Hyperfine coupling with metal nucleus

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.

As an example on the relationship between proton relaxivity, electron relaxation and coordination environment, we report the case of azurin and its mutants. The relaxivity of wild type azurin is very low (Fig. 6) due to a solvent-protected copper site, the closest water being found at a distance of more than 5 A from the copper ion. The fit, performed with the Florence NMRD program, able to take into account the presence of hyperfine coupling with the metal nucleus (Ay = 62 x 0 cm , see Section II.B) indicates Tie values of 8 X 10 s. Although the metal site in azurin is relatively inaccessible, several mutations of the copper ligands open it up to the solvent. The H NMRD profiles indicate the presence of water coordination for the... 

Fig. 5. Water NMRD profiles for solutions of superoxide dismutase at various temperatures (124). The solid lines are best-fit curves obtained with the inclusion of the effect of hyperfine coupling with the metal nucleus (27).

C) A = 0.016 cm , A = 0.005 cm and different angles (0 = 0, 30, 45, 60, 90°). The profile in bold shows the relaxation rate values calculated without including hyperfine coupling with the metal nucleus effects (Solomon profile). 

The electronic term which is the first term in the Hamiltonian written in Eq. (3.13) and used to derive the Solomon and Bloembergen equations (Eqs. (3.16), (3.17), (3.19), (3.20), (3.26), (3.27)) may be inappropriate in many cases, since the electron energy levels may be strongly affected by the presence of ZFS or hyperfine coupling with the metal nucleus. Therefore, the electron static Hamiltonian to be solved to find the cos values, i.e. all electron energy transitions, and their probabilities, will be, in general,... 

Figure 4 Diagram of the metrical parameters involved in a simple model for electron-point dipole—nuclear point-dipole hyperfine coupling, where the nucleus of interest is hydrogen. The paramagnetic metal center is indicated by M, with the hgand (e.g., a porphyrin) indicated by the dark horizontal line, X is a donor atom such as F, O, S, N, etc. Also shown is a second H, hydrogen-bonded to X, which can also be coupled to M (but with metrical parameters omitted for clarity)...

Once a description of the electronic structure has been obtained in these terms, it is possible to proceed with the evaluation of spectroscopic properties. Specifically, the hyperfine coupling constants for oligonuclear systems can be calculated through spin projection of site-specific expectation values. A full derivation of the method has been reported recently (105) and a general outline will only be presented here. For the calculation of the hyperfine coupling constants, the total system of IV transition metal centers is viewed as composed of IV subsystems, each of which is assumed to have definite properties. Here the isotropic hyperfine is considered, but similar considerations apply for the anisotropic hyperfine coupling constants. For the nucleus in subsystem A, it can be... 

The separation (A) of the hyperfine lines in the ESR spectra of metal-amine, and metal-ether solutions represents a direct measure of the average s-electron (spin) density of the unpaired electron at the particular metal nucleus (12,156). When this splitting is compared to that of the free (gas-phase) atom, we obtain a measure of the "percent atomic character of the paramagnetic species. The percent atomic character in all these fluid systems increases markedly with temperature, and under certain circumstances the paramagnetic species almost takes on "atomic characteristics (43, 53, 160). Figure 9 shows the experimental data for fluid solutions of K, Rb, and Cs in various amines and ethers, and also for frozen solutions (solid data points) of these metals in HMPA (17). The fluid solution spectra have coupling con-... 

Several authors have measured the copper and cobalt hyperfine interaction constants, A and B (Table VI), arising from coupling between the electronic spin and the nuclear spin of the central metal ion. Four lines are seen in the case of copper phthalocyanine due to interaction between the electron and the nuclear spin of Cu83 (I = ) single crystals of cobalt phthalocyanine diluted in zinc phthalocyanine gave eight components due to interaction with the nucleus of Co69 (I = ) (167). 

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