G-factor hyperfine

The quantitative theory of CIDNP [93-96] is developed to a state where the intensity ratios of CIDNP spectra can be computed on the basis of reaction and relaxation rates and the characteristic parameters of the radical pair (initial spin multiplicity, p) the individual radicals (electron g factors, hyperfine coupling constants, a) and the products (spin-spin coupling constants, J). On the other hand, the patterns of signal directions and intensities observed for different nuclei of a reaction product can be interpreted in terms of the hyperfine coupling constants of the same nuclei in the radical cation intermediate. 

The EPR spectrum of the intrinsic STH was also recorded by ODMR in studies of nominally pure AgCl [171,172] and was later identified [173-175]. The self-trapped hole and shallowly trapped electron undergo donor-acceptor pair recombination which contributes to a blue-green (500 nm) luminescence from AgCl [69]. The species observed in the ODMR spectrum has g-factors, hyperfine, and superhyperfine matrices that are identical, within experimental error, to those observed earlier by EPR methods [68]. 

Software for this purpose is often developed in laboratories specialized in single crystal measurements, but the programs are not always available. The computer programs listed in Table 3.4 that the authors are aware of contain several steps, (1) to provide the experimental data (g-factors, hyperfine couplings, zero-field splittings, ENDOR or ESEEM frequencies) as function of crystal orientation, (2) to perform a least squares fitting of a theoretical model to the data, and (3) to make an error analysis of the parameter values, i.e. the principal values and direction cosines of the principal axes of the coupling tensors. 

Electronic g Factor. Hyperfine (hf) Coupling Constants Experimental Results... 

Yb " ) in tetragonal RASO4 (R is usually Y) have been carried out. The g-factors, hyperfine constants, magnetic interaction, symmetry parameters, and pair interactions of R ions were determined in these studies (Schowalter, 1971 Kalbfleisch, 1972 Hillmer et al., 1972 Schwab, 1975 Schwab and Hillmer, 1975 Mehran et al., 1979). 

Electron spin resonance is abbreviated as ESR. Radicals, e.g., Pb(CH3)3 , are characterized by their g-factors hyperfine splittings a are given in G values. 

Apart from the already mentioned (Sect. 7.6.1) determination of the nuclear g-factors of W through Mossbauer measurements with tungsten diluted in an iron foil [225, 229] where a hyperfine field at the W site of 70.8 2.5 T was... 

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)... 

Here, /3 and / are constants known as the Bohr magneton and nuclear magneton, respectively g and gn are the electron and nuclear g factors a is the hyperfine coupling constant H is the external magnetic field while I and S are the nuclear and electron spin operators. The electronic g factor and the hyperfine constant are actually tensors, but for the hydrogen atom they may be treated, to a good approximation, as scalar quantities. 

For the hydrogen atom, two such resonance conditions occur, giving rise to two lines separated by 506 G, which is just the value of a for the hydrogen atom [Eq. (ID)]. The spectrum would look the same for a single crystal or for a polycrystalline sample because the g factor and the hyperfine constant are isotropic. 

At either frequency the sensitivity of the instrument is quite remarkable. The exact signal-to-noise ratio depends upon a number of factors including apparent line width (including g and hyperfine anisotropy), ease of saturation, the temperature, and the linear density of the sample in the quartz tube. For a relatively narrow line with peak-to-peak separation of two gauss it is possible to observe the spectrum for concentrations as low as 1014 spins per gram of sample. As the spectrum becomes more anisotropic, the sensitivity of course decreases. Lowering the temperature increases the sensitivity since the population difference An increases [(Eqs. (26) and (3°)]. 

The spin Hamiltonian for the hydrogen atom will be used to determine the energy levels in the presence of an external magnetic field. As indicated in Section II.A, the treatment may be simplified if it is recognized that the g factor and the hyperfine constant are essentially scalar quantities in this particular example. An additional simplification results if the z direction is defined as the direction of the magnetic field. For this case H = Hz and Hx = Hv = 0 hence,... 

EPR spectroscopy is the most important method for determining the structures of transient radicals. Information obtained from the EPR spectra of organic radicals in solution are (i) the centre position of the spectra associated with g factors, (ii) the number and spacing of the spectral lines related to hyperfine splitting (hfs) constants, (iii) the total absorption intensity which corresponds to the radical concentration, and (iv) the line widths which can offer kinetic information such as rotational or conformational barriers. The basic principles as well as extensive treatments of EPR spectroscopy have been described in a number of books and reviews and the reader is referred to this literature for a general discussion [28 30]. 

In general the NMRD profiles are affected also by other parameters characterizing the electron spin system such as the g -factor, the hyperfine coupling with the metal nuclear spin (for I > 1/2 systems) and the ZFS (for S > 1/2 systems). 

Table II I4I, 149-162) consists of a summary of 9-factors, D values and hyperfine coupling constants observed for ions of the first transition series. A molecular orbital (MO) treatment of the metal ion and ligand orbitals has been discussed by Stevens 163) and Owen 164) to account for covalent bonding and resulting hyperfine structure from hgands of transition element ions. Expressions derived for g-factors and hyperfine coupling constants from a MO treatment allow an estimation of the amount of charge transfer of metal electrons to ligand orbitals. Owen 164) has given a MO treatment of Cr +, Ni++ and Cu++ assuming no t bonding.

The calculation of magnetic parameters such as the hyperfine coupling constants and g-factors for oligonuclear clusters is of fundamental importance as a tool for the evaluation of spectroscopic data from EPR and ENDOR experiments. The hyperfine interaction is experimentally interpreted with the spin Hamiltonian (SH) H = S - A-1, where S is the fictitious, electron spin operator related to the ground state of the cluster, A is the hyperfine tensor, and I is the nuclear spin operator. Consequently, it is... 

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