Electron nuclear dipolar interaction

In actual practice the unpaired electron is not free. It is generally associated with one or more nuclei, which may have a nuclear spin magnetic moment. This moment generates a magnetic field at the location of the unpaired electron, due to the so-called contact or Fermi hyperfine interaction (the electron has a finite probability of penetrating to the atomic nucleus) and to the through-space dipolar interaction between nuclear and electronic magnetic spin moment, represented 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... 

It is assumed that most of the electron spin density resides on the metal, but that a certain small part of it, given by the quantity p , is delocalized to the ligand heteroatom L. The first term is the point-dipole interaction term, the second corresponds to the dipolar interaction between the nuclear spin under consideration and the spin-density on the atom L and the last term describes the cross-correlation of the two dipolar interactions (we discuss the issue of cross-correlation phenomena in more general terms in Section II. D and III.B). The quantity is the effective distance from the nuclear spin... 

The relaxivity enhancement of water protons in the aqueous solutions of paramagnetic complexes arises from time fluctuation of the dipolar coupling between the electron magnetic moment of the metal ion and the nuclear magnetic moment of the solvent nuclei (13,14). The dipolar interaction... 

Bloembergen and Rowland (78) have also shown that associated with the exchange interaction is a pseudo-dipolar interaction, which as the name implies, has the same functional form as the dipolar interaction. This interaction arises from the presence of the electron-coupled nuclear spin interaction and the dipole-dipole interaction and its magnitude is dependent on the relative amount of p- or d-character of the electronic wave functions in the solid. 

It was noted that for 78b and 79b, 7hf and 7cf are dependent on the molecular conformation, but this is not the case with 7nf. which is independent of the conformation. It is well known that the internuclear couplings are electron coupled interactions for which there are three possible mechanisms (1) the nuclear moments interact with the electronic currents produced by the orbiting electrons (2) there is a dipolar interaction between the nuclear and electronic magnetic moments (3) there is an interaction between the nuclear moments and the electronic spins in i-orbitals, the so-called Fermi contact term. ... 

Let us now refer to a set of molecules with their jc, y and z axes iso-oriented in an idealized solid state (Fig. 2.5). If the external magnetic field is aligned with the z axis, the dipolar interaction energy between the nuclear magnetic moment and the electron magnetic moments, according to Eq. (1.4), is... 

Our aim is that of evaluating the energy of the dipolar interaction between the nuclear and electron magnetic moments from the classical expression (see Eq. 

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). 

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