Hyperfine Couplings hfc

To first order the hyperfine couplings (hfc) are directly obtained from the corresponding splitting between the lines. The splitting is in general independent of the microwave frequency. Multi-frequency measurements are therefore useful for distinguishing features due to anisotropic g-factors and hfc (Section 4.2.2). Differences in the hyperfine stmcture of spectra obtained at different frequencies can, however, occur in two cases  

The first effect may be eliminated experimentally by measurements at a higher frequency band. It is also relatively easy at least in the case of axial symmetry to evaluate the couplings from the measured splitting obtained at a lower frequency by applying the higher order corrections exemplified in Chapter 3 and Chapter 5. The second effect is more important in applied studies. 

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It is well-known that the hyperfine interaction for a given nucleus A consists of three contributions (a) the isotropic Fermi contact term, (b) the spin-dipolar interaction, and (c) the spin-orbit correction. One finds for the three parts of the magnetic hyperfine coupling (HFC), the following expressions [3, 9] ... 

If inhomogeneous broadening of the EPR linewidth is primarily due to unresolved hyperfine couplings (hfc), at higher frequencies the g-an iso (ropy will dominate over the hyperfine interactions, i.e., the condition (Ag/gIS0H0) > AHhk must be fulfilled. 

In the anion-radicals of nitro compounds, an unpaired electron is localized on the nitro group and this localization depends on the nature of the core molecule bearing this nitro substituent. The value of the hyperfine coupling (HFC) constant in the electron-spin resonance (ESR) spectrum reflects the extent of localization of the unpaired electron values of several nitro compounds are given in Table 1.1. 

Electron spin resonance spectra of ion radicals reveal a quantitative distribution of the spin density. The ESR spectrum determines the hyperfine coupling (HFC) constant for the ith... 

As a second point of the comparison, the selectivity factors mentioned are in accord with values of hyperfine coupling (HFC) constants in ESR spectra of the corresponding cation radicals. Thus, for the cation radical of 1,2,3,5-tetramethylbenzene, the HFC constant = 0.3 mT, whereas a V-Mc = 1.7 mT (Dessau et al. 1970). For the p-methy-lanisole cation radical, a= 0.02 mT and aMe = 1.5 mT for the anisole cation radical,... 

HMO) formalism, because its singly occupied molecular orbital (SOMO) is constrained by symmetry to be on those atoms. More sophisticated molecular orbital analysis finds not only equal, positive spin densities on the end carbons but also a small negative 7T-spin density on the central carbon due to spin polarization. At the UB3LYP/6-31G level, the spin density p ) - p(C3) = +0.700, mostly from 7T-spin contributions, and p(C2) = -0.275.27 The experimental numbers estimated for TT-spin density (not overall spin density) are p(C ) = p(C3) = +0.582 and p(C2) = -0.164 from electron paramagnetic resonance (EPR) studies of 13C hyperfine coupling (hfc).28... 

Aminium radical cations and aminoalkyl radicals have substantially different spin density distributions and, therefore, substantially different hyperfine coupling (hfc) patterns. Aminium radical cations have appreciable proton hfcs only in the position adjacent to the nitrogen center whereas the neutral aminoalkyl radicals have sizable hfcs in both the a- and (3-positions. CIDNP effects induced in these species are expected to reflect these differences. 

Group 3 (Sc, Y, La) metallofullerenes exhibit ESR hfs, which provides us with important information on the electronic structures of the metallofullerenes. Typical ESR-active monometallofullerenes are La Cs2, Y Cs2, and Sc C82- The ESR hfs of a metallofullerene was first observed in La Cs2 by the IBM Almaden group (Johnson et al., 1992) (Eigure 15) and was discussed within the framework of an intrafullerene electron transfer. The observation of eight equally spaced lines provides evidence of isotropic electron-nuclear hyperfine coupling (hfc) to La with a nuclear spin quantum number I = 7/2. The observed electron g-value of 2.0010, close to that measured for the Ceo radical anion (Allemand et al., 1991 Krusic et al., 1991), indicates that a single unpaired electron resides in the LUMO of the carbon cage. They also observed hyperfine... 

Here, the spin-spin interaction between an electron spin and a nuclear spin can be represented by the isotropic term (AS I ) when the radical rotates very fast in solution. This term is called the hyperfine coupling (HFC) and the coefficient (A) the (isotropic) HFC constant. When it is fixed in a crystal or solid matrix, however, the interaction becomes anisotropic, but the latter case is not considered in this section. 

M. From Eqs (3-11) and (3-13), the S-T conversion of radical pars was found to be influenced by the following terms (a) the Zeeman term which is characterized by AgjUgB, (b) the hyperfine coupling (HFC) terms which are characterized by i4, and At, and (c) the exchange term which is characterized by J. Thus, the MFEs on chemical reactions through radical pairs can be classified by the following typical mechanisms ... 

In contrast to the HOMO and LUMO, the singly occupied molecular orbital (SOMO) can be correlated both qualitatively and quantitatively with experimentally measurable EPR hyperfine couplings (hfcs). As a result, host-guest systems that have redox-active guests that are stable as radicals provide excellent tools for studying the effects of noncovalent interactions on redox properties. 

Next, we outline the derivations of Fernandez et al. [53] and the generalization for DFT. The hyperfine coupling (HFC) Hamiltonian is scaled with a perturbation strength parameter x equation such that the total energy and the wave function parameters are functions of x... 

There are three mechanisms of spin Hipping solvent-induced spin relaxation (spin-lattice relaxation), SOC, and hyperfine coupling (HFC) (see also Chapter 3). Although the first of these mechanisms is quite slow in the absence of paramagnetic impurities, HFC is important in biradicals in which the two radical centers are relatively far apart (1,6-biradicals and longer), and SOC dominates in short biradicals, which are observed in numerous photochemical reactions. For these systems, the order of magnitude of SOC is about 0.1 to 5 cm, which is much larger than that of the typical HFC, which is about 0.0001 cm We will therefore concentrate on the SOC mechanism only. 

The possible contribution of electron-nuclear hyperfine coupling (HFC) as a mechanism for intersystem crossing between TT encounter pairs of different multiplicity was strongly suggested by recent resonance-Raman-spectroscopic determinations of k2 = 5.3 X 10 Af s and 2.1 X 10 s (Eq. 67)... 

In the case of exchange-coupled dimeric complexes, the projection factors for the isotropic hyperfine coupling (HFC) terms are given as follows [26, 27] ... 

Abstract Multi-resonance involves ENDOR, TRIPLE and ELDOR in continuous-wave (CW) and pulsed modes. ENDOR is mainly used to increase the spectral resolution of weak hyperfine couplings (hfc). TRIPLE provides a method to determine the signs of the hfc. The ELDOR method uses two microwave (MW) frequencies to obtain distances between specific spin-labeled sites in pulsed experiments, PELDOR or DEER. The electron-spin-echo (ESE) technique involves radiation with two or more MW pulses. The electron-spin-echo-envelope-modulation (ESEEM) method is particularly used to resolve weak anisotropic hfc in disordered solids. HYSCORE (Hyperfine Sublevel Correlation Spectroscopy) is the most common two-dimensional ESEEM method to measure weak hfc after Fourier transformation of the echo decay signal. The ESEEM and HYSCORE methods are not applicable to liquid samples, in which case the FID (free induction decay) method finds some use. Pulsed ESR is also used to measure magnetic relaxation in a more direct way than with CW ESR. 

First order spectra First order spectra are obtained when the microwave energy hv D (the zero field splitting, for 5 > 1) or /iv a (the hyperfine coupling, hfc, for I 0). The zero-field or hyperfine couplings can be read directly from the spectra and the g-factor can be measured at the centre of the spectrum. 

In addition to the spatial structure of the reaction center (RC) of Rhodopseudomonas (Rps.) viridis obtained from X-ray crystallography (1) a knowledge of the electronic structure is required for a basic understanding of the functional details of the RC. This can be obtained for the radical ions formed in the charge separation process by EPR and ENDOR techniques (2) which yield electron-nuclear hyperfine couplings (hfc s). From the hfc s a map of the valence electron spin distribution over the molecule is obtained. In this work we studied the intermediate electron acceptor radical anion I", a monomeric bacteriopheophytin (BPh) b (3)> Fig. 1,that was trapped at low temperature (77 K) in the RC ( ). EPR and ENDOR results on I" had been reported earlier (5). Improved instrumental design enabled us to measure additional hfc s with higher accuracy. 

The observed interval of the g-factor values at various a is characteristic of ARs. Therefore, in analyzing ESR spectra, the anisotropic magnetic parameters determined for low-molecular ARs were used [47]. It is commonly recognised for low-molecular ARs that the z axis is aligned with the 2p-orbital of the unpaired electron of the N atom, and that this direction determines the maximum value of the A -tensor and g-tensor value close to that for free electrons. The x axis is aligned with the N-O bond characterised by the maximum value of the g-tensor (2.0088-2.0104) and small (0.5-0.7 mT) A valne. The y axis determines a g-tensor value of 2.006-2.007, and the hyperfine coupling (HFC)-tensor value approximately corresponds to [55]. 

The rates of the electron transfer processes in reaction centers (RC s) of photosynthetic bacteria are controlled both by the spatial and the electronic structure of the involved donor and acceptor molecules. The spatial structure of bacterial RC s has been determined by X-ray diffraction for Rhodopseudomonas (Rp.) viridis and for Rhodobacter (Rb.) sphaeroides,- The electronic structure of the transient radical species formed in the charge separation process can be elucidated by EPR and ENDOR techniques. The information is contained in the electron-nuclear hyperfine couplings (hfc s) which, after assignment to specific nuclei, yield a detailed picture of the valence electron spin density distribution in the respective molecules. 

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