Anisotropic hyperfine

A t)tpical feature of the Mossbauer spectra of five- or six-coordinate iron(IV) with an axial oxo group (or a OCH3, a nitrido or a imido group) is a low isomer shift (+0.1 0.15 mm s ), a large and positive quadrupole splitting (1-2 mm s ), an anisotropic hyperfine coupling tensor with moderately large values for A x/gNl N and (—16 to —23 T) and a rather small value for A Jg i (0 to —10 T)... 

Konovalova, T. A., S. A. Dikanov et al. (2001a). Detection of anisotropic hyperfine components of chemically prepared carotenoid radical cations ID and 2D ESEEM and pulsed ENDOR study.. /. Phys. Chem. B 105 8361-8368. 

An exception to this rule arises in the ESR spectra of radicals with small hyperfine parameters in solids. In that case the interplay between the Zeeman and anisotropic hyperfine interaction may give rise to satellite peaks for some radical orientations (S. M. Blinder, J. Chem. Phys., 1960, 33, 748 H. Sternlicht,./. Chem. Phys., 1960, 33, 1128). Such effects have been observed in organic free radicals (H. M. McConnell, C. Heller, T. Cole and R. W. Fessenden, J. Am. Chem. Soc., 1959, 82, 766) but are assumed to be negligible for the analysis of powder spectra (see Chapter 4) where A is often large or the resolution is insufficient to reveal subtle spectral features. The nuclear Zeeman interaction does, however, play a central role in electron-nuclear double resonance experiments and related methods [Appendix 2 and Section 2.6 (Chapter 2)]. 

Hyperfine interactions likewise produce characteristic inflections in the derivative curve. Anisotropic hyperfine coupling is usually accompanied by anisotropic g values and as a result, the powder spectra are often quite complex. Typical powder spectra for paramagnetic species having one nucleus with / = are shown in Fig. 16. An unambiguous analysis of the more complex experimental spectra often requires the use of two microwave frequencies and a variation in the nuclear isotopes. The latter technique is illustrated by a comparison of the spectra for 14N02 and 15N02 on MgO as shown in Fig. 17. 

MgO, respectively. Photolysis by an incandescent lamp is necessary to produce the radical on MgO, and the light significantly alters, both in amplitude and shape, the spectrum of the species on silica-alumina. Both spectra are interpreted in terms of very anisotropic hyperfine interactions. This is consistent with work on radical anions such as nitrobenzene on MgO (90) however, it is a bit surprising in light of the motional averaging found for most cations on silica-alumina. 

An indirect mode of anisotropic hyperfine interaction arises as a result of strong spin-orbit interaction (174)- Nuclear and electron spin magnetic moments are coupled to each other because both are coupled to the orbital magnetic moment. The Hamiltonian is... 

The impurity interacts with the band structure of the host crystal, modifying it, and often introducing new levels. An analysis of the band structure provides information about the electronic states of the system. Charge densities, and spin densities in the case of spin-polarized calculations, provide additional insight into the electronic structure of the defect, bonding mechansims, the degree of localization, etc. Spin densities also provide a direct link with quantities measured in EPR or pSR, which probe the interaction between electronic wavefunctions and nuclear spins. First-principles spin-density-functional calculations have recently been shown to yield reliable values for isotropic and anisotropic hyperfine parameters for hydrogen or muonium in Si (Van de Walle, 1990) results will be discussed in Section IV.2. 

An unambiguous identification of anomalous muonium with the bond-center site became possible based on pseudopotential-spin-density-functional calculations (Van de Walle, 1990). For an axially symmetric defect such as anomalous muonium the hyperfine tensor can be written in terms of an isotropic and an anisotropic hyperfine interaction. The isotropic part (labeled a) is related to the spin density at the nucleus, ip(0) [2 it is often compared to the corresponding value in vacuum, leading to the ratio i7s = a/Afee = j i (O) Hi/) / (O) vac- The anisotropic part (labeled b) describes the p-like contribution to the defect wave function. 

Several recent papers have reported Density Functional Theory (DFT) calculations on the primary oxidation and reduction products observed in irradiated single crystals of the common nucleobases thymine [53], cytosine [54], guanine [55], and adenine [56]. The theoretical calculations include estimates of spin densities and isotropic and anisotropic hyperfine couplings which can be compared with experimental results (obtained from detailed EPR/ENDOR experiments). 

Compound Isotropic and Anisotropic Hyperfine Coupling Constants (Mc/sec) ... 

Table 14. Unpaired electron distributions in diatomic halide radical anions. Sa, Pa indicate the spin population of the valence s and p orbitals of atom A, derived from the isotropic and anisotropic hyperfine coupling constants 67)...

Once a description of the electronic structure has been obtained in these terms, it is possible to proceed with the evaluation of spectroscopic properties. Specifically, the hyperfine coupling constants for oligonuclear systems can be calculated through spin projection of site-specific expectation values. A full derivation of the method has been reported recently (105) and a general outline will only be presented here. For the calculation of the hyperfine coupling constants, the total system of IV transition metal centers is viewed as composed of IV subsystems, each of which is assumed to have definite properties. Here the isotropic hyperfine is considered, but similar considerations apply for the anisotropic hyperfine coupling constants. For the nucleus in subsystem A, it can be... 

From the anisotropic contributions to the HFCs, it is confirmed that the reduced site is the main source of anisotropy in the system. The computed values reproduce the rhombicity of all anisotropic hyperfine tensors, but there is a clear tendency of overestimation. In any case, since the anisotropic components are at least an order of magnitude smaller than the isotropic contributions to the HFC, it is more appropriate and useful to focus on the latter. All isotropic HFCs have the correct signs with respect to the... 

As added evidence for our confidence in the parameters shown in Table 6, the zero applied field spectra taken at low temperatures are shown in Fig. 13. Since the A-values for site 1 are almost isotropic, it is expected that the absorption peaks from this site would dominate the Mossbauer spectra in both zero and applied magnetic field. Comparison of Fig. 14 and Fig. 3 reveals that the absorption in these spectra at — 6 mm/S results from an isotropic hyperfine interaction of about —17 gauss at one of the iron sites in the reduced proteins. The anisotropic hyperfine interaction at site 2 results in a broad, unresolved absorption which accounts for the difference in shape between the spectra. 

Some Theoretically Computed Estimates of Isotropic and Anisotropic Hyperfine... 

These workers (Adrian et al., 1962) also studied the spin resonance spectrum of DCO radicals and obtained remarkably narrow lines and shoulders which gave sufficient detail that the anisotropic hyperfine tensor could be deduced. This result then enabled them to extract the data tabulated from the spectrum of HCO. In particular, it is pointed out that as the g- and hyperfine-anisotropies have different principal axes, there has to be an extra term (Ayz) where the hyperfine tensor is expressed in terms of the axes of the gr-tensor. A careful analysis of all the data led these authors to the conclusion, based entirely upon experiment, that the large isotropic hyperfine coupling must be positive. 

Table 14 Anisotropic hyperfine coupling constants (in MHz) of H2GN (X2B2). The values of the present work were obtained with the van Duijneveldt AO basis in combination with the MRD-CI/BK method.

McGarvey (421) also developed expressions for the anisotropic hyperfine interaction and the reduced form of these equations were used by Maki and co-workers (420) in their analysis of the hyperfine coupling in metallo-tris(dithiolenes). These equations are given below ... 

Figure 18-8. Proton hyperfine couplings for a planar > C — Ha fragment showing the principal values and directions of the proton anisotropic hyperfine coupling...

From these results one can see the incredible power of the combined EPR/ENDOR experiment. While the EPR spectrum of irradiate adenosine had rather narrow lines, the spectrum was unresolved due to the overlap of several radicals. The ENDOR spectra were easy to follow for complete rotations about all three crystallographic axes. Analysis of the ENDOR data yielded accurate anisotropic hyperfine tensors that could be related to two different free radicals. From these results one can confidently say that Radical I is the N3 protonated adenine anion A(N3+H) and Radical II is the N6 deprotonated adenine cation A(N6-H) With ENDOR data one is able to determine the protonation state of a radical, and if care is taken in the analysis, to even discern slight deviations from planarity of radicals. 

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