Single ENDOR

TRIPLE was first demonstrated as a CW technique applied to organic radicals in fluid solution, for which the signs of coupling constants could provide important information on the nature of the SOMO. For bioinorganic systems, their inherently broad linewidths mean that maximum resolution is needed, thus the most meaningful form of TRIPLE is as a pulsed technique. A Davies pulse sequence is shown for TRIPLE in Figure 9. All aspects of the pulse sequence are the same as for a standard (i.e., single ENDOR)... 

Thus far, we have established that the nuclear hyperfine parameters of the spin Hamiltonian are desirable for assessing the chemically interesting problem of structure-funetion eorrelation and reaction control. The advanced EMR methods known as ENDOR and ESEEM best recover this information from samples in which the ehemieal agent of interest is paramagnetic, and, in principle, there are methods that enable the spectroscopist to cope with the sometimes pathologieal behavior of spin systems, in other word, coax a spectrum out of a sample. In this section, however, we shall address the question of whether there is neeessary and sufficient information in a single ENDOR or ESEEM spectrum and how to design an experimental approaeh that enables one to fully parameterize the spin Hamiltonian. 

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... 

Figure 2.13 Example of an ENDOR experiment for a single spin-1/2 nucleus. See text for explanation.

For maximum ENDOR enhancement, the Zeeman modulation amplitude has to be about one half of the width of the EPR line which is saturated at an extremum of its first derivative. However, in an EPR spectrum with line widths of typically 1 mT this Zeeman modulation contributes 20 kHz to the width of a proton ENDOR line. It turns out that in many cases a remarkably better resolution of the spectra may be obtained with a single coding in which only the rf field is modulated. 

In powder samples with broad EPR lines, large Zeeman modulation amplitudes have to be applied to improve the sensitivity. Such amplitudes often produce microphonic noise in the cavity and cause an uncertainty in the orientation selection in single crystal-like ENDOR spectra (Sect. 4.1). A modulation technique which avoids these problems in powder ENDOR studies has been proposed by Hyde et al.32). In this scheme the Zeeman modulation is replaced by a 180° modulation of the phase of the microwave signal. 

The ENDOR frequencies to first order for a single nucleus with spin I and arbitrary... 

First order ENDOR frequencies of nonequivalent nuclei or of pairs of magnetically equivalent nuclei are given by Eq. (3.3) which is derived from the direct product spin base. To obtain correct second order shifts and splittings, however, adequate base functions have to be used. We start the discussion of second order contributions with the most simple case of a single nucleus and will then proceed to more complex nuclear spin systems. 

Recently similar doublet structures have been observed in other systems with inversion symmetry58,66). Fujimoto et al.58) used a somewhat different perturbation approach for the explanation of the 14N-ENDOR spectra in copper-doped a-glycine, whereas Brown and Hoffman66) determined the nitrogen ENDOR frequencies of Cu(TPP) and Ag(TPP) by numerical diagonalization of the spin Hamiltonian matrix for an electron interacting with a single pair of equivalent 14N nuclei. 

Fig. 9. Second order splittings in spin systems with two magnetically equivalent 1=1 nuclei Single crystal nitrogen ENDOR spectrum of Cu(sal)2 diluted into Ni(sal)2. (Ref. 62)...

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))... 

Signs of the hyperfine principal values of a single nucleus. According to (3.3) and (3.4) the first order ENDOR frequencies of a single nucleus with spin I = 1/2 are given by... 

Relative signs of the hyperfine splittings of two nuclei. In single crystal ENDOR studies the relative signs between hfs constants of different nuclei may sometimes be determined from the cross-term (3.18). If this second order term between nuclei I and K is... 

Orientation selection 4.1 Determination of hf and quadrupole coupling constants from single crystal-like ENDOR spectra... 

Proper single crystal-like ENDOR spectra can best be obtained by saturating the low-and high-field flanks of an EPR spectrum. At these field positions the resolution of the ENDOR spectrum is increased and distortions of the ENDOR lines are minimized78- 79). 

Fig. 12 a, b. Orientation selection in ENDOR. a) Powder EPR spectrum of Co(salen)py. Arrow indicates EPR observer b) Single crystal-like ENDOR spectrum of the pyridine nitrogen with B0 along g . (From Ref. 80)... 

A simpler way is to use a frequency modulated rf field and to switch off the Zeeman modulation. With this single coding of the ENDOR line, the EI-EPR spectrum is directly displayed as an absorption signal20,35). 

Cu(acacen) diluted into Ni(acacen) 1/2 H20 has been chosen as a typical example to demonstrate the separation of magnetically nonequivalent sites in a single crystal by proton EI-EPR. For the specific orientation shown in Fig. 14, the ordinary EPR spectrum of site II is difficult to analyze (Fig. 14 a). In the corresponding EI-EPR spectrum (Fig. 14 b), a high-frequency proton ENDOR line of this site has been used as an observer. Since site I is completely suppressed in the EI-EPR spectrum, the analysis of the hf data of site II becomes straightforward. 

Fig. 18 a, b. DOUBLE ENDOR spectrum of Cu(TPP) in a frozen nematic glass (Merck Phase 5). a) Two-dimensional nitrogen ENDOR spectrum with B0 in the complex plane. ENDOR observer frequency (v = 19 MHz) used in b) is marked by an arrow, b) DOUBLE ENDOR spectrum the corresponding ENDOR frequencies cN( 1/2) = AJ72 3/2 Qj vN obtained from single crystal work1 are marked by arrows. (Ref. 84)... 

This example demonstrates that the data Af1, Q, A2, Q2. evaluated from the nematic glass, together with the values A3, Q3, obtained from the single crystal-like ENDOR spectrum, allow the determination of the full nitrogen hfs and quadrupole tensors of Cu(TPP) without the use of a single crystal. 

Multiple quantum transitions (MQT) in ENDOR spectra may be observed for nuclei with I 1 if two or more (rf) photons of the same or of different frequencies combine to produce an ENDOR transition41,62,99"101). In a MQT the magnetic quantum number nij changes by An = n. The MQT should therefore be clearly distinguished from corresponding forbidden single quantum transitions (SQT) with Am] > 0 discussed in Sect. 3.3. 

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. ... 

CP-ENDOR has been introduced by Schweiger and Giinthard104 to reduce the density of ENDOR lines of complicated paramagnetic systems with a large number of interacting nuclei. ENDOR spectra of solutions (liquid or frozen), polycrystalline powders and single crystals can often be simplified remarkably using this technique. 

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