ENDOR Transition Frequencies

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. 

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... 

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... 

For spin Hamiltonians of systems with low symmetry, expressions for ENDOR transition frequencies to second order have been given by several authors " In most of these papers the spin Hamilton operator chosen is not general enough to describe the observed ENDOR spectra of transition metal complexes. For instance, some authors consider only one single nucleus make use of the assumption oi even neglect... 

Due to the inclusion of A, A then becomes asymmetric. Since the expression (3.25) for the first order ENDOR transition frequencies contains the term R.sCgA + Ag)R.3, which is linear in A, all nine matrix elements of the hfs tensor A can, in principle, be determined by ENDOR. If, in the third term of (5.13), the spin densities (k N) can be neglected (ionic modehpk = 0, 0m = 1). the hfs tensor A is described by... 

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 second order, however, eight ENDOR frequencies are obtained for each ms-state. The transition frequencies tabulated in Appendix B, Eqs. (B 5) are again described by al5 a2 and a3 defined in (3.12). If the hfs is resolved in the EPR spectrum, the number of induced transitions depends on the mp-value of the saturated line in the EPR quintet. For mF = 0 six transitions, for mF = 1 four transitions, and for mF = 2 one transition are observed in the ENDOR spectrum of each ms-state62). 

Fig. lOa-c. Higher order splittings in symmetry planes Single crystal nitrogen ENDOR spectrum of Cu(TPP) diluted into (H20)Zn(TPP) with Bo normal to the porphyrin plane B0 = 327.7 mT. a) Observed spectrum. (Adapted from Ref. 66) b) Transition frequencies obtained by numerical diagonalization of the full spin Hamiltonian matrix (Four nitrogen nuclei). (Ref. 68) c) First order frequencies, (Eq. (3.10))... 

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. 

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). 

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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The principle of the ENDOR method is illustrated in Fig. 1. It refers to the most simple spin system with an electron spin S = 1/2 and a nuclear spin I = 1/2 for which an isotropic hf interaction, aiso, is considered. In a steady state ENDOR experiment4, an EPR transition (A, D), called the observer, is partly saturated by microwave radiation of amplitude B while a driving rf field of amplitude B2, called the pump, induces nuclear transitions. At frequencies vj and v2, the rf field tends to equalize the populations within the ms-states. This alters the degree of saturation of the observer so that, in the display of the EPR signal height versus the radio frequency, two ENDOR lines at transition frequencies vj = aiso/2 - vn (A, B) and v2 = ais0/2 + v (C, D) will be observed (v = / NgnBo denotes the nuclear Zeeman frequency for a static field B0). 

Fig. 2 a, b. EPR and ENDOR spectrum of the low-spin Co(II) Schiff base complex Co(acacen) diluted into a Ni(acacen) 1/2 H20 single crystal, temperature 8K. a) EPR spectrum the two magnetically nonequivalent sites coincide for this particular orientation (EPR observer is marked by an arrow) b) ENDOR spectrum of H, 13C (enriched) and 14N ligand nuclei vp free proton frequency denote the AmN = 2 nitrogen ENDOR transitions. (From Ref. 12)... 

Another method that is important for structure assignment is the electron-nuclear-nuclear triple resonance (TRIPLE) spectroscopy (Endeward et al., 1998 Makinen et al., 1998), which is an extension of the ENDOR method. In the general TRIPLE experiment, transitions of different nuclei are driven simultaneously. One ENDOR transition is irradiated saturating rf power at a constant frequency, while the entire ENDOR frequency range is swept to obtain the TRIPLE spectrum. 

Figure 18-4. ENDOR energy level diagram for an electron Ms = 1/2 in the local magnetic field of a proton Mj = 1 /2. To observe an ENDOR transition, the external magnetic field H0 is positioned on an EPR line, in this case the transition from Ms = —1/2, Ml = +1/2 > to Ms = +1 /2, M, = + 1/2 >. Then a radio-frequency transmitter is scanned through the various NMR frequencies (typically 10-100 MHz). This diagram shows two ENDOR transitions of energy haq and hu2 that correspond to the hyperfine couplings of a nuclear spin with Mj = 1/2...

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