Hyperfine coupling quadrupole interaction

Fig. 19. X-band Mims ENDOR spectrum showing resolved deuteron hyperfine couplings in nitrile hydratase. Solid trace represents sample in buffer, and dashed trace is sample in HjO buffer. The patterns are centered at the Larmor frequency of 1.97 MHz (vertical bar) and show first-order splittings from both the hyperfine and quadrupole interactions. Conditions 3000 G, 9.4 GHz, 16 nsec pulse lengths, t = 376 nsec, rf pulse length 60 /isec, repetition rate 5 Hz, temperature 2 K. (Adapted from Jin et al. )...

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 ... 

In summary, NMR techniques based upon chemical shifts and dipolar or scalar couplings of spin-1/2 nuclei can provide structural information about bonding environments in semiconductor alloys, and more specifically the extent to which substitutions are completely random, partially or fully-ordered, or even bimodal. Semiconductor alloys containing magnetic ions, typically transition metal ions, have also been studied by spin-1/2 NMR here the often-large frequency shifts are due to the electron hyperfine interaction, and so examples of such studies will be discussed in Sect. 3.5. For alloys containing only quadrupolar nuclei as NMR probes, such as many of the III-V compounds, the nuclear quadrupole interaction will play an important and often dominant role, and can be used to investigate alloy disorder (Sect. 3.8). 

ESEEM is a pulsed EPR technique which is complementary to both conventional EPR and ENDOR spectroscopy(74.75). In the ESEEM experiment, one selects a field (effective g value) in the EPR spectrum and through a sequence of microwave pulses generates a spin echo whose intensity is monitored as a function of the delay time between the pulses. This resulting echo envelope decay pattern is amplitude modulated due to the magnetic interaction of nuclear spins that are coupled to the electron spin. Cosine Fourier transformation of this envelope yields an ENDOR-like spectrum from which nuclear hyperfine and quadrupole splittings can be determined. 

HypB protein, 47 289 HypC protein, 47 289 Hyperfine coupling, 13 149-178 anisotropic, 13 150-161 Hyperfine coupling anisotropic dipolar, 13 150-154 nuclear Zeeman interaction, 13 155 quadrupole interaction, 13 154, 155 factors affecting magnitude of metal influence of charge on metal, 13 169-170 isotropic and anisotropic, 13 166-170 libration, 13 170... 

In addition to the isomer shift and the quadrupole splitting, it is possible to obtain the hyperfine coupling tensor from a Mossbauer experiment if a magnetic field is applied. This additional parameter describes the interactions between impaired electrons and the nuclear magnetic moment. Three terms contribute to the hyperfine coupling (i) the isotropic Fermi contact, (ii) the spin—dipole... 

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. 

Figure 8.31. Nuclear hyperfine splitting of the J = 1 rotational level of CsF in its X 1 + state. The major splitting is due to the 133Cs quadrupole interaction, and the smaller doublet splitting arises from the 19F nuclear spin-rotation coupling. The diagram is drawn for zero apphed electric field, and the strongest electric dipole transitions are indicated.

The magnetic hyperfine interaction terms were given in equation (8.351) and the electric quadrupole interaction in equation (8.352). We extend the basis functions by inclusion of the 7Li nuclear spin I, coupled to J to form F the value of / is 3/2. We deal with each term in turn, first deriving expressions for the matrix elements in the primitive basis set (8.353), and then extending these results to the parity-conserved basis. All matrix elements are diagonal in F, and any elements off-diagonal in S and / can of course be ignored. 

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 femperafure-dependenf linewidfhs of fhe ESR hfs of La Cs2, Sc C82 and Gd C82 have been discussed by Kato et al. (1993, 1995a,b, 1996) in terms of fhe spin-rofafion coupling interaction. Dinse and co-workers (Ruebsam et al., 1995,1996a,b) investigated temperature dependence of ESR line widths of La Cs2/ La C9o, and Sc Cs2 in different solvents and obtained irrformation on the nuclear quadrupole interactions in these metallofullerenes. Dunsch and co-workers (Bartl et al., 1994,1997 Seifert et al., 1998) studied Y satellite structures of M C82 (M = Sc, Y, La) in detail and reported that the manifold of hfc (hyperfine constants) could be interpreted by the calculated spin density distributions. 

A nuclear quadrupole interaction is by definition anisotropic (parameters P, rj) as is an electronic quadrupole interaction (i.e., zfs parameters D, E), since these are described by a nonzero field gradient. Both of these effects have been briefly mentioned above, but the most important manifestation of anisotropy in ENDOR is with respect to g valnes and to hyperfine coupling interactions. 

The general cases of symmetric and asymmetric tops have been reviewed.56 For deuterium, the nuclear quadrupole interaction is small and the hyperfine structure is not always resolved, so that the deuteron quadrupole coupling constant must be obtained by curve-fitting. The accuracy of the data diminishes as the size and the asymmetry of the molecule increases. 

Figure 2 Spectrum of the 7 = 8-7 rotational transition of Xe Cu Cl. The compUcated hyperfine structure arises from nuclear quadrupole interactions of Cu (7cu = 3/2) and C1 (7qi = 3/2). All transitions are spUt into Doppler doublets as a result of the molecular expansion traveling parallel to the microwave cavity axis. For clarity of the picture, the quantum number assignments of only a few hyperfine components are given as Fj -F/, F -F". The angular momentum coupling scheme Fi = Icu + J F = Fi + Iq was used. The compound was produced using laser ablation of a copper rod in a molecular expansion of a mixture of 0.1% CI2, 15% Xe, and 85% Ar. The particular isotopomer was measured in its natural abundance of 6.3%. This spectmm was recorded using 15 000 averaging cycles with a total accumulation time of about 3.5 h...

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