Spin-dipole term

Spin-orbit coupling may produce an orbital magnetic moment on the ligands. This leads to a modification of the main spin-dipole term by a small correction term proportional to (g — 2). 

The term involving two nuclei is analogous to the electron-electron spin-dipole term in eq. (10.77). The corresponding Fermi contact term disappears since nuclei cannot occupy the same position at energies relevant for chemistry. Note that the direct spin-spin coupling is independent of the electronic wave function it only depends on the molecular geometry. 

There are two terms of interest. First there is a classical electron spin-nuclear spin dipole-dipole interaction... 

Equation (28) can be simplified if we recognize that since the electric dipole operators are independent of spin any term will be zero unless M=M =M". Furthermore, as noted earlier, the axis of spin quantization is the direction of the applied magnetic field and terms will also be zero unless y=y. Therefore,... 

In addition to the isomer shift and the quadrupole splitting, it is possible to obtain the hyperfine coupling tensor from a Mossbauer experiment if a magnetic field is applied. This additional parameter describes the interactions between impaired electrons and the nuclear magnetic moment. Three terms contribute to the hyperfine coupling (i) the isotropic Fermi contact, (ii) the spin—dipole... 

Other Terms. Some small terms have not been included in Eq. (5) because it has never been necessary to include them to account for the observed ESR spectra. These include such terms as the nuclear spin-nuclear spin dipole interactions and the nuclear chemical-shift terms. These terms... 

The direct dipole-dipole interaction between electron spins given in Eq. (14) can also contribute to D and E in the spin Hamiltonian. Various estimates of its contribution have shown it to be much smaller than the spin-orbit terms for transition-metal ions. For systems in which the crystal field is greatly distorted, this term can become large, however, and it is found to be the major source of D in the spin Hamiltonian of organic triplet-state molecules, where the spin-orbit terms are small as a result of the small size of the spin-orbit coupling parameter. 

Finally, the interaction between the dipole and quadrupole of donor and acceptor molecules [13] is generally much weaker than the dipole-dipole interaction. The dipole—quadrupole term [/ (r) r-8] is typically 10—100 times weaker than the dipole—dipole term, though if the acceptor absorption spectrum is symmetry-forbidden (and so weak) but not spin-forbidden, the dipole transition moment for the acceptor is small [127]. Such is the case for energy transfer between rare-earth ions in tungstates typically separated by 1.7 nm [146]. The kinetics of dipole—quadrupole energy transfer are discussed in Chap. 4, Sect. 2.6. 

For the evaluation of probabilities for spin-forbidden electric dipole transitions, the length form is appropriate. The velocity form can be made equivalent by adding spin-dependent terms to the momentum operator. A sum-over-states expansion is slowly convergent and ought to be avoided, if possible. Variational perturbation theory and the use of spin-orbit Cl expansions are conventional alternatives to elegant and more recent response theory approaches. 

The irreducible tensor product between two (spherical) vectors is defined in Eq. (37). An important feature of this Hamiltonian is that it explicitly describes the dependence of the coupling constants J, Am, and T, on the distance vectors rPP between the molecules and on the orientations phenomenological Hamiltonian (139). Another important difference with the latter is that the ad hoc single-particle spin anisotropy term BS2y, which probably stands implicitly for the magnetic dipole-dipole interactions, has been replaced by a two-body operator that correctly represents these interactions. The distance and orientational dependence of the coupling parameters J, A, , and Tm has been obtained as follows. 

The terms in equation (4) are generally referred to as the orbital-dipolar interaction (o) between the orbital magnetic fields of the electrons and the nuclear spin dipole, the spin-dipolar interaction (D) between the spin magnetic moments of the electrons and nucleus and the Fermi contact interaction (c) between the electron and nuclear spins, respectively. Discussion of the mathematical forms of each of these three terms appears elsewhere. (3-9)... 

On the contrary, the dipole-dipole terms play no role at all for coupling constants, because they vanish after integration over spin coordinates, and exchange integrals only are significant in NMR. 

The magnetic hyperfine splitting (MHS) depends on the nuclear spin quantum numbers and /g of the excited and ground state of the Mossbauer nucleus and on the effective magnetic field at the Mossbauer nucleus, which includes contributions from the local electronic spin, from the orbital momentum, from dipole terms, and from external fields. 

An increasing interest is being paid to spin-spin couplings between directly bonded two carbon nuclei. Four important papers by Cremer and coworker have been devoted to the mechanisms governing NMR spin-spin coupling and to the question if one can derive the information on the Jt character of a CC bond with the help of this parameter. An analysis of the spin-dipole and paramagnetic spin orbital transmission mechanisms led the authors to the conclusion that these terms are a sensitive indicator of the Jt character of a CC bond. 

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