Dipolar interactions electrons

All atoms and molecules attract one another as a result of transient dipole-dipole interactions. A molecule need not have a net charge to participate in a dipolar interaction electron density can be highly asymmetric if interacting atoms have different electronegativities. 

The perturbation theory is the convenient starting point for the determination of the polarizability from the Schrodinger equation, restricted to its electronic part and the electric dipole interaction regime. The Stark Hamiltonian —p. describes the dipolar interaction between the electric field and the molecule represented by its... 

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 fact that dynamic 13C polarization is only possible through the indirect way via tire 1H spins suggests the mechanism of polarization transfer. Since the polarization transfer between the electrons and nuclei are driven by the dipolar interactions between them, and the fraction of the guest triplet molecules was small, it would be natural to assume that the polarization of the electron spins in the photo-excited triplet state is given to those H spins which happen to be close to the electron spins, and then the 1H polarization would be transported away over the whole volume of the sample by spin diffusion among the 1H spins. 

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 ... 

C. Elsasser, M. Brecht and R. Bittl, Pulsed electron-electron double resonance on multinuclear metal clusters Assignment of spin projection factors bsed on the dipolar interaction, J. Am. Chem. Soc., 2002, 124, 12606. 

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 S S term describes dipolar interaction the elements of the D-tensor in Equation 11.4 are directly related to the dipole-dipole interaction by averages over the electronic wavefunction ... 

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... 

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... 

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