Hyperfine coupling tensor metal

The Florence NMRD program (8) (available at www.postgenomicnmr.net) has been developed to calculate the paramagnetic enhancement to the NMRD profiles due to contact and dipolar nuclear relaxation rate in the slow rotation limit (see Section V.B of Chapter 2). It includes the hyperfine coupling of any rhombicity between electron-spin and metal nuclear-spin, for any metal-nucleus spin quantum number, any electron-spin quantum number and any g tensor anisotropy. In case measurements are available at several temperatures, it includes the possibility to consider an Arrhenius relationship for the electron relaxation time, if the latter is field independent. 

Fig. 4. Effect of (A) axial zero field splitting for the spin systems S = 1,3/2,2, and 5/2 (with Bo applied along the z direction of the ZFS tensor), and (B) isotropic hyperfine coupling with the metal nucleus for systems with I = 1/2, S = 1/2 and I = 3/2, S = 1/2.

In general, fluctuations in any electron Hamiltonian terms, due to Brownian motions, can induce relaxation. Fluctuations of anisotropic g, ZFS, or anisotropic A tensors may provide relaxation mechanisms. The g tensor is in fact introduced to describe the interaction energy between the magnetic field and the electron spin, in the presence of spin orbit coupling, which also causes static ZFS in S > 1/2 systems. The A tensor describes the hyperfine coupling of the unpaired electron(s) with the metal nuclear-spin. Stochastic fluctuations can arise from molecular reorientation (with correlation time Tji) and/or from molecular distortions, e.g., due to collisions (with correlation time t ) (18), the latter mechanism being usually dominant. The electron relaxation time is obtained (15) as a function of the squared anisotropies of the tensors and of the correlation time, with a field dependence due to the term x /(l + x ). 

Complexes in which the spin rbit coupling gives rise to anisotropy in the hyperfine coupling to the metal nucleus and in the g tensors. 

The isotropic and anisotropic hyperfine coupling terms in a arise from interactions between electron and nuclear spins, and provide information about the nature of the orbital containing the unpaired electron and the extent to which it overlaps with orbitals on adjacent atoms. The anisotropic term can cause similar difficulties to the g tensor anisotropy in analysing spectra of polycrystalline powders extracting coupling constants from spectra of transition metal ions or radicals in zeolites can be difficult or impossible without computer simulation. 

The EPR spectrum of this species reveals an axial g tensor with g values indicative of a metal centered radical (gj = gy = 2.15, g = 1.96, no resolved hyperfine couplings). 

Anisotropic g- and A-tensors, negligible b When the nuclear Zeeman energy is small compared to the hyperfine coupling as is usually the case for transition metal ions, the spectrum is independent of microwave frequency. The hyperfine coupling K depends on the crystal orientation according to the equation (4.11) ... 

Bryce and Autschbach performed the accurate calculation of the isotropic and anisotropic (AT) parts of indirect nuclear spin spin coupling tensors for diatomic alkali metal halides (MX M = Li, Na, K, Rb, Cs X = F, Cl, Br, I) with the relativistic hybrid DFT approach. The calculated coupling tensor components were compared with experimental values obtained from molecular-beam measurements on diatomic molecules in the gas phase. Molecular-beam experiments offer ideal data for testing the success of computational approaches, since the data are essentially free from intermolecular effects. The hyperfine Hamiltonian used in analyzing molecular-beam data contains Hc IkDIi and //C4/a /l terms. The relationships between the parameters C3 and C4, used in molecular-beam experiments, and Rdd, A/, and used in NMR spectroscopy, are summarized in the following equations ... 

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