Interaction dipolar hyperfine

Hyperfine Interaction (dipolar and scalar) 2,0 Electron relaxation, may be complicated Paramagnetic systems and Impurities [17-191... 

The relationships between the various forms of the dipolar Hamiltonian are explained in appendix 8.2. As we see from (1.59), the dipolar interaction has various components in the molecule-fixed axis system but the most important one, and often the only one to be determined from experiment, is Tq(C). This leads us to define a constant to, the axial dipolar hyperfine component, given in SI units by,... 

The dipolar hyperfine interaction is a through-space interaction of the electron and nuclear spin magnetic moments. As such, it is similar to the nuclear spin-nuclear spin dipolar interaction discussed earlier in connection with the H2 molecule in its ground electronic state. We shall meet the dipolar hyperfine interaction in many examples described later, so at the risk of seeming somewhat pedantic and repetitive, we here... 

The axial component of the magnetic hyperfine interaction for the 2 n 3/2 component is designated //3/2 in terms of the original Frosch and Foley constants [25] h n is equal to a + (1 /2)(b + c), and in terms of our preferred hyperfine constants it is a + (l/2)(fa + 21), the latter constants describing the orbital, Fermi contact and dipolar hyperfine interactions separately. Specifically, our constants are given by,... 

However the fourth term, representing the dipolar hyperfine interaction, is unsuitable for the basis set chosen. Instead we use a different form for this interaction, discussed in chapter 8, and particularly appendix 8.1, which recognises the strong coupling of S and I. This form is... 

Figure 10.39. 13C hyperfine and electron spin-rotation splitting of the N = 0 and 1 rotational levels of 13CO+, and the observed transitions [111]. The large splitting is mainly due to the 13C Fermi contact interaction. The smaller splittings are due to the spin-rotation interaction and the dipolar hyperfine coupling. 

Comparison of the observed value of by with the known contact interaction constant of the Mn+ ion gives a value for cf of0.573. In other words the 3da and 4s hybridisation is a nearly perfect one-to-one mixture. The dipolar hyperfine constant c depends upon a sum of contributions from the 3d unpaired electrons in the 9atomic orbitals, a value which agrees well with the measured value of —48.199 MHz. As we have commented elsewhere, the quadrupole coupling constant involves all of the electrons, and is not readily amenable to a simple semi-empirical treatment. 

As we have shown in Appendix 8.5, and elsewhere, to is the axial component of the dipolar interaction obtained from the fourth term in equation (11.2). The large value of the Fermi contact constant is consistent with a model in which the unpaired electron occupies a a-type molecular orbital which has 45% N atom, v character. Radford produced convincing arguments to show that the model is also consistent with the small dipolar hyperfine constant, and also the electric quadrupole coupling constant. 

The only rigorous quantum number is F, although N may also be taken as good since the separation of different N levels is very large compared with the dipolar hyperfine interaction. Hence the problem of deriving expressions for the energies of the hyperfine levels in 17,1 is tackled by setting up the five matrices for F = N + 2... 

When the magnitudes of the dipolar hyperfine interactions in the dimers are compared with a theoretical value of 67.5 G for an unpaired spin localized in a Ni 3d orbital (87), it can be seen that the molecular orbital containing the unpaired spin has a relatively small contribution from Ni (<30%). A similar situation is observed in H2ases. When bacteria are raised on a source of 61Ni, hyperfine is observed in the EPR signal originating from H2ase (22). (In fact, observation of this hyperfine was... 

In organic metals, the nature of the molecular tt orbitals that form the conduction bands leads to a dipolar hyperfine interaction that may be nonnegligible when compared with the contact contribution discussed above [23]. The various terms in the dipolar interaction modify K and Tx 1 in different ways. The dipolar component [3] can be written as a sum of terms, some of which produce anisotropic Knight shifts (or line broadening in powder samples) and contribute to the spin-lattice relaxation rate. 

We now return to eq. (2-13) and consider briefly the last term describing the anisotropic dipolar hyperfine interaction and its effect on ESR spectra. Let us consider an electron in a p-orbital of a magnetic nucleus in the presence of an external magnetic field. When the applied field is parallel to the symmetry axis of the orbital, the nuclear spin is quantized strictly along the direction of the applied field, and the additional field at the electron AH due to the nucleus is in the same direction as the applied field. When the external field is at an angle 0 to this orbital axis, the nuclear spin should be quantized relative to this new axis. However, the isotropic component of the interaction due to spin polarization is usually larger than the anisotropic component, and the isotropic component is always parallel to the applied field. This allows the quantization of the nucleus to remain in the direction of the applied field, and the relatively small anisotropic splitting can be expressed by (29)... 

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

Long range dipolar interactions between an unpaired electron and nuclear spins on adjacent atoms will not normally be resolved in conventional powder EPR spectra.The pulse technique of electron spin echo modulation (ESEM) is in favourable cases able to detect very weak hyperfine interactions not seen in CW EPR. The method measures modulation of the electron spin echo signal by dipolar hyperfine coupling in the time domain at fixed magnetic field. Until recently,... 

Fermi contact interaction and the dipolar hyperfine interaction contained in... 

Analogously, the Fermi contact and dipolar hyperfine interaction terms originate in the interaction between the electronic magnetic moment and the internal magnetic field generated by the nucleus... 

The effect of k0 is transferred to a higher order where it is negligible. The second contribution involves the internal (dipolar) magnetic field and represents the dipolar hyperfine interaction term... 

Terms depending on electron and nuclear spins 39 dipolar hyperfine interaction i/° (4b)... 

Finally, the matrix elements of the fluorine dipolar hyperfine interaction (equation (10.76)) are given by... 

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