Angular selection

Figure 13. The symmetry value obtained by angular selection about the center of mass (marked by +) is greater than the symmetry value obtained by angular selection about the center of symmetry (marked by ).

Figure 14. (a) Original occluded shape, its centroid (+) and its center of symmetry ( ). (b,c) The closest Cs-symmetric shapes following angular selection about the centroid (b) and about the center of symmetry (c). 

Several factors unique for ENDOR affect the intensities, i.e. magnetic relaxation, hyperfine enhancement, and angular selection. The two first effects also affect spectra of liquid and crystalline samples, while the third is typical for powder spectra of species with anisotropic g-values. Methods that take the two latter effects into account have been developed and are usually incorporated in software developed for the simulation of ENDOR spectra in the solid state. Simulations that take magnetic relaxation effects into account have been employed only to analyse ENDOR spectra in the liquid state [2]. It is possible that the commonly observed poor agreement between experimental and simulated intensities in the solid state is at least in part due to relaxation effects that are not taken into account in any software we are aware of. 

Fig. 3.26 Schematic powder ENDOR spectra of an S = Vi species with axially symmetric g and H hyperfine structure. ENDOR spectra with the magnetic field locked at g and gi, respectively, are single-crystal like due to angular selection. The lines for electronic quantum numbers ms = Vi and -V2 are separated by distances equal to A and Aj, the principal values of the hyperfine coupling tensor as indicated in the figure...

Angular selection can affect the powder spectrum shape as schematically shown in Eig. 3.26. 

Ligand structure of transition metal ions by angular selection analysis... 

The angular selection method established by Rist and Hyde [47] for the analysis of ligand ENDOR of metal complexes in powders has been further developed and applied for biological systems. Measurements at X- and Q-band are often adequate due to an appreciable -anisotropy. We refer to recent reviews for further account of this application [48]. 

Fig. 3.30 Simulated powder ENDOR spectrum (in absorption) of NO-ligated ferrocytochrome c heme a3, at the field setting (g = 2.079) marked in the X-band (v = 9.32 GHz) ESR spectrum. The parameters g = (2.082, 1.979, 1.979) A( N-His) = (16.5, 16.1, 19.3) MHz, Q(> N-His) = (+0.67, -1.12, + 0.45 ) MHz, A( N-NO) = (30.56, 30.56 59.90) MHz, Q( N-NO) = (+1.03, -0.51, -0.52) MHz were employed for the simulation, using a method teiking angular selection into account. For experimenUil spectra see [R. LoBrutto et aL, J. Biol. Chem. 258 (1983) 7437], for simulation with an exact method see [49]. The spectrum is adapted from [R. Erickson, Chem. Phys. 202, 263 (1996)] with permission from Elsevier...

A notable feature of this and other systems with S > Vi is that angular selection is achieved, not only by -anisotropy but is mainly due to zero-field splitting. Not all simulation software described below can handle this case, which can more easily be taken into account by the general simulation programs exemplified in Table 3.5. 

The ENDOR signal is assumed to be proportional to the ESR absorption with the field locked at the ESR transition - /2, i> -> /2, j>, i.e. to s(B - By)V as indicated in Eig. 3.38 [53]. This factor affects the shape of the calculated ENDOR spectra, and gives rise to angular selection even when the g- or other anisotropy is not completely resolved in the corresponding ESR spectra. 

Fig. 3.38 Mechanism of angular selection in powder ENDOR. The ENDOR signal for the transition between the states M, J>. o- M, k>, M = V2 with the field locked at the ESR transition I-V2, i>...

Simulation of powder ESEEM spectra is usually performed by a numerical integration over the magnetic field directions. Frequently used Equations [54, 57, 61, 82-85] are reproduced below. Angular selection can be taken into account in a manner analogous to that used in powder ENDOR simulations. 

Powder ENDOR Hyperfine couplings obtained by the angular selection method with the field set at anisotropic gx, gy and gz features can give single-crystal-like ENDOR spectra from randomly oriented samples. The enhanced resolution of g-anisotropy at high magnetic field increases orientation selectivity of ENDOR spectra in amorphous systems. 

The principal values and even the orientation of the principal axes of the Na hyperfine coupling tensor with respect to axes of the g tensor could be determined from Mims and Davies pulsed ENDOR spectra, refer to Section 2.3.3 in Chapter 2. The values Axx( Na) = Ayy( Na) = 6.3 and Azz( Na) = 10.9 MHz were obtained by simulation taking angular selection into account. The so-called hyperfine enhancement of ENDOR intensities due to the interaction between the radio frequency field and the electron spin could lead to pronounced differences in the ENDOR intensities between signals from different rris electron spin states in experiments at conventional MW frequencies such as in X-band, but also at the W-band. The Na (I = 3/2) nuclear quadrupole tensor is almost coaxial to the A tensor, 2zz = 0.48 MHz, Qyy = -0.07 MHz, and Qxx = -0.41 MHz. Simulation of orientation-selective ENDOR spectra as described in [26, 33] serves to refine the principal values of the hyperfine coupling tensors estimated from experiment. In... 

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