Magnetic dipole electron spin

Relaxation of a nucleus (x) in a paramagnetic compound is generally dominated by contributions from nuclear spin-electron spin magnetic dipole-dipole interaction and isotropic (scalar) nuclear-electron spin exchange. The relaxation effects of the two mechanisms are additive... 

Ja corresponds to such interactions with the electronic spin magnetic dipole moments. 

We consider the familiar case of spin space first. In this case, the vector h in equation (2) is given by an external magnetic field B, hQ vanishes, and Hi represents the spin Zeeman term in the one-electron Hamiltonian. Using for the electron spin magnetic dipole moment... 

Just as orbital angular momentum L gives rise to a magnetic dipole moment pL, spin angular momentum S gives rise to a spin magnetic dipole moment fis. Dirac s relativistic theory of the electron showed that... 

This term is called the Fermi contact term. That part of the electron-nucleus magnetic-dipole interaction represented by (8.104) depends on the angular coordinates of the electron and is therefore anisotropic in contrast, the Fermi contact energy (8.108) is isotropic. The contact term plays an important role in the electron-coupled nuclear spin-spin interactions seen in the NMR spectra of liquids. 

This term represents the coupling of the spin magnetic dipole moment with the applied field, and was derived previously for a single electron in equation (3.101). Turning to the fourth term in (3.140) we note that in the field free case we retained only the leading term (i.e. Pf). However, the term linear in Af, although formally of order c 3, has been found to contribute measurably to the Zeeman effect in some cases. The resulting term... 

Because of the symmetry of the homonuclear diatomic molecule, every alternate rotational level is missing those that exist have N odd and positive parity, as shown for the first three rotational levels in figure 10.43. The magnetic dipole transitions arise from coupling of the electron spin magnetic moment with the oscillating magnetic field, represented by the interaction term... 

Pauli spin vector Dirac spin vector electron spin magnetic moment nuclear spin magnetic moment rotational magnetic moment electric dipole moment Ioldy Wouthuysen operator gradient operator Laplacian... 

This contains an TCP of the TpaL tensor, which is derived from the electron spin and dipole-dipole interaction tensor(See equation (11)). Hence, the first question we confront is whether those tensors are correlated or not. In case they are not the total TCP can be decomposed into a product of auto correlations for the the electron spin and dipole-dipole interaction tensor, respectively. In case they are, however, it is necessary to consider the whole TCP and the electron spin has to be correlated with the dipole-dipole interaction tensor. The time dependence in the electron spin tensor can be obtained by integrating the time dependent Schrbdinger equation for the electron spin under the electron spin Hamiltonian. The electron spin is just like the nuclear spin precessing around the external magnetic field and influenced by molecular dynamics. 

The SOC operator / so is a sum of one- and two-electron terms. We consider only the more essential one-electron terms, which represent the interaction of the spin magnetic dipole moment of an electron with the magnetic dipole moment induced by its own orbital motion (Section 1.4). Approximate inclusion of the two-electron part can be done by introducing effective SOC constants for the individual atoms, which correct for the effect of the two-electron part. The atomic SOC constants increase roughly with the fourth power of the atomic number Z. Thus, for an unpaired electron occupying an LCAO-MO, the main... 

The magnetic moment is due to unpaired electron spins. Magnetic susceptibilities are positive as shown in Table 33.5, because the magnetic moments line up with H and this leads to an increase in B. However, adjacent magnetic dipoles essentially behave independently there is no interaction between them. It is this lack of an interaction that separates paramagnetic materials from ferromagnets. Most first row transition metals, e.g., Ti and Cr, are... 

The terms 7 2, 3, H4 (crucial for the NMR experiment) correspond to the magnetic dipole-dipole interaction involving nuclear spins (the term H5 of the Breit Hamiltonian) the classical electronic spin - nuclear spin interaction (7 2) plus the corresponding Fermi contact term (Tia) and the classical interaction of the nuclear spin magnetic dipoles... 

---