Electron spin transitions

Figure Bl.15.8. (A) Left side energy levels for an electron spin coupled to one nuclear spin in a magnetic field, S= I =, gj >0, a<0, and a l 2h)<(a. Right side schematic representation of the four energy levels with )= Mg= , Mj= ). +-)=1, ++)=2, -)=3 and -+)=4. The possible relaxation paths are characterized by the respective relaxation rates W. The energy levels are separated horizontally to distinguish between the two electron spin transitions. Bottom ENDOR spectra shown when a /(21j)< ca (B) and when co < a /(2fj) (C).

Several types of spin-lattice relaxation processes have been described in the literature [31]. Here a brief overview of some of the most important ones is given. The simplest spin-lattice process is the direct process in which a spin transition is accompanied by the creation or annihilation of a single phonon such that the electronic spin transition energy, A, is exchanged by the phonon energy, hcoq. Using the Debye model for the phonon spectrum, one finds for k T A that... 

In Equation (6) ge is the electronic g tensor, yn is the nuclear g factor (dimensionless), fln is the nuclear magneton in erg/G (or J/T), In is the nuclear spin angular momentum operator, An is the electron-nuclear hyperfine tensor in Hz, and Qn (non-zero for fn > 1) is the quadrupole interaction tensor in Hz. The first two terms in the Hamiltonian are the electron and nuclear Zeeman interactions, respectively the third term is the electron-nuclear hyperfine interaction and the last term is the nuclear quadrupole interaction. For the usual systems with an odd number of unpaired electrons, the transition moment is finite only for a magnetic dipole moment operator oriented perpendicular to the static magnetic field direction. In an ESR resonator in which the sample is placed, the microwave magnetic field must be therefore perpendicular to the external static magnetic field. The selection rules for the electron spin transitions are given in Equation (7)... 

One of the important possible mechanisms of MF action on biological systems is the influence of free radical production. Chemical studies predict that MFs may affect free radical reactions through the radical pair mechanism [201]. A reaction between two free radicals can generate a free radical pair in the triplet state with parallel electron spins. In this state free radicals cannot recombine. However, if one of the electrons overturns its spin, then free radicals can react with one another to form a diamagnetic product. Such electron spin transition may be induced by an alternative MF. 

A major effect of the introduction of static ZFS is that of reducing the amplitude of the cosic dispersion, because the energy of most electronic spin transitions increases and can be much larger than the Zeeman energy, and larger than so that for those transitions at all magnetic fields... 

Figure 10 Schematic representation of the electronic and electron spin transitions of polysilane and its radical ions.

Solid-state theories ascribe electron relaxation to the coupling of electronic spin transitions with transitions between lattice vibrational levels, or more generally with phonons. Disappearance (depopulation of a vibrational level) or creation (population of a vibrational level) of phonons modulate the orbital component of the electron magnetic moment. 

Powell et al. give an excellent review of several approaches to interpret the frequency dependence of Tle and T2e in these systems [71]. One convenient approach is that developed by Hudson and Lewis [72], who showed that the eigenvalues of the relaxation matrix R as defined in Bloch-Wangsness-Red-field (BWR) theory [73] are functions of rv and the experimental frequency co, and are related to the relaxation time T2ei of the i-th allowed electron spin transition by the expression ... 

If, however, the electron spin transition is saturated (this is shown by the wide arrows in Fig. 11.64A), then the populations of the electron spin-up and spin-down states are forced to become equal Nm N, and = N j. Under these conditions, the spin populations will depend only on the rate of... 

Figure 9.25. Zeeman splitting of the N = 1 and 2 rotational levels in the CN radical. In region 1 the rotational transition is electric dipole allowed and magnetically tunable. In region 3 the magnetically-tunable transitions are magnetic dipole electron spin transitions the electric dipole transitions are not magnetically tunable. Region 2 is intermediate between these limiting cases.

During the excited triplet state lifetime, hyperhne interactions between polarized electrons and neighboring (guest and host" ) nuclei permit polarization transfer via (a) mixing of states, (b) cross-relaxation or (c) applied electromagnetic helds (nearly) resonant with the electron-spin transitions, i.e., the the solid effect . The relative importance of these mechanisms depends on the system and the experimental conditions the distinctions can be a bit subtle, and merit some further discussion. 

These so-called transient nutations are observed if resonance between an electron spin transition and a coherent radiation field is suddenly achieved. The phenomenon can be understood when viewing the motion of the magnetization vector, M, in a... 

When the molecules of a solid esdiibit paramagnetism as a result of the presence of unpaired electron spins, transitions can be induced between spin states by applying a magMtic field and then supplying electromagnetic energy, usually in the microwave range of... 

Analyze for known reactions of chemical moiety Pyrolysis with chromatographic or mass spectrographic identification of fragments Energy of unpaired electron spin transitions, which depends on chemical environment Weight loss due to temperature-dependent decomposition and evaporation Mass of fragments reflects chemical composition Characteristic ions emitted from surface... 

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