Degeneracy electron spin

Firstly, consider the spatial degeneracies of spin-parallel electronic arrangements within the configurations tig ej. Parallel spins must be placed in different... 

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. 

When an electron is placed in a magnetic field, the degeneracy of the electron spin energy levels is lifted as shown in Figure 1.1 and as described by the spin Hamiltonian. ... 

Figure 2.1 Splitting pattern for one of the electron spin energy levels coupled to four equivalent protons. Note that the degeneracies of the levels are not shown. See Section 2.5 for details.

Figure 3.10 Removal of degeneracy of the a and P electron spin states by a magnetic field. (Adapted with permission from Figure 2.16 of Cowan, J. A. Inorganic Biochemistry, An Introduction, 2nd ed., Wiley-VCH, New York, 1997. Copyright 1997, Wiley-VCH.)...

The configurational entropy evaluated above omits all mention of electron spin. Because there are two spin directions, a spin degeneracy of 2, these must be included in the possible configurations. When this term is included, the Heikes equation becomes the Chaikin-Beni equation ... 

AF, FO and FI stand for the antiferro-, ferro- and ferri-magnetic interactions, respectively, expected for the D/A pair. Symbols s, d, t, q and p signify the single, double, triple, quadruple and quintuple degeneracy of the partially occupied orbitals. The superscript number corresponds to the total number of electron spins in those degenerate orbitals. 

Above room temperature, the mobile 3 d electrons are well described by a random mixture of Fel" and FeB ions with the mobile electrons diffusing from iron to iron, some being thermally excited to FeA ions, but the motional enthalpy on the B sites is AH < kT. As the temperature is lowered through Tc, the Seebeck coefficient shows the influence of a change in mobile-electron spin degeneracy, and at room temperature the Seebeck coefficient is enhanced by correlated multielectron jumps that provide a mobile electron access to all its nearest neighbors. The electron-hopping time xi, = coi = 10" s... 

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