Anisotropic hyperfine interaction

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)]. 

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... 

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. 

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. 

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 ... 

Since the electron is not localized at one position in space. Equation 1.35 must be averaged over the electron probabihty distribution funcbon. H is averaged to zero when the electron cloud is spherical (as in s orbitals) and comes to a finite value for axially symmetric orbitals. The magnitude of the anisotropic hyperfine interaction then depends on the orientation of the paramagnehc system with respect to the external field. 

At small distances, the two unpaired electrons will experience a strong dipole-dipole interaction analogous to the interaction between electronic and nuclear magnetic dipoles, and this gives rise to anisotropic hyperfine interactions. The electron-electron interaction is described by the spin-spin Hamiltonian given by ... 

Anisotropic hyperfine interaction (dipolar term) x, y, z . principal axes of hyperfine interaction tensor A... 

Here g and gjL are the electronic g factors for the magnetic field, respectively parallel and perpendicular to the symmetry axis, A is now the isotropic hyperfine interaction constant, and B is the anisotropic hyperfine interaction constant. The dependence on magnetic field orientation is given by the function (3 cos —1), where Oh is the angle between the magnetic field and the symmetry axis. 

Figure 5. Typical ESR line shape for a randomly oriented, nonrotating free radical having an anisotropic g factor and an anisotropic hyperfine interaction as described by Equation 2...

Irradiated anhydrous sodium or potassium acetate shows a complex ESR pattern (Figure 1) with no lines owing to CH3 apparent. The radicals giving the dominant lines have anisotropic hyperfine interactions,... 

Anisotropic Hyperfine Interaction. The anisotropic component of the hyperfine coupling has two contributions a local anisotropy owing to spin density in p- or type orbitals on the atom of observation, and nonlocal dipolar coupling with spin on other atoms. The first type of interaction is proportioned to the orbital coefficient (squared) of the pid orbiteds. To a first approximation the second term can be considered as a classic point dipolar interaction between the nucleus and the electron spin on a nearby atom. This depends on the total electron spin density at the neighbor (p ), the distance between the spins (r,2), and the orientation of the vector between them with respect to the external magnetic field (denoted by angle 0). In the point dipole approximation,... 

Fig. 39. EPR (electron paramagnetic resonance) spectra of above N C6o centre N Qi (COOEt)2 together with below a simulation. The triplet splitting (above) is due to the isotropic hyperfine interaction of the electron systems with the nuclear spin Z = 1 of (natural abundance 99.6 %). Since the electronic spin is S = 3/2 (three unpaired electrons), each of the lines is three-fold degenerate. The occurrence of this degeneracy implies that the fine structure, quadrupole interaction and anisotropic hyperfine interaction are zero (complete spherical symmetry of nitrogen). In the adduct N C6i(COOEt)2 the icosahedral cage symmetry and therefore the degeneracy of nitrogen p orbitals is broken giving rise to new lines (centre). The simulation (below) is performed with the hyperfine interaction and g factor of N Cgo but in addition a fine structure interaction (D =2 G and E = 0.13 G) is included. The effect of the deviation from spherical symmetry on the quadrupole or anisotropic hyperfine interaction is too small to be detected...

The Ng radical is formed on irradiation of Ng by 600 keV electron pulses the kinetics have been followed and a mechanism has been proposed. In order to diflferentiate between N and Ng-, both of which have unpaired electrons, unpaired spin densities have been calculated by the INDO method, including a consideration of the anisotropic hyperfine interaction. ... 

E.2.9 An ESEEM signal occurs in the presence of an anisotropic hyperfine interaction that is of a magnitude comparable to the nuclear Zeeman energy. The schematic ESR spectrum in the left part of the figure below contains allowed and forbidden lines due to a mixing of nuclear states. For an / = Vi nucleus the ESEEM amplitude is proportional to A = sin a/Z cos of/2 = 7o /, where a is the angle between the effective fields acting on the nucleus for ms = /2 and lo and li are the amplitudes of the outer and inner ESR lines. 

A more general spin Hamiltonian of the form (3.9) is applied when zero-field splittings (S > V2), anisotropic hyperfine interactions (/ 0), and nuclear quadrupole couplings (/ > 1) occur. 

Freed et al. [3] evaluated the relaxation rate of polymer chains by the analysis of the anisotropic spectra of nitroxide spin labels. The main triplet spectrum was due to hyperfine coupling caused by the nitrogen nucleus. It narrowed with an increase in mobility of the radicals because of motional averaging of the anisotropic hyperfine interaction. The rotational correlation time of nitroxide spin labels can be estimated using the procedure of Freed et al. by taking into account the anisotropic rotational motion. The ESR line width, AHmsi of the spectrum can be expressed as follows ... 

In real media, nitroxides change their orientations with respect to the external magnetic field due to the Brownian thermal rotational mobility usually characterized by the rotational correlation time, The anisotropic hyperfine interaction between the unpaired electron and nitrogen nucleus is modified by these changes with a frequency dependent on Xj. In this way, frequency-dependent perturbations are generated, which modify the energy levels and transition probabilities in the system. As a result, the line shape of ESR spectra of nitroxides (and of other free radicals in which anisotropic magnetic interactions occur) depends on the correlation time x. ... 

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