Powder ENDOR

Density functional theory (DFT) calculations to interpret the powder ENDOR and HYSCORE spectra Establish the use of the g-tensor parameters to detect the presence of dimers... 

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. 

Since many planar metal complexes have nearly axially symmetric g and AM tensors, two-dimensional powder ENDOR spectra can easily be obtained from such compounds oriented in nematic glasses84. As mentioned, interpretation of this type of spectra will be discussed in Sect. 4.3. 

Powder-like ENDOR spectra obtained with arbitrary Bo orientations show a much less pronounced structure and are usually difficult to interpret For systems with nearly axial g and metal hfs tensors, however, there often exist turning points in the EPR spectrum which conespond to all the Bq orientations in the complex plane. Thus, a setting of the magnetic field at such a turning point results in a powder ENDOR spectrum which is a superposition of the ENDOR spectra arising from all these Bq orientations. We call it therefore a two-dimensional ENDOR spectrum. For a ligand nucleus with I = 1/2, the two extreme values of the hfs in the complex plane can immediately be found For a nucleus with 1 1, however, the evaluation of the two extreme coupling constants of both the hf and the quadrupole interaction, which are not necessarily principal values of A and Q, requires more sophisticated ENDOR techniques (Sect. 4.3). 

Fig. 2.15 Experimental (a) and simulated (b), (c) powder ENDOR spectra at 110 K of H2CNHCOC6H5 radical in X-irradiated hippuric acid. Only the region of N-signals is shown. The simulations were made including (b) and excluding (c) the nqc. The figure is adapted from [32] with permission from Elsevier...

Powder ENDOR lines are usually broadened by the anisotropy of the hyperfine couplings. The parameters of well resolved spectra can be extracted by a visual analysis analogous to that applied in ESR. The principle is indicated in Fig. 3.25 for an 5 = V2 species with anisotropic H hyperfine structure, where the hyperfine coupling tensor of axial symmetry is analysed under the assumption that 0 < A < Aj. < 2 vh- The lines for electronic quantum numbers ms = V2 and -Vi, centered at the nuclear frequency vh 14.4 MHz at X-band, are separated by distances equal to the principal values of the hyperfine coupling tensor as indicated in the figure. Absorption-like peaks separated by A in the 1st derivative spectrum occur due to the step-wise increase of the amplitude in the absorption spectrum, like in powder ESR spectra (Section 3.4.1). The difference in amplitude commonly observed between the ms = /2 branches is caused by the hyperfine enhancement effect on the ENDOR intensities first explained by Whiffen [45a]. The effect of hyperfine enhancement is apparent in Figs. 3.25 and 3.26. 

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...

Anisotropic hyperfine couplings of rhombic symmetry give rise to powder ENDOR spectra of the type shown in Exercise E3.20. Absorption-like peaks in the ENDOR spectrum occur also in this case. 

Technical procedures to simulate powder ENDOR spectra are given in Appendix A3.3. Simulation is employed in several applications, of which some are exemplified below. 

F. 3.27 (a) First-derivative X-band ESR spectrum from a polycrystaUine sample of tiltmine. X-irradiated at 295 K and measured at 221 K. The arrows indicate field positions of ENDOR spectra in (b) and (c). (b) Experimental (top) and simulated powder ENDOR spectrum due to radical R1 at 221 K. The experimental spectrum was obtained by saturating the central ESR line at arrow b in (a), (c) Experimental (top) and simulated powder ENDOR spectrum due to radical R2 at 221 K. The experimental spectrum was obteiined by saturating the ESR line at arrow c in (a). The figure is reproduced from [12] vidth permission from Springer... 

Fig. 3.28 Experimental top) and simulated powder ENDOR spectrum due to CO2 ion radicals formed by X-irradiation of a polycrystalline lithium formate sample at room temperature. The experimental spectrum was obtained by saturating the central ESR resonance line. The simulated spectra represent the components due to the hyperflne couplings of Li at four different positions in the vicinity of the CO2 ion. The sum spectrum is obtained by addition of the components. The low frequency branches of the transitions are weak or not observable in experimental and theoretical spectra probably due to different hyperflne enhancement effects for = Vi and -Vi. The figure is reproduced from [K. Komaguchi et al. Spectrochimica Acta Part A 66,754 (2007)] with permission from Elsevier...

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...

The powder ENDOR spectra in this book were calculated with software developed by Erickson [53]. The main equations employed are reproduced, in slightly different notation from that used previously [12, 53]. The powder line shape at the ENDOR frequency v and static magnetic field B is thus given as ... 

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. 

Liquid state ENDOR/TRIPLE spectra of BPh b (270 K) showed 9 H hfc s including signs. Comparison of these data (Table 1) with those from BPh a , that were obtained earlier in detail (8), enabled us to assign the hfc s to molecular positions (note additional hfc s for the ethylidene group - 4a/4b - in BPh b ). From a deconvolution of the poorly resolved powder ENDOR spectrum of BPh b at 100 K we obtained estimates for the hf tensor components of the methyl groups in position 5a All = 10.3, Ax = 8.1 giving A = 8.9 MHz, and la An 9.6,... 

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