Nuclear hyperfine interaction parameters

Nuclear hyperfine interaction parameters for the lanthanide metals in degrees Kelvin. (Conversion factor - 1 MHz = 0.047994 mK) Note The signs are given for those cases only where the sign can be unambiguously determined. 

Even at 4 K the nuclear contribution dominates the heat capacity of holmium by about 85%. Thus Krusius et al. (1969) in measurements below 0.6 K were essentially looking at Cn only, and obtained the hyperfine interaction parameters given in table 5.2. These parameters agree fairly well with those of van Kempen et al. (1964), whose Cn results showed considerably more scatter, although Krusius et al. (1969) felt that the fit to their own results was not as good as for the other lanthanides they have measured. The results of NMR (Mackenzie et al. 1974) give slightly lower parameter values. 

Advanced EMR methods may be used to conduct quantitative measurements of nuclear hyperfine interaction energies, and these data, in turn, may be used as a tool in molecular design because of their direct relation to the frontier orbitals. The Zeeman field dependence of hyperfine spectra enables one to greatly improve the quantitative analysis of hyperfine interaction and assign numeric values to the parametric terms of the spin Hamiltonian. Graphical methods of analysis have been demonstrated that reduce the associated error that comes from a multi-parameter fit of simulations based on an assumed model. The narrow lines inherent to ENDOR and ESEEM enable precise measures of peak position and high-resolution hyperfine analyses on even powder sample materials. In particular, ESEEM can be used to obtain very narrow lines that are distributed at very nearly the zero-field NQI transition frequencies because of a quantum beating process that is associated with... 

Finally, quantitative analytical techniques draw their reliability from correlation to other proven methods, and quantitative EMR measures of hyperfine parameters must likewise be subjected to a form of quality assurance so that their applicability to chemical reactivity may be proven. Nuclear quadrupole interaction parameters e2Qq zz and rj are recognized as powerful tools in the chemist s investigation of frontier orbital interactions. The electric field gradient, for example, reflects the hybridization, polarization, and bond order effects and will therefore vary as the covalent bonds are distorted, such as occurs when vibrational modes are excited. NQI parameters that are obtained by ESEEM or ENDOR may be refined by examining their temperature dependence (i.e., the Baeyer effect, 1951 observed by... 

By the observation of quantum beat Q, one can determine the details on the nuclear levels, from which the hyperfine interaction parameters are evaluated precisely. 

The importance of accurate estimates for the cfi parameters is twofold. As discussed above, the cfi affects the electron spin relaxation, and flius contributes to the relaxivity of MRI contrast agents. Second, flic cfi affects the direction of the electron spin quantization axis, which leads to certain effects in nuclear transition spectra (e.g., electron-nuclear double resonance, ENDOR) that are necessary to take into account in order to accurately determine the electron-nuclear hyperfine interaction ihfi) and the distance from the Gd(III) ion to the ligand protons. 

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)]. 

The Mu spin Hamiltonian, with the exception of the nuclear terms, was first determined by Patterson et al. (1978). They found that a small muon hyperfine interaction axially symmetric about a (111) crystalline axis (see Table I for parameters) could explain both the field and orientation dependence of the precessional frequencies. Later /xSR measurements confirmed that the electron g-tensor is almost isotropic and close to that of a free electron (Blazey et al., 1986 Patterson, 1988). One of the difficulties in interpreting the early /xSR spectra on Mu had been that even in high field there can be up to eight frequencies, corresponding to the two possible values of Ms for each of the four inequivalent (111) axes. It is only when the external field is applied along a high symmetry direction that some of the centers are equivalent, thus reducing the number of frequencies. 

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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