Electric hyperfine coupling

The leading term in T nuc is usually the magnetic hyperfine coupling IAS which connects the electron spin S and the nuclear spin 1. It is parameterized by the hyperfine coupling tensor A. The /-dependent nuclear Zeeman interaction and the electric quadrupole interaction are included as 2nd and 3rd terms. Their detailed description for Fe is provided in Sects. 4.3 and 4.4. The total spin Hamiltonian for electronic and nuclear spin variables is then ... 

We have also performed the calculation of hyperfine coupling constants the electric quadrupole constant B and magnetic dipole constant A, with inclusion of nuclear finiteness and the Uehling potential for Li-like ions. Analogous calculations of the constant A for ns states of hydrogen-, lithium- and sodiumlike ions were made in refs [11, 22]. In those papers other bases were used for the relativistic orbitals, another model was adopted for the charge distribution in the nuclei, and another method of numerical calculation was used for the Uehling potential. 

Extension of these edge studies (21) to the blue copper site in plastocyanin indicates that there is less than 1% p orbital mixing into d 2 2 and in particular that this involves the p and p orbitals. The Is to 3d 2 2 transition at 8979 eV occurs only wheX the polarization vector of the synchrotron radiation is in the xy plane. This can be seen from the Is to 3d transition reproduced in Figure 15 which appears only with the electric vector perpendicular to the Cu-methionine bond. As emphasized above, this p, p mixing cannot account for the small copper hyperfine coupling constant of... 

The most important examples of 2S states to be described in this book are CO+, where there is no nuclear hyperfine coupling in the main isotopomer, CN, which has 14N hyperfine interaction, and the Hj ion. A number of different 3E states are described, with and without hyperfine coupling. A particularly important and interesting example is N2 in its A 3ZU excited state, studied by De Santis, Lurio, Miller and Freund [19] using molecular beam magnetic resonance. The details are described in chapter 8 the only aspect to be mentioned here is that in a homonuclear molecule like N2, the individual nuclear spins (1 = 1 for 14N) are coupled to form a total spin, It, which in this case takes the values 2, 1 and 0. The hyperfine Hamiltonian terms are then written in terms of the appropriate value of h As we have already mentioned, the presence of one or more quadrupolar nuclei will give rise to electric quadrupole hyperfine interaction the theory is essentially the same as that already presented for1 + states. 

The CN radical in its 21 ground state shows fine and hyperfine structure of the rotational levels which is more conventional than that of CO+, in that the largest interaction is the electron spin rotation coupling../ is once more a good quantum number, and the effective Hamiltonian is that given in equation (10.45), with the addition of the nuclear electric quadrupole term given in chapter 9. The matrix elements in the conventional hyperfine-coupled case (b) basis set were derived in detail in chapter 9,... 

The theory of the magnetic hyperfine interactions in NCI is essentially the same as that already described for the PF radical in the previous section, except that the nuclear spins / are 1 for 14N and 3/2 for 35C1. The form of the effective Hamiltonian for the quadrupole interaction and its matrix elements for two different quadrupolar nuclei was described in some detail in chapter 8 when we discussed the electric resonance spectra of CsF and LiBr. We now use the same case (b) hyperfine-coupled basis set as was used for PF. The quadrupole Hamiltonian for the two nuclei can be written as the sum of two independent terms as follows ... 

The axial component of the total magnetic hyperfine interaction, A 3/2, in the 2n3/2 component is equal to a+ (b + c)/2, where a, b and c are the Frosch and Foley [192] constants. In the 2n1/2 component the axial hyperfine constant, h /2, is equal to a — (b + c)/2. Since both fine-structure components can usually be studied by pure microwave experiments, a partial separation of the magnetic hyperfine constants can be achieved. The electric quadrupole coupling constant, eq0 Q, is obtained for both isotopes. 

The most interesting hyperfine interaction in the three molecules is that of55 Mn in the MnO molecule, illustrated in figure 10.91. The Frosch and Foley [192] hyperfine constants and the electric quadrupole coupling constant are found to have the following values (in MHz) ... 

As we have shown in Appendix 8.5, and elsewhere, to is the axial component of the dipolar interaction obtained from the fourth term in equation (11.2). The large value of the Fermi contact constant is consistent with a model in which the unpaired electron occupies a a-type molecular orbital which has 45% N atom, v character. Radford produced convincing arguments to show that the model is also consistent with the small dipolar hyperfine constant, and also the electric quadrupole coupling constant. 

Results for dipole moments are shown in Table 29. ° Clearly, coupled with good basis sets, correlated methods can do quite well for this property. Elsewhere, we have used relaxed density-based CC and MBPT methods to study spin densities and the related hyperfine coupling constants to evaluate relativistic corrections (Darwin and mass-velocity term) when impor-tant and to evaluate highly accurate electric field gradients to extract nuclear quadruple moments. 

Hyperfine coupling con- Relate to electric field q depends on the detailed... 

Kim] Kimball, C.W., Phillips, W.C., Nevitt, M.V., Preston, R.S., Magnetic Hyperfine Interactions and Electric Quadrupolar Coupling in Alloys of Iron with the a-Manganese Stracture , Phys. Rev., 146(2), 375-378 (1966) (Crys. Structure, Experimental, Magn. Prop., 18)... 

The electric field gradients at P and H, the anisotropic (dipolar) magnetic hyperfine coupling... 

Electric quadrupole coupling constants, nuciear-spin rotation coupling constants, tensor and scalar nuclear spin-spin coupling constants, Fermi contact and anisotropic hyperfine parameters, magnetic nuclear-orbital coupling constants... 

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