Electron-nucleus dipolar interaction

This is the beauty of this quantity which provides specifically a direct geometrical information (1 /r% ) provided that the dynamical part of Equation (16) can be inferred from appropriate experimental determinations. This cross-relaxation rate, first discovered by Overhau-ser in 1953 about proton-electron dipolar interactions,8 led to the so-called NOE in the case of nucleus-nucleus dipolar interactions, and has found tremendous applications in NMR.2 As a matter of fact, this review is purposely limited to the determination of proton-carbon-13 cross-relaxation rates in small or medium-size molecules and to their interpretation. 

The electron-nuclear dipolar interaction (see equation (10.76)) for the phosphorus nucleus is as follows ... 

Paramagnetic centers can exert dramatic effects on the chemical shifts of nuclei with which they interact. The observed shift of a nucleus in a paramagnetic molecule is the sum of its hypothetical shift in an isostructural diamagnetic molecule (SjiJ and its shift due to the electron-nucleus (hyperfine) interaction (5hf), which in turn has dipolar (pseudocontact, 5pc) and scalar (contact. Scon) contributions ... 

The fine structure of atomic line spectra and the hyperfine splittings of electronic Zeeman spectra are non-symmetric for those atomic nuclei whose spin equals or exceeds unity, / > 1. The terms of the spin Hamiltonian so far mentioned, that is, the nuclear Zeeman, contact interaction, and the electron-nuclear dipolar interaction, each symmetrically displace the energy, and the observed deviation from symmetry therefore suggests that another form of interaction between the atomic nucleus and electrons is extant. Like the electronic orbitals, nuclei assume states that are defined by the total angular momentum of the nucleons, and the nuclear orbitals may deviate from spherical symmetry. Such non-symmetric nuclei possess a quadrupole moment that is influenced by the motion of the surrounding electronic charge distribution and is manifest in the hyperfine spectrum (Kopfer-mann, 1958). 

Aniosotropic hyperfine coupling results primarily from dipolar interactions between a magnetic nucleus and an unpaired electron in a p, d, or f orbital. Such interactions give rise to a Hamiltonian... 

The absolute sign of the isotropic part of the hf coupling can be determined if the dipolar interaction of a ligand nucleus with the electron in the metal orbitals dominates... 

The sole presence of an electron spin causes nuclear relaxation. The correlation time for the electron nucleus interaction is presented as well as equations valid for dipolar and contact interaction. To do so, electron relaxation mechanisms need to be quickly reviewed. All the subtleties of nuclear relaxation enhancements are presented pictorially and quantitatively. 

Relaxation measurements provide a wealth of information both on the extent of the interaction between the resonating nuclei and the unpaired electrons, and on the time dependence of the parameters associated with the interaction. Whereas the dipolar coupling depends on the electron-nucleus distance, and therefore contains structural information, the contact contribution is related to the unpaired spin density on the various resonating nuclei and therefore to the topology (through chemical bonds) and the overall electronic structure of the molecule. The time-dependent phenomena associated with electron-nucleus interactions are related to the molecular system, and to the lifetimes of different chemical situations, for the resonating nucleus. Obtaining either structural or dynamic information, however, is only possible if an in-depth analysis of a series of experimental results provides sufficient data to characterize the system within the theoretical framework discussed in this chapter. 

Two-dimensional (2D) spectroscopy is used to obtain some kind of correlation between two nuclear spins 7 and J, for instance through scalar or dipolar connectivities, or to improve resolution in crowded regions of spectra. The parameters to obtain 2D spectra are nowadays well optimized for paramagnetic molecules, and useful information is obtained as long as the conditions dictated by the correlation time for the electron-nucleus interaction are not too severe. Sometimes care has to be taken to avoid that the fast return to thermal equilibrium of nuclei wipes out the effects of the intemuclear interactions that are sought through 2D spectroscopy. 

The lines in an EPR spectrum can be split by interaction of the electron spin with the nuclear magnetic moment of atoms on which the unpaired electron is located (Parish, 1990). Only atoms with nuclear spin (I) nonzero exhibit this type of interaction, which can be of two types (1) contact interaction that is isotropic and results from the delocalization of the unpaired electron onto the nucleus and (2) dipolar interaction between electron spin and the nucleus. In the second case, the interaction is dependent on orientation and, therefore, anisotropic (Campbell and Dwek, 1984). 

Equation (1) represent, respectively, the scalar and dipolar interactions between the electron and nucleus and are given by... 

The scalar interaction is proportional to the square of the unpaired electron s wavefunction at the nucleus, i//(0) 2. In general, this quantity is not known or cannot be determined, making the scalar interaction difficult to predict except in certain and simple situations.4 The dipolar term is heavily dependent on the distance r between the two spins, leading to the distance (and time) dependence of the Overhauser effect. Further discussions of the dipolar interaction term are available in the literature.23... 

This is a very important result. The first term in the last line of (4.13) represents the so-called Fermi contact interaction between the electron and nuclear spin magnetic moments, and the second term is the electron-nuclear dipolar coupling, analogous to the electron-electron dipolar coupling derived previously in (3.151). The Fermi contact interaction occurs only when the electron and nucleus occupy the same position in Euclidean space, as required by the Dirac delta function S(-i Rai). This seemingly... 

The pseudocontact interaction (perhaps more appropriately called a dipolar interaction) arises from the magnetic dipolar fields experienced by a nucleus near a paramagnetic ion. The effect is entirely analogous to the magnetic anisotropy discussed in Section 4.5. It arises only when the g tensor of the electron is anisotropic that is, for an axially symmetric case, j> g . The g value for an electron is defined as... 

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