Spin rotation interaction

Hubbard P. S. Theory of nuclear magnetic relaxation by spin-rotational interactions in liquids. Phys. Rev. 131, 1155-65 (1963). 

Courtney J. A., Armstrong R. L. A nuclear spin relaxation study of the spin-rotation interaction in spherical top molecules. Can. J. Phys. 50, 1252-61 (1972). 

The process of spin-lattice relaxation involves the transfer of magnetization between the magnetic nuclei (spins) and their environment (the lattice). The rate at which this transfer of energy occurs is the spin-lattice relaxation-rate (/ , in s ). The inverse of this quantity is the spin-lattice relaxation-time (Ti, in s), which is the experimentally determinable parameter. In principle, this energy interchange can be mediated by several different mechanisms, including dipole-dipole interactions, chemical-shift anisotropy, and spin-rotation interactions. For protons, as will be seen later, the dominant relaxation-mechanism for energy transfer is usually the intramolecular dipole-dipole interaction. 

When other relaxation mechanisms are involved, such as chemical-shift anisotropy or spin-rotation interactions, they cannot be separated by application of the foregoing relaxation theory. Then, the full density-matrix formalism should be employed. 

A model which takes into account the spin-rotation interaction has been found to satisfactorily explain the 0 rotation band of PHg. The millimetre-wave spectra of HCP and DCP have been compared with those of HCN and DCN. A method of estimating frequencies of bands in this region due to processes such as pseudorotation has been suggested. This new approach involves calculation of the rovibronic energy levels from the effects of quantum-mechanical tunnelling. ... 

For liquids, the dominant relaxation mechanism is the nuclear-nuclear dipole interaction, in which simple motion of one nucleus with respect to the other is the most common source of relaxation [12, 27]. In the gas phase, however, the physical mechanism of relaxation is often quite different. For gases such as the ones listed above, the dominant mechanism is the spin-rotation interaction, in which molecular collisions alter the rotational state of the molecule, leading to rotation-induced magnetic fluctuations that cause relaxation [27]. The equation governing spin-rotation relaxation is given by... 

The first possibility is that the attractive potential associated with the solid surface leads to an increased gaseous molecular number density and molecular velocity. The resulting increase in both gas-gas and gas-wall collision frequencies increases the T1. The second possibility is that although the measurements were obtained at a temperature significantly above the critical temperature of the bulk CF4 gas, it is possible that gas molecules are adsorbed onto the surface of the silica. The surface relaxation is expected to be very slow compared with spin-rotation interactions in the gas phase. We can therefore account for the effect of adsorption by assuming that relaxation effectively stops while the gas molecules adhere to the wall, which will then act to increase the relaxation time by the fraction of molecules on the surface. Both models are in accord with a measurable increase in density above that of the bulk gas. 

In Equation (15), R others encompasses all secondary interactions which are not included in the first two terms (for instance the interaction with an unpaired electron, the spin-rotation interaction,...). By contrast, the expression of the cross-relaxation rate is simply... 

Since these terms are proportional to tr, they increase with decreasing temperature.1 There are several line-width contributions, included in oc0, which do not depend on m,-. These include magnetic field inhomogeneity and the spin rotation interaction, the latter increasing with 1/tr and thus with increasing temperature. These and other line-width effects have been studied in some detail and are discussed elsewhere.13... 

This phenomenon of antiparamagnetic paramagnetic terms clearly needs a name and is called here the Cornwell effect (ideally the Cornwell-Santry effect). Positive contributions to op (which may or may not be positive overall) are expected in heteronuclear diatomics if they have a IT state this excludes, e.g., HF, InF, and TIF. In homonuclear diatomics, the IT -> a excitation is symmetry-forbidden. The possibility has been mentioned for XeF (34), although, from the chemical shift and calculated values of aa, the resultant Op ( F) is negative in XeFg and KrFj (cf. Fig. 7). Another candidate is FC DH, from the evidence of the fluorine chemical shift and spin-rotation interaction (96). According to this interpretation there should be a substantial upheld shift of the... 

For example, the spin-rotation interaction for a molecule in a state can be generally represented as... 

Figure 8.4 Magnetic field dependence of the Zeeman (the full curves) and hyperfine relaxation (the dashed curves) cross sections at zero electric field (a), = 10 kV/cm (b), and E = 10 kV/cm (c). The symbols in the upper panel are the results of the calculations without the spin-rotation interaction. The collision energy is 0.1 K x kg. Adapted with permission from Ref. [86].

The diamagnetic contribution for H2 is easily calculated theoretically, and it turns out that the paramagnetic contribution is related to something called the spin-rotation interaction constant, which can be measured experimentally. 

Finally, spin-orbit interaction has often been considered as the cause of states of mixed permutational symmetry. There are, however, a variety of other spin interactions which may accomplish such mixing electron spin-electron spin, electron spin-nuclear spin, spin-other-orbit, and spin rotation interactions. That other such spin interactions may enhance spin-forbidden processes in organic molecules is frequently ignored, though they may be of importance.66,136... 

Aside from the question of the precise model by which relaxation times are interpreted there is the more practical problem of isolating that part of the relaxation specifically caused by diffusion. The contributions of exchange processes (see below), spin-rotation interaction (9), and spin diffusion (9) can be identified by temperature dependences different from that which is solely the result of the motionally modulated nuclear dipolar interaction as sketched above, and corrections can be made. The molecular rotation contributions to dipolar relaxation can be removed or corrected for by (a) isotopic substitution methods (19), (b) the fact that rotation is in some cases much faster than diffusion, and its relaxation effects are shifted to much lower temperatures (7, 20), and (c) doping with paramagnetic impurities as outlined above. The last method has been used in almost all cases reported thus far, more by default than by design, because commercial zeolites are thus doped by their method of preparation this... 

Spin-rotation interaction (I/TOsr = 21ikT/2[h(2jr)-1]2 Ceff2xJ 4... 

Recent reports of spin-rotation constants for aluminum chloride (35) and aluminum isocyanide (36) have made possible the comparison of experimental and ab initio calculated shielding results. If one were able to measure the27A1 chemical shift of one or both these compounds, it would be possible, in principle, to establish an absolute shielding scale for aluminum however, the high reactivity of these compounds has so farprecludedsuchmeasurements. High-resolution microwave measurements have also been recently carried out on A1H (37) however, analysis of the data did not consider the 27A1 spin-rotation interaction (vide infra). 

The energies of these states are further modified by the spin-rotation interaction, so that for27A1 (/= 5/2) the three frequencies and relative intensities associated with the J-1 - 0 transition are ... 

The authors of [315] applied linearly polarized synchrotron radiation (45-66 nm) for ionization, which corresponds to photon energy from 18.76 eV (threshold) + 0.7 eV up to 27 eV. The measured V values, as dependent on photon energy, changed correspondingly from 0.052 down to approximately half the value, which made it possible to determine the value of r within the range 0.4-0.7. Further improvement of the experiment and refinement of the theoretical description was carried out in [179]. Accounting for the hyperfine and spin-rotational interaction effect made it possible to refine the photoionization channel relation r, which yielded values of 0.2-0.4 for photon energies between threshold and 32 eV. 

Huber, R., Knapp, M., Konig, F., Reinhard, H. and Weber, H.G. (1980). Magnetic shielding and spin-rotation interaction in ground state alkali molecules, Z. Physik A-Atoms and Nuclei, 296, 95-99. 

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