Electron spin magnetism

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... 

It has been verified by electron-spin magnetic-resonance spectroscopy that for copper(II) bis-acetylacetonate26 in mole-percent solution in a crystal of palladium(IJ) bis-acetylacetonate and for copper (II) bis-salicylaldehyde-imine27 in mole-percent solution in a crystal of nickel(II) bis-salicylaldehyde-imine the four coplanar short bonds formed by the copper atom are largely covalent and the two long bonds have very little covalent character. 

A study of the hyperfine structure of the electron spin magnetic resonance spectrum, resulting from the interaction with the nuclear spins, has led to the conclusion9 that structure I contributes 65 percent and structure II35 percent, and that the odd electron occupies a 2pr orbital with 2.5 percent s character. 

The influence of the electron spin relaxation on the relaxivity of gadolinium based contrast agents is essentially governed by the decay of the electron spin magnetization in the direction parallel to the external magnetic field, described... 

Owing to the fact that the proton mass is higher than the electron mass, the nuclear magnetic moments are about 2000 times smaller than the electron spin magnetic moments. 

Wertz, J. E. Nuclear and Electron Spin Magnetic Resonance, Chem. Revs., 55, 829 (1955). 

Electron spin magnetic moment)-(electron spin magnetic moment) dipolar interaction energy ... 

We deal first with molecules containing one unpaired electron (S= I /2) where magnetic nuclei are not present. The electron spin magnetic moment then interacts with the magnetic moment due to molecular rotation, the interaction being represented by the Hamiltonian term... 

The development of the effective Hamiltonian has been due to many authors. In condensed phase electron spin magnetic resonance the so-called spin Hamiltonian [20,21] is an example of an effective Hamiltonian, as is the nuclear spin Hamiltonian [22] used in liquid phase nuclear magnetic resonance. In gas phase studies, the first investigation of a free radical by microwave spectroscopy [23] introduced the ideas of the effective Hamiltonian, as also did the first microwave magnetic resonance study [24], Miller [25] was one of the first to develop the more formal aspects of the subject, particularly so far as gas phase studies are concerned, and Carrington, Levy and Miller [26] have reviewed the theory of microwave magnetic resonance, and the use of the effective Hamiltonian. 

Electron spin magnetic moment and angular momentum... 

Equation (3.159) describes the spin-orbit coupling, the two terms involving the nuclear and electronic potentials respectively. It is interesting to note that these terms arise from the interaction between the electron spin magnetic moment and the effective magnetic field created by the passage of the electron through the electric field created by the other particles. 

So much for the first term on the right-hand side of in equation (4.7). The second term is a familiar one and yields the interaction between B and the electron spin magnetic moment. The third term is new, however, and may be developed in much the same manner as the corresponding term involving A in chapter 3 (see (3.146) to (3.151)). We have... 

The dipolar interaction between the electron spin magnetic moments is also similar to the interaction between two nuclear spins. It may therefore be represented by a classical dipolar interaction term, but with the electron spin magnetic moments represented by their quantum mechanical operators ... 

In this book and in the scientific literature, one frequently encounters the dipolar interaction between two electron spin magnetic moments it always occurs in the description of electronic states of triplet or higher spin multiplicity. Several different operator... 

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... 

The spin-dynamic interpretation is that the up spin associated with the p orbital polarizes (unpairs) the paired spins on s and h. This is of course dynamically incorrect because the electron spin magnetic moments are not large enough to produce the observed polarization. 

Spin-orbit coupling The interaction of the electron spin magnetic moment with the magnetic moment due to the orbital motion of the electron. One consequence of spin-orbit couphng is the mixing of zero-order states of different multiplicity. This effect may result in fine structure called spin-orbit splitting. 

Where i, j, and k are unit vectors along the x, y, and z directions. The expectation value of this operator is the electron spin magnetization vector, which describes the bulk electron spin state for a given radical. 

Unless (v iG)spin = ( i E)spin. then the spin component is zero and the transition is spin-forbidden. Nevertheless, spin-forbidden transitions are observed as weak features (as in Fig. 2.18) typically with 10 -10 the intensity of fully allowed transitions. This is because of the interaction between the electron spin magnetic moment and the magnetic moment due to the orbital motion of the electron (spin-orbit coupling). The La-porte selection rule, furthermore, states that only transitions between wave functions with one having gerade and the other ungerade character are allowed (hence all d-d transitions are Laporte forbidden). This arises since the spatial component can be further broken down ... 

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