Hyperfine interactions isotropic analysis

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,... 

Thus, as a consequence of the selection of orientation subsets by choice of field value, the ENDOR spectrum changes as a function of the external field position or g value at which it is measured. A series of ENDOR spectra collected at fields across the EPR envelope samples different sets of molecular orientations. An example of this is shown in Fig. 6B. It can be seen that at the extreme g values (g, and g ) the ENDOR spectrum is the least complex, whereas at intervening g values the ENDOR spectrum shows multiple frequencies. The analysis of such spectra taken at several magnetic field positions gives the full tensor of the hyperfine interaction A, from which the isotropic and anisotropic components can be deduced. Procedures for this analysis have been described in detail elsewhere. 

To extract detailed hyperfine information from an ESE spectrum, however, it is necessary to calculate the expected modulation pattern for a certain assumed nuclear geometry. By varying the assumed hyperfine interaction for a simulated modulation pattern until it fits the observed modulation pattern, the weak hyperfine parameters may be determined. The general analysis procedure is to analyze the ESE spectrum in terms of a number of equivalent nuclei located at an average distance from the paramagnetic center. The assumption is then that there is a small overlap of the unpaired electron wave function on the closest nuclei to give an isotropic hyperfine coupling constant... 

Isotropic Hyperfine Analysis. The special case of isotropic g and hyperfine interaction will now be considered. This simplification is valid when the anisotropic interactions are averaged by rapid tumbling The quadrupole interaction will be omitted because it is purely anisotropic. The resulting simplified spin Hamiltonian is given in equation 5. 

The impurity interacts with the band structure of the host crystal, modifying it, and often introducing new levels. An analysis of the band structure provides information about the electronic states of the system. Charge densities, and spin densities in the case of spin-polarized calculations, provide additional insight into the electronic structure of the defect, bonding mechansims, the degree of localization, etc. Spin densities also provide a direct link with quantities measured in EPR or pSR, which probe the interaction between electronic wavefunctions and nuclear spins. First-principles spin-density-functional calculations have recently been shown to yield reliable values for isotropic and anisotropic hyperfine parameters for hydrogen or muonium in Si (Van de Walle, 1990) results will be discussed in Section IV.2. 

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