Nuclear dipole

Although the Femii contact mechanism dominates most couplings, there are smaller contributions where a nuclear dipole physically distorts an orbital, not necessarily of s type [18]. There are many useful compilations of J and K values, especially for FIFI couplings (see [9], eh 4, 7-21 and [12, 13,14 and 15]). 

Nuclear dipole-dipole interaction is a veiy important relaxation mechanism, and this is reflected in the relationship between 7, and the number of protons bonded to a carbon. The motional effect is nicely shown by tbe 7 values for n-decanol, which suggest that the polar end of the molecule is less mobile than the hydrocarbon tail. Comparison of iso-octane with n-decanol shows that the entire iso-octane molecule is subject to more rapid molecular motion than is n-decanol—compare the methyl group T values in these molecules. 

Hfi includes a nuclear Zeeman term, a nuclear dipole-dipole term, an electron-nuclear dipole term and a term describing the interaction between the nuclear dipole and the electron orbital motion. 

For liquids, the dominant relaxation mechanism is the nuclear-nuclear dipole interaction, in which simple motion of one nucleus with respect to the other is the most common source of relaxation [12, 27]. In the gas phase, however, the physical mechanism of relaxation is often quite different. For gases such as the ones listed above, the dominant mechanism is the spin-rotation interaction, in which molecular collisions alter the rotational state of the molecule, leading to rotation-induced magnetic fluctuations that cause relaxation [27]. The equation governing spin-rotation relaxation is given by... 

A further contribution to the first order ENDOR frequencies arises from the nuclear dipole-dipole interaction = IDK between the two nuclei I and K. The shifts of the ENDOR lines of nucleus I due to %CD are described by mKD33(ms), with D33(m ) = R3CI(ms)DCK(ms)R3/cI(ms)cK(ms). In transition metal complexes this interaction is... 

Assignment of ENDOR lines to the corresponding pair of nuclei which are coupled by a direct nuclear dipole-dipole interaction. 

Discrimination between splittings which originate from nuclear dipole-dipole couplings and splittings produced by slight deviations from magnetic equivalence. 

Electron-nuclear dipole-dipole coupling. The electron-nuclear dipole-dipole coupling (5.1 a) of the ligand nucleus N is described by... 

The dipolar parts of the analyzed hfs tensors have been compared with calculated values obtained from first order expressions of the electron-nuclear dipole interaction (5.3)57. The coefficients of the atomic orbitals used in this computation, which considers all two- and three-center contributions, are obtained from an extended Huckel calculation (ethyl groups replaced by protons). It has been found that almost 100% of the unpaired electron is located on the CuS4 fragment so that the replacement of the ethyl groups by protons is of minor importance for the calculation of the atomic orbital coefficients. The experimental and theoretical hfs data, summarized in Table 8, are found to... 

As stated in Section II.B of Chapter 2, the actual correlation time for electron-nuclear dipole-dipole relaxation, is dominated by the fastest process among proton exchange, rotation, and electron spin relaxation. It follows that if electron relaxation is the fastest process, the proton correlation time Xc is given by electron-spin relaxation times Tie, and the field dependence of proton relaxation rates allows us to obtain the electron relaxation times and their field dependence, thus providing information on electron relaxation mechanisms. If motions faster than electron relaxation dominate Xc, it is only possible to set lower limits for the electron relaxation time, but we learn about some aspects on the dynamics of the system. In the remainder of this section we will deal with systems where electron relaxation determines the correlation time. 

The electron magnetic moment may also interact with the local magnetic fields of the nuclear dipole moments of nuclei around it. A single electron centered on a nucleus of spin I will experience 2/ -f 1 different local magnetic fields due to the 27 - - 1 different orientations of the nuclear spin I in the external magnetic field. This interaction, which is of the order of 10 cm. i, causes a hyperfine structure in the EPR spectrum. This structure is further discussed and illustrated in Section III,B. 

The fine sfrucfure is caused by fhe so-called indirect spin-spin coupling, indirect because it occurs through the chemical bonds. Nuclear dipoles can also be coupled to each other directly through space. 

The electron-phonon operator is a tensor product between the electronic dipole and the nuclear dipole operators. A mixing between the AA and BB via the singlet-spin diradical AB state is possible now. A linear superposition of identical vibration states in AA and BB is performed by the excited state diradical AB. If the system started at cis state, after coupling may decohere by emission of a vibration photon in the trans state furthermore, relaxation to the trans... 

Dipolar (or direct) coupling between nuclear dipoles is the second mechanism of spin-spin interaction (see Section 4.1.1.2. for scalar coupling). Acting through space209-212 it is dependent on the distance r between the dipoles as well as the angle between their vectors and the direction of the external field B0. 

The efficiency of spin-lattice relaxation of a given nucleus is also dependent on the number of nearby nuclear dipoles. In fortunate cases this can be used to obtain structural information. For example, there are more protons spatially close to the methine carbons in the c/.v-configurated tricyclic compound 3 than in the trans-isomer220. Thus, the 7 value of the methine carbons in the (Tv-isomer is considerably smaller. 

In quantum theory, the nuclear dipole-moment operator is proportional to the nuclear spin, i.e., nothing else but the gyromag-netic ratio yj multiplied by the nuclear spin operator Ih... 

It is interesting to note that a similar radiative association process is not possible for the two hydrogen atoms. On the symmetry grounds the dipole moment of the H — H system (which is inversion symmetric) vanishes. In that case the nuclear dipole moment is identically 0 and the electronic dipole moments induced in the two approaching atoms have opposite orientations and cancel each other. For the H — H system (which lacks the inversion symmetry) the dipole moment (in the adiabatic and non-relativistic approximation) is finite. In that case the hadronic moment is e R and the induced leptonic moments of H and H have the same orientations and add together to a non vanishing dipole moment (which tends to 0 in the limit of infinite separation R between the atoms). 

Intermolecular interactions between an electron and a nuclear dipole usually contribute to line-widths unless the solvent has no magnetic nuclei. If exchange of solvent molecules is rapid these will be largely... 

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