Electrons dipolar

The electron-electron dipolar term, Ho, equals S1.D.S2. The tensor D is completely anisotropic and only mixes T-states with one another. It is therefore dropped. The nuclear Zeeman term, tlzi =... 

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. 

Further complicating the situation is the fact that the same term can arise from two quite different physical effects electron-electron dipolar interaction and spin-orbit coupling. 

The Hamiltonian term for the electron-electron dipolar interaction is ... 

We now will show that spin-orbit coupling can give a spin Hamiltonian term identical to that we obtained from the electron dipolar interaction. Consider the... 

Notice that the fine structure term found here has the same form (and the tensor is given the same symbol) as that obtained from the electron dipolar interaction. Unlike the dipolar D-tensor, however, the spin-orbit coupling D-tensor in general does not have zero trace. Nonetheless, we introduce analogous parameters ... 

Although it is unfortunate that spin-orbit coupling and the electron dipolar interaction give fine structure terms of the same form, it is possible to separate the effects. Since the spin-orbit contribution to D is related to the g-tensor ... 

The difference between the fine structure parameters computed from the experimental g-tensor and those measured from the spectrum are presumed to be the electron dipolar contributions. 

In the spin-correlated RP the two radicals interact via electron-electron dipolar and exchange interaction which leads to line splitting. The ET process creates the RP in a strongly spin-polarized state with a characteristic intensity pattern of the lines that occur either in enhanced absorption (A) or emission (E).144 145 The spectrum is therefore very intense and can directly be observed with cw EPR (transient EPR) or by pulse methods (field-swept ESE).14 To study the RPs high field EPR with its increased Zeeman resolution proved to be very useful the first experiment on an RP was performed by Prisner et al. in 1995146. From the analysis of the RP structure detailed information about the relative orientation of the two radicals can be extracted from the interaction parameters. In addition kinetic information about the formation and decay of the RP and the polarization are available (see references 145,147). 

If the molecular tumbling rate is slow enough that larger electron-electron dipolar couplings are not motionally averaged, Fourier deconvolution can be used to analyze dipolar interactions in fluid solution.18 Distances in doubly spin-labelled rhodopsin were measured by Fourier deconvolution of CW line-shape changes in room temperature solution.78 The broadening function was modelled as the sum of Pake patterns from a distribution of distances. As a reference point for the distance measurements one label was attached at the cytoplasmic termination of transmembrane helix 1. The second label was attached near the cytoplasmic termination of transmembrane helix 7 or in the short helix 8. The distances and conformational flexibility in the dark state are... 

Anisotropy due to nuclear-electron hyperfine splitting, to spin-orbit coupling ( -factor), and particularly to strong electron-electron dipolar splitting in molecular triplets and radical pairs, provides a great deal of orientational information. It also makes it possible to shift peak positions in the spectrum, creating new windows through which to observe minor components that would be completely obscured in powder spectra. 

By measuring zero-field splitting (zfs) from electron-electron dipolar coupling in triplet radical pairs and proton hyperfine splitting (hfs), Segmuller developed a detailed picture of the motions of these radicals. The sequence of... 

Restricting ourselves to metal-centered nuclear relaxation, the fluctuation of the electron dipolar field at the nucleus due to electron relaxation can be easily visualized as depicted in Fig. 3.1 A. We now want to mention other mechanisms, besides electron relaxation, which occur in solution and through which unpaired electrons cause nuclear relaxation. All of these mechanisms will be discussed in detail in this chapter. 

Fig. 3.1. Pictorial representation of the motions causing nuclear relaxation electron spin relaxation (A), molecular rotation (B) and chemical exchange (C). It can be seen that the electron dipolar field at the nucleus fluctuates with time in direction (A), intensity (C) or both (B).

FLC phases in the surface stabilized geometry possess a single C2 axis of symmetry, and therefore polar order and non-zero x<2) in the simple electronic dipolar model. Thus, it is not surprising that experiments aimed at measuring this property were first reported shortly after the Clark-Lagerwall invention. Early studies (14-15) described second harmonic generation in (S)-2-Methylbutyl 4-(4-decyloxybenzylideneamino)cin-namate, the first ferroelectric liquid crystal, also known as DOBAMBC (1). 

Fig. 2. Electronic dipolar nature of the peptide unit. The numbers adjacent to each atom give the approximate fractional electronic charge attributed to each atom (in units of fundamental electronic charge). The magnitude of the dipole moment is 0.72 ek = 3.46 D.

Fig. 11. Diagrammatic view of contacts between ethacrynic acid and deoxyhemoglobin A. The ligand is covalently bound to cysteine-93 of the p chain. and indicate fractional charges due to the electronic dipolar nature of the o-dichlorobenzene moiety. Broken lines indicate hydrogen bonds and dotted lines van der Waals contacts. Oxygen-aromatic interactions involving aspartate-94 and cysteine-93 are shown schematically. Reproduced with permission from Perutz et al. (1986).

In low-symmetry molecules, diagonal and off-diagonal matrix elements of the electronic dipolar coupling tensor may contribute to ( h[)0 ) J ssl b ). Therefore, they are specified mostly in terms of their Cartesian components. If symmetry is C2V or higher, the off-diagonal matrix elements of the tensor operator in Eq. [163] vanish (i.e., the principal axes diagonalizing the SCC tensor coincide with the inertial axes). For triplet and higher multiplicity states, one then obtains... 

This unitary transformation redefines the variables of the field (ak, E, A, etc.) and displaces the momentum operator of each charge. Retaining only the electronic dipolar terms, the total hamiltonian becomes... 

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... 

It follows that the nuclear nuclear and electron-electron dipolar interactions may also be represented in irreducible tensor form by operator expressions equivalent to (8.449), with the appropriate replacements, and with an overall positive sign. Again to avoid confusion we list the appropriate operators. 

Two nitroxides, separated by the distance r, are coupled through space via electron-electron dipolar interactions arising from the unpaired electrons. Spin coupling induces line splitting dependent on their separation and their orientation with respect to the magnetic field according to... 

The Hamiltonian for interradical interactions can be decomposed into two terms corresponding to the electron exchange interaction and the electron dipolar interaction... 

The orientation of electron spins in this manner influences the electron-electron dipolar interaction described above. For strong magnetic fields, the diffusive... 

The dinitroxide (20) is one of several nitroxide biradicals used to test the point-dipole approximation for electron-electron dipolar interactions/ ... 

For molecules with the same number of electrons, dipolar molecules are associated with less volatile substances than are molecules with only London forces. 

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