Electron spins, interaction with environment

The prominence of these quantum dynamical models is also exemplified by the abundance of theoretical pictures based on the spin-boson model—a two (more generally a few) level system coupled to one or many harmonic oscillators. Simple examples are an atom (well characterized at room temperature by its ground and first excited states, that is, a two-level system) interacting with the radiation field (a collection of harmonic modes) or an electron spin interacting with the phonon modes of a surrounding lattice, however this model has found many other applications in a variety of physical and chemical phenomena (and their extensions into the biological world) such as atoms and molecules interacting with the radiation field, polaron formation and dynamics in condensed environments. 

Often the electronic spin states are not stationary with respect to the Mossbauer time scale but fluctuate and show transitions due to coupling to the vibrational states of the chemical environment (the lattice vibrations or phonons). The rate l/Tj of this spin-lattice relaxation depends among other variables on temperature and energy splitting (see also Appendix H). Alternatively, spin transitions can be caused by spin-spin interactions with rates 1/T2 that depend on the distance between the paramagnetic centers. In densely packed solids of inorganic compounds or concentrated solutions, the spin-spin relaxation may dominate the total spin relaxation 1/r = l/Ti + 1/+2 [104]. Whenever the relaxation time is comparable to the nuclear Larmor frequency S)A/h) or the rate of the nuclear decay ( 10 s ), the stationary solutions above do not apply and a dynamic model has to be invoked... 

Unpaired electrons can interact with other magnetic dipoles in the system. Such interactions do not dissipate energy and hence do not directly contribute to returning the spin systems to equilibrium. However, the spin-lattice transition may be enhanced if the interaction with the magnetic dipoles brings the excess energy to a position for transfer to the lattice. A variety of dipoles are frequently part of an unpaired electron s environment for example, other unpaired electrons, magnetic nuclei of the lattice, and various electronic and impurity dipoles. Since dipolar interactions decrease with the cube of the separation, i.e., ai = many... 

In part the interest arises from the fact that the spectroscopic state 87/2 is the same for the atom, 4f 6s as for the divalent ion, 4f . The former has been studied by atomic beam triple resonance (Sandars and Woodgate 1960, Evans et al. 1965), and the latter by ENDOR (Baker and Williams 1962) in Cap2, an environment with cubic symmetry. For a half-filled shell, with no orbital momentum and a spherical distribution of electron spin moment with zero density at the nucleus, both the magnetic dipole and electric quadrupole interactions should be zero. Experimentally, they are small compared with the values for other odd-proton lanthanide isotopes with comparable nuclear moments, for which the hyperfine... 

Generally, it is assumed that the electrons in free radicals and paramagnetic materials are completely independent and noninteracting. Several effects become important when electron spins interact magnetically and chemically with each other and with their environment. 

These nuclei (and they form by far the majority of the NMR-active nuclei ) are subject to relaxation mechanisms which involve interactions with the quadrupole moment. The relaxation times Tj and T2 (T2 is a second relaxation variable called the spin-spin relaxation time) of such nuclei are very short, so that very broad NMR lines are normally observed. The relaxation times, and the linewidths, depend on the symmetry of the electronic environment. If the charge distribution is spherically symmetrical the lines are sharp, but if it is ellipsoidal they are broad. 

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. 

Figure 6. Li MAS NMR spectrum of the layered compound Li2MnOs acquired at a MAS frequency, Vr, of 35 kHz. Spinning sidebands are marked with asterisks. The local environment in the Mn +/Li+ layers that gives rise to the isotropic resonance at 1500 ppm is shown. Spin density may be transferred to the 2s orbital of Li via the interaction with (b) a half-filled t2g orbital and (c) an empty d/ Mn orbital to produce the hyperfine shifts seen in the spectrum of Li2MnOs. The large arrows represent the magnetic moments of the electrons in the t2g and p orbitals, while the smaller arrows indicate the sign of the spin density that is transferred to the Li 2s and transition-metal d orbitals.

Since a chemical environment does not normally interact directly with electron spins, the spin multiplicity of a state is unaffected by the splitting and the split states will have the same multiplicity as the parent free ion state. The quantum number J also remains unaltered. For this reason, multiplicities and J values are left out in Table 12-5.1. 

One other point needs to be mentioned regarding the splitting of terms of the free ion in chemical environments, and this concerns the spin multiplicity. The chemical environment does not interact directly with the electron spins, and thus all of the states into which a particular term is split have the same spin multiplicity as the parent term. 

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