Dipole internuclear relaxation contribution

For a two spin system, the explicit formulation (18) for dipole internuclear relaxation contribution, p(j- -i), between a receptor nucleus i and donor nucleus j, is shown in [3]. 

Expression [7] is only strictly valid if the replacement of the proton by deuterium causes no alteration in the internuclear separation and if tc(1H-1H) is identical to t .(1H-2H), both of which are perfectly reasonable assumptions. Thus replacement of a proton by a deuterium reduces the dipole-dipole relaxation contribution from that site to ca. 6% of its original value. 

Nuclear magnetic dipole relaxation interactions may occur with other nuclei, or with unpaired electrons. These processes usually dominate the relaxation of spin - nuclei. Both intra- and intermolecular interactions may contribute to dipole-dipole nuclear relaxation times. The value of due to the intramolecular dipole-dipole process is proportional to the sixth power of the internuclear separation. Consequently, this process becomes rather inefficient in the absence of directly bonded magnetic nuclei. However, it follows that a measurement of can be provide an estimate of internuclear separation that can be of chemical interest. The nuclear Overhauser effect (NOE) depends upon the occurrence of dipole-dipole relaxation processes and can similarly provide an estimate of internuclear separation. 

Given the specific, internuclear dipole-dipole contribution terms, p,y, or the cross-relaxation terms, determined by the methods just described, internuclear distances, r , can be calculated according to Eq. 30, assuming isotropic motion in the extreme narrowing region. The values for T<.(y) can be readily estimated from carbon-13 or deuterium spin-lattice relaxation-times. For most organic molecules in solution, carbon-13 / , values conveniently provide the motional information necessary, and, hence, the type of relaxation model to be used, for a pertinent description of molecular reorientations. A prerequisite to this treatment is the assumption that interproton vectors and C- H vectors are characterized by the same rotational correlation-time. For rotational isotropic motion, internuclear distances can be compared according to... 

Temperature Dependence of Spin-Lattice Relaxation. The spin-lattice relaxation rate T ) is comprised of various contributions to the relaxation process, including homo- and heteronuclear dipolar interactions, quadrupolar interactions, chemical shift anisotropy, spin-rotation, and others (10). When the relaxation mechanism is dominated by inter- and intramolecular dipole-dipole interactions, the will increase with temperature, pass through a maximum, and decrease with increasing temperature. Since the relaxation rate is the inverse of the relaxation time, the Ti will decrease, pass through a minimum (Timin), and then increase with increasing temperature (77). The T lmin values are proportional to the internuclear distances. 

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