Spin-dependent resonance integrals

Because the iron ions carry a magnetic moment, the Hall data are difficult to interpret. The conventional theory of the Hall effect utilizes a spin-independent resonance (transfer-energy) integral, and an adequate theory incorporating a spin-dependent resonance integral needs to be developed for antiferromagnetic materials. 

The interactions between localized spins on neighboring cations are treated by a perturbation theory in which the spin-dependent resonance integrals for parallel and antiparallel coupling of spins are... 

Multiplying the resonance integral by the quadrupled transferable spin bond order PoL = CQ- (3.14) results in the resonance energy of the m-th bond which is the only nontrivial contribution to the molecular energy at this (FAFO) level of approximate treatment of the MINDO/3 Hamiltonian using the SLG trial wave function. Within this picture the hybridization tetrahedra interact and the interaction energy depends on separations between centers of the tetrahedra, their mutual orientation, with respect to the bond axis. 

The efficiency with which the NOE is generated depends on the physical distance between the irradiated and the observed spins. The dipolar interaction scales as r , thus making the effect diminish severely with increasing internudear distance r. But this strong distance dependence is what makes the NOE so useful. Only spins that are very close in space will exhibit a strong dipolar interaction that may, upon irradiation of the resonances from one of the spins, increase the integrated intensity of the receiving spin s resonance in the NOE difference spectrum. 

The electron spin resonance spectrum of a free radical or coordination complex with one unpaired electron is the simplest of all forms of spectroscopy. The degeneracy of the electron spin states characterized by the quantum number, ms = 1/2, is lifted by the application of a magnetic field, and transitions between the spin levels are induced by radiation of the appropriate frequency (Figure 1.1). If unpaired electrons in radicals were indistinguishable from free electrons, the only information content of an ESR spectrum would be the integrated intensity, proportional to the radical concentration. Fortunately, an unpaired electron interacts with its environment, and the details of ESR spectra depend on the nature of those interactions. The arrow in Figure 1.1 shows the transitions induced by 0.315 cm-1 radiation. 

The description of imaging experiments in reciprocal space is not restricted to k space, the Fourier conjugate space of physical space. The modification of the spin density by other parameters like resonance frequencies, coupling constants, relaxation times, etc., can be treated in a similar fashion [Miil4]. For the frequency-dependent spin density, the Fourier transformation with respect to 2 is already explicitly included in (5.4.7). Introduction of a Ti-dependent density would require the inclusion of another integration over T2 in (5.4.7) and lead to a Laplace transformation (cf. Section 4.4.1). 

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