Nuclear Zeeman frequency

HYSCORE spectra of zeaxanthin radicals photo-generated on silica-alumina were taken at two different magnetic fields B0=3450G and B0=3422G, respectively. In order to combine the data from the two spectra, the field correction was applied (Dikanov and Bowman 1998). The correction consists of a set of equations that allow transformation of spectra to a common nuclear Zeeman frequency. The set of new frequencies was added to that of the former spectrum and plotted as the squares of the frequencies v2a and v2p. Examples of these plots can be found in Focsan et al. 2008. 

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). 

Overlap of lines can make analysis difficult when several nuclei contribute in the one-dimensional (ID) two- and three-pulse ESEEM spectra. Eollowing the development in NMR, methods to simplify the analysis involving two-dimensional (2D) techniques have therefore been designed. The Hyperfine Sublevel Correlation Spectroscopy, or HYSCORE method proposed in 1986 [14] is at present the most commonly used 2D ESEEM technique. The HYSCORE experiment has been applied successfully to study single crystals, but is more often applied to orienta-tionally disordered systems. It is a four-pulse experiment (Fig. 2.23(a)) with a k pulse inserted between the second and the third k/2 pulse of the three-pulse stimulated echo sequence. This causes a mixing of the signals due to the two nuclear transitions with m.s = Vi of an 5 = Vi species. For a particular nucleus two lines appear at (v , V ) and (V ", v ) in the 2D spectrum as shown most clearly in the contour map (d) of Fig. 2.23. The lines of a nucleus with a nuclear Zeeman frequency... 

Fig. 2.23 Schematic HYSCORE spectrum showing (a) the HYSCORE sequence, (b) the 2D time-domain modulation signal, (c) the 2D HYSCORE spectrum and (d) the contour plot of a single crystal sample for an 5 = Vi species containing a H nucleus with an axitilly symmetric hyper-fine coupling. The magnetic field is at an angle 0 = 10° with the A axis. The nuclear Zeeman frequency vh 15 MHz is larger than the hyperflne coupling, i.e. Ai I < A < 2 vh...

HYSCORE has a higher sensitivity in the region of low nuclear frequencies than that of ENDOR spectroscopy. Single crystal measurements have therefore been applied to studies of nitrogen-containing paramagnetic species (nuclear Zeeman frequency v( " N) = 1 MHz at X-band) of interest in biochemical and fundamental applications. The local structure around the species may be obtained as discussed below for the radical H3CCHCOO in irradiated /-alanine. 

Fig. 3.33 Schematic HYSCORE contour plot for an S = Vi single crystal species with an anisotropic hyperfine coupling due to two I = Vi nuclei. The spots symmetrically displaced from the diagonals correspond to nuclear frequencies with electron quantum number ms = 14.The correlation between the nuclear transitions for a particular nucleus is achieved by the Jt pulse inserted between the second and the third tt/2 pulse of the three-pulse stimulated echo sequence. The spots in the right quadrant are due to a nucleus with frequencies (Vd, vpi) for the two nuclear transitions corresponding to ms = 14. The frequencies to the right are small compared to the nuclear Zeeman frequency, while the spots in the left quadrant are for the opposite case with large frequencies (v, vpa)...

Separation of interactions allows for precise measurements of the small interactions of the observed electron spin with remote spins in the presence of line broadening due to larger contributions. Such techniques are therefore most useful for solid materials or soft matter, where ESR spectra are usually poorly resolved. The most selective techniques for isolating one type of interaction from all the others are pulsed double resonance experiments, such as ENDOR and electron-electron double resonance (ELDOR), which are discussed in more detail in Chapter 2. If the hyper-fine couplings are of the same order of magnitude as the nuclear Zeeman frequency, ESEEM techniques may provide higher sensitivity than ENDOR techniques. In particular, the two-dimensional hyperfme sublevel correlation (HYSCORE) experiment provides additional information that aids in the assignment of ESEEM spectra. These experiments are also discussed in Chapter 2. 

Overlap of signals from different chemical elements is an inherent weakness of ENDOR spectroscopy at conventional ESR frequencies of 9.6 GHz (X band) as can be seen in Fig. 9. To overcome this problem, pulse ENDOR techniques have been developed that separate ENDOR signals according to the nuclear Zeeman frequency or the magnitude of the hyperfine couphng. Provided the hardware is available, high-field ENDOR provides a more simple alternative. At an ESR frequency of 95... 

Fig. 9. Nuclear Zeeman frequencies (vertical markers) and ENDOR frequency ranges (horizontal bars) for selected isotopes at magnetic fields of 0.35 T (conventional ENDOR) and 3.35 T (high-field ENDOR).

Since V/ is known, one can determine Vdd, and hence the distance between the electron and nuclear spin, even in the presence of small, unknown isotropic hyperfine couplings. The second-order shift with respect to twice the nuclear Zeeman frequency is small. Hence, two-pulse ESEEM with its inferior resolution is not well suited for measuring this shift. The sum combination frequency can be introduced into stimulated-echo ESEEM by inserting an mw tz pulse halfway through the evolution period of length T (sequence in Fig. 11 with fi = 2 = T/2). 

The vector h contains the direction cosines of the magnetic field orientation. The symbols vp and 1 describe the nuclear Zeeman frequency (for protons) and the unit matrix. In this notation, g 6,f) is the effective g-factor, which describes the resonance magnetic field for a given microwave frequency Vq, with h as Planck s constant, as... 

The above-mentioned pseudo-nuclear contribution to the gn value, combined with the low nuclear Zeeman frequency of the protons at the g = 6, position makes interpretation of the proton ESEEM spectra very difficult... 

Figure 4. X-band SMART HYSCORE spectrum of aquometmyoglobin taken at observer position g = 6. The double-quantum cross-peaks are separated over four times the effective nuclear Zeeman frequency, which clearly differs from the tabulated value (dashed lines, separation 4vv). From this shift, the positive sign of the hyperfine value can be determined [93,94],...

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