will be repeated at constant frequency, and the intensity of the resulting electron spin echo is recorded as a function of changing rf frequency.

Davies ENDOR. The second pulsed ENDOR technique is called Davies ENDOR. In this experiment (Fig. 7B) a preparation v microwave pulse of duration Tp inverts spin packets, burning a hole of approximate width 1 /Tp in a broad EPR line. The resulting magnetization is subsequently detected by a vll-v two-pulse echo sequence. The application of an on-resonance rf pulse after the preparation phase increases the magnetization measured by the two-pulse detection sequence. 

Although it has the ability for hyperfine selection, the Davies ENDOR sequence is not so sensitive to blind spots as in a Mims ENDOR, and thus it is more useful for detecting powder-pattern ENDOR line shapes. The Davies sequence, however, generally does not give so large a percent ENDOR effect typical Davies ENDOR effects in proteins are approximately 1-15% of the spin echo amplitude. 

Fig. 2 Pulsed ENDOR on a neutral flavin radical. E. coli CPD photolyase was investigated with pulsed Davies ENDOR spectroscopy at r = 80 K (for details, see [25]). Detectable protons are marked accordingly...

Fig. 2.26 (a) Q-band FSE EPR (EIE) spectrum of peridinin triplet (A) absorption, (E ) emission (b) Davies ENDOR pulse sequence (c) Q-band H ENDOR spectra recorded at the three canonical orientations Xn, Yn, Zn, which are marked with arrows in the ESR spectrum of panel (a) using the conditions in panel (b). At the proton Larmor frequency vh a narrow and intense line is visible resulting from nuclear transitions in the mg = 0 manifold. The frequency axis gives the deviation from Vh in the respective spectra. The excitation wavelength was 630 nm. Left numbering and spin density plot of peridinin in its excited triplet state. The orientation of the ZFS tensor axes X, Y, and Z is also given. The figure is adapted from [51] with permission from the American Chemical Society... 

More recently, pulsed ENDOR methods have been introduced. There are two commonly used ENDOR pulse sequences, both of which are based on the impact of RF pulses on the intensity of a spin echo that is formed from a series of three pulses at the microwave frequency. These techniques are sometimes called ESE-ENDOR. In Mims ENDOR the pulse at the RF frequency is applied between the second and third microwave pulses whereas in Davies ENDOR the RF pulse is applied between the first and second microwave pulses. The Mims ENDOR experiment is particularly effective for weakly coupled nuclei, but has some blind spots (frequencies that cannot be observed). It is often advantageous to combine data from both ENDOR methods. 

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.

Pulsed ENDOR. In both the inversion recovery (Fig. 5b) and stimulated echo experiment (Fig. 5c), the echo amplitude is influenced by a radiofrequency pulse applied during the interpulse delay of length T, if this pulse is on-resonance with a nuclear transition. In the former experiment, such a pulse exchanges magnetization between inverted and noninverted transitions, so that echo recovery is enhanced (Davies ENDOR) (32). In the latter experiment the on-resonance radiofrequency pulse induces artificial spectral diffusion, so that the echo amplitude decreases (Mims ENDOR) (33). These pulsed ENDOR experiments exhibit less baseline artifacts and are easier to set up compared with CW ENDOR experiments, as the required mean radiofrequency power is smaller and the ENDOR effect does not depend on a certain balance of relaxation times. Davies ENDOR is better suited for couplings exceeding 1-2 MHz, while Mims ENDOR is better suited for small couplings, for instance matrix ENDOR measurements. 

The Davies ENDOR experiment requires that the frequency shift A is larger than the hole width. It is thus best suited for large hyperfine couplings. For small couplings, the experiment needs to be performed with very long mw pulses to create a very narrow hole. This leads to low sensitivity, as only a small fraction of the ESR line contributes to the ENDOR signal. 

Fig. 7. Davies ENDOR experiment, (a) Pulse sequence. The frequency of the rf pulse is varied and integrated echo intensity is recorded, (b) Changes in the ESR Une. At point I before the first pulse, the whole line comprises equilibrium polarization. The first n pulse bums a hole into the line (point II). A resonant rf pulse shifts one-half of the hole to two side holes at frequency difference A (point HI).

Figure 14. Pulse sequence Pot the Davies ENDOR (a) and Mims ENDOR (b) experiments. The inter-pulse delays are kept constant while the radio frequency is incremented over the desired frequency range. Modified with permission from [7]. Copyright 2001, Oxford University Press.

Figure 15. Populations of the energy levels of a two-spin system during the Davies ENDOR experiment (a) selective m.w. ti pulse inverts the polarization of EPR transition (1,3), (b) population after the r.f. ti pulse, on-resonance with nuclear transition (1,2), or off-resonance (no effect).

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