Zeeman interaction analysis

An exception to this rule arises in the ESR spectra of radicals with small hyperfine parameters in solids. In that case the interplay between the Zeeman and anisotropic hyperfine interaction may give rise to satellite peaks for some radical orientations (S. M. Blinder, J. Chem. Phys., 1960, 33, 748 H. Sternlicht,./. Chem. Phys., 1960, 33, 1128). Such effects have been observed in organic free radicals (H. M. McConnell, C. Heller, T. Cole and R. W. Fessenden, J. Am. Chem. Soc., 1959, 82, 766) but are assumed to be negligible for the analysis of powder spectra (see Chapter 4) where A is often large or the resolution is insufficient to reveal subtle spectral features. The nuclear Zeeman interaction does, however, play a central role in electron-nuclear double resonance experiments and related methods [Appendix 2 and Section 2.6 (Chapter 2)]. 

Prior to an effective Hamiltonian analysis it is, in order to get this converging to the lowest orders, typical to remove the dominant rf irradiation from the description by transforming the internal Hamiltonian into the interaction frame of the rf irradiation. This procedure is well established and also used in the most simple description of NMR experiments by transforming the Hamiltonian into the rotating frame of the Zeeman interaction (the so-called Zeeman interaction frame). In the Zeeman interaction frame the time-modulations of the rf terms are removed and the internal Hamiltonian is truncated to form the secular high-field approximated Hamiltonian - all facilitating solution of the Liouville-von-Neumann equation in (1) and (2). The transformation into the rf interaction frame is given by... 

There remain two other important magnetic interactions involving the nuclear spin magnetic moments, which cannot be derived from the present analysis, although their presence is reasonably self evident by analogy with corresponding electron spin terms which we have derived earlier. They are the nuclear Zeeman interaction,... 

They appeared as the first two terms in the analysis of the Zeeman interaction for3 NH (see equation (9.135)). 

It is desirable to apply fields of strong enough amplitude so that dominates all other interaction Hamiltonians except for the Zeeman interaction. The rf pulses can then be treated as infinitely short delta pulses, and the analysis of the experimental spectra becomes comparatively simple. However, arcing in the probe limits useful amplitudes to the order of 200 kHz, so that in solid-state NMR the delta-pulse approximation must be treated with care for the dipole-dipole interaction among protons, and it breaks down for the quadrupole interaction. 

ENDOR measurements of nuclear quadrupole coupling tensors of I > Vi nuclei A slightly lengthier analysis is required in the presence of nuclear quadrupole interactions, (nqi), from I > V2 nuclei. When the hyperfine and nuclear Zeeman interactions dominate over that caused by the nqi a simple method involves separate measurements of the parameters, G+ and P+ and/or G and P for ms = Vi of a free radical, as illustrated with the energy diagram in Fig. 3.11 for / = 1. 

The analysis of the solid-state NMR spectra of polymers begins with an examination of the heteronuclear dipolar coupling. The heteronuclear dipolar coupling arises from an interaction between the nuclear magnetic moments of two different nuclear spins. (By convention, nuclear spins are labeled as I for abundant spins, for example, that of the proton, and S for rare spins such as that of C or N nuclei.) In an external magnetic field, the Zeeman interaction describes the energy of the spin I based on its orientation, either parallel (spin up, t) or antiparallel (spin... 

All foregoing studies were performed at X-band microwave frequencies. B. Hoffman and coworkers showed, however, in a number of studies on chloroperoxi-dase and P450cam that a combination of cw-, Davies- and Mims-ENDOR experiments at Q-band (35 GHz) can largely facilitate the analysis of low-spin ferric heme proteins [31,32]. Indeed, due to the magnetic-field dependence of the nuclear Zeeman interaction, the spectral contributions stemming from N, N, H, H, and... 

In the spin-correlated RP the two radicals interact via electron-electron dipolar and exchange interaction which leads to line splitting. The ET process creates the RP in a strongly spin-polarized state with a characteristic intensity pattern of the lines that occur either in enhanced absorption (A) or emission (E).144 145 The spectrum is therefore very intense and can directly be observed with cw EPR (transient EPR) or by pulse methods (field-swept ESE).14 To study the RPs high field EPR with its increased Zeeman resolution proved to be very useful the first experiment on an RP was performed by Prisner et al. in 1995146. From the analysis of the RP structure detailed information about the relative orientation of the two radicals can be extracted from the interaction parameters. In addition kinetic information about the formation and decay of the RP and the polarization are available (see references 145,147). 

Our purpose in this analysis is to show how the observed spectrum arises, but we again point out that this is a simple matter if one knows the values of the molecular constants involved. In practice one has the much more difficult but interesting task of determining the constants from the observed Zeeman pattern. We have described this particular system in some detail because it illustrates a number of the features which we shall encounter later. It is not often that one observes a fully resolved hyperfine pattern from two different nuclei, with both magnetic and electric interactions present. 

The most straightforward way to understand the origin of ESEEM and the physical chemistry behind its detection and analysis is to step back ft om this Cu(II) center and focns on an 5 = 1 /2, 7 = 1/2 coupled spin system. The spin Hamiltonian for this system consists of electronic Zeeman, nuclear Zeeman, and electron-nnclear hyperfine interaction terms. For the case of an isotropic electron -matrix and an axial hyperfine interaction, this Hamiltonian can be conveniently written in the laboratory reference Ifame,... 

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