Electron nuclear dipolar interaction distances

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... 

Eqs. 3 and 4 show the electron-nuclear relaxation-rates for the spin-lattice (longitudinal) and spin-spin (transverse) relaxation-rates. In both of these equations, the first terms reflect the dipolar term, and the second part reflects the scalar interaction. The dipolar term contains a distinct r distance term between the electron of the metal atom and the respective carbon atom in contrast, the scalar term has none. 

With modem methods such as ENDOR or ESEEM, it is not only possible to identify direct ligands to the paramagnetic centre, but also to detect nuclei with a nuclear spin I up to distances of ca. 0.6 nm. Because, for these more distant nuclei, the interaction with the electron spin is mostly dipolar, the distance and, in specific cases, also the orientation with respect to the paramagnetic molecule can be determined. This has been done, for example, in great detail for the transient semiquinone radical Q of bacterial reaction centres [5] [12],... 

Pseudocontact or dipolar shifts are the results of dipolar interaction between the electronic magnetic moment and the nuclear spin which do not vanish in magnetically anisotropic systems. Like the Fermi contact shift their magnitude is proportional to and the distance between the two spins. 

Echo detection of selectively-burned holes in photosynthetic systems led to estimates of distances between 25 and 50 A. If the contributions to spectral diffusion from motion, nuclear spin flip-flops, and instantaneous diffusion are smaller than the contribution from dipolar interaction between unpaired electrons, the spectral diffusion can be used to determine the interspin distance. (97-100). 

Einally, pulsed EPR experiments in solids allow determination of spin-lattice relaxation and phase memory times (Ti, Tm), whose dependence on temperature and nature of the environment can be analyzed to give information on the collective relaxation phenomena due to nuclear spin diffusion, electron-electron dipolar interaction, and instantaneous diffusion [9]. Note that the electron-electron dipolar interaction is also exploited in the DEER (PELDOR) technique for measuring the distance between paramagnetic centers. Instantaneous diffusion can give information on the microconcentration of radicals produced by high-energy irradiation in solids [e.g., 10]. 

The direct contribution (c3)dir arises from the through-space dipolar coupling of the nuclear magnetic moments and, as expected, it decreases as the internuclear distance increases with increasing v, because of its R l dependence. The second contribution (C3)ec is the axial component of the tensorial electron-coupled spin-spin interaction the scalar part of this interaction is given by the value of C4. In the v = 0 level the direct contribution is estimated by English and Zorn [51] to be 1.15 kHz, and the electron-coupled part is -0.23 kHz. 

The through-space interaction is a dipolar coupling between the electron and nuclear magnetic moments. When the Zeeman interaction for both the electron and nuclear spins is the dominant term in the spin Hamiltonian of the system, the energy of the dipole-dipole interaction is inversely proportional to the third power of the dipole-dipole distance fis according to... 

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