ENDOR transitions

ENDOR transitions can be easily understood in temis of a simple system consisting of a single unpaired electron spin (S=2) coupled to a single nuclear spin (1=2). The interactions responsible for the various... 

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. 

In this section analytical expressions for ENDOR transition frequencies and intensities will be given, which allow an adequate description of ENDOR spectra of transition metal complexes. The formalism is based on operator transforms of the spin Hamiltonian under the most general symmetry conditions. The transparent first and second order formulae are expressed as compact quadratic and bilinear forms of simple equations. Second order contributions, and in particular cross-terms between hf interactions of different nuclei, will be discussed for spin systems possessing different symmetries. Finally, methods to determine relative and absolute signs of hf and quadrupole coupling constants will be summarized. 

According to (3.3), 4 I ENDOR transitions will be observed for a nucleus with arbitrary spin I and with an unresolved hf structure in the EPR display. If the hf structure is resolved, however, each mrstate can be saturated individually and either a four-line ENDOR spectrum (EPR observer -1 < mi < I) or only a two-line ENDOR spectrum (EPR observer m, = I) will be observed. 

Nuclear spin decoupling 4.4 two rf fields 2.5 Assignment of ENDOR transitions... 

Disregarding incorrect matching of the ENDOR resonance condition, the line shape of the EI-EPR spectrum is only identical to that of the EPR spectrum if35 (a) the induced ENDOR transition belongs to an I = 1/2 nucleus, (b) only cross relaxation processes of the type (ms, m() <- (ms - 1, mi 1) occur, (c) no relaxation takes place between different mr-states within a given ms-manifold. 

For nuclei with I > 1, the two ENDOR transitions c( 1/2) are split by the quadrupole interaction. As a consequence, only those EPR transitions which have a level in common with the induced ENDOR transition are observed in the EI-EPR spectrum. This selection of the nuclear spin states reduces the number of lines in the EI-EPR spectrum and allows the determination of the relative signs of hf and quadrupole interactions20,35. ... 

DQT generated by a single rf field may be helpful, for example, to elucidate complicated energy level schemes or to assign ENDOR transitions to the corresponding nucleus4. ... 

The ENDOR transitions induced by rf fields rotating in the right hand (r.h.) or left hand (l.h.) sense depend on the orientation of Btff with respect to B0. For an isotropic spin system the effect of a circularly polarized rf field is readily illustrated in Fig. 22. Two cases (where aiso > 0, g > 0, ge = 2, S = 1/2) have to be distinguished ... 

The inversion of Bcff for the low-frequency line takes place at a = 2 vn = 2 Ng B0. As a consequence the nuclear spin states belonging to ms = 1/2 change their precession direction from l.h. (ais0 < a J) to r.h. (aiso > aj J). For ms = -1/2, ENDOR transitions are only observed with a l.h. rotating field. 

The efficiency of the PM-ENDOR technique is illustrated in Fig. 26 by a simple experimental example. Figure 26a shows part of a conventional single crystal proton ENDOR spectrum of Cu(II) diluted into Mg(NH4)2(S04)2 6(H20). Figures 26 b, c, which depict the two types of displays mentioned above, show that the parameters q>m and AI0 are significantly different for each ENDOR transition. 

The hfs and quadrupole tensors of one of the nitrogen ligands have been determined with ENDOR by Calvo et al.63). The 14N-ENDOR transition frequencies observed between 11 and 23 MHz were found to depend significantly on the nuclear quantum number mCu of the EPR observer line. These shifts are due to Cu-N crossterms (Sect. 3.2) and amount to more than 1 MHz for certain orientations of B0. ENDOR resonances of... 

Figure 38 shows the angular dependence of the ENDOR transitions of the amino protons in Cu(II)-doped TGS for B0 normal to a m The observed eight-line pattern... 

As mentioned above it is not possible to identify the number of magnetically equivalent nitrogens from first order expressions of the ENDOR transition frequencies. Since... 

Single crystal Cu-ENDOR spectra of Cu(acac)2 have been studied by Kita et al.158) up to 100 MHz. The ENDOR transitions of the isotopes 63Cu and 65Cu are found to be well separated for most orientations of Bq. The angular dependence of some Cu-ENDOR frequencies shows pronounced double-minima instead of a single minimum in the region where the hf coupling is smallest. Similar rotation patterns have been observed in Co-ENDOR spectra of Co(acacen) (Fig. 43 b). 

The 14N hf and quadrupole parameters observed in Co(acacen) by Rudin et al.59 are the first magnetic data reported on equatorial nitrogen ligand nuclei in a low-spin Co(II) complex. Only two of the four predicted AmN = 1 ENDOR transitions (3.9) were observed for each nitrogen nucleus. A numerical calculation of the transition probabilities shows that the corresponding transitions in the other ms-state are at least ten times less intense (hyperfine enhancement). 

Figure 43 a shows the angular dependence of the four Co-ENDOR transitions for rotations of the crystal around three cartesian axes. For rotation I, the angular dependence shows a noteworthy peculiarity near

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