Motional effects

Nuclear dipole-dipole interaction is a veiy important relaxation mechanism, and this is reflected in the relationship between 7, and the number of protons bonded to a carbon. The motional effect is nicely shown by tbe 7 values for n-decanol, which suggest that the polar end of the molecule is less mobile than the hydrocarbon tail. Comparison of iso-octane with n-decanol shows that the entire iso-octane molecule is subject to more rapid molecular motion than is n-decanol—compare the methyl group T values in these molecules. 

First calculations of the optimum distance between the reactants, R, taking into account the dependence of the probability of proton transfer between the unexcited vibrational energy levels on the transfer distance have been performed in Ref. 42 assuming classical character of the reactant motion. Effects of this type were considered also in Ref. 43 in another model. It was shown that R depends on the temperature and this dependence leads to a distortion of the Arrhenius temperature dependence of the transition probability. 

The general relativistic Hohenberg-Kohn-Sham formalism, outlined above, contains the spin degrees of freedom in a complete form. Consequently, the spin and kinetic motion effects are not separable. Indeed, they are contained in the external potential term as one can see if such term is written using the orbital current... 

If one likes to include molecular motional effects of the ligand when bound to the macromolecule, one can introduce an order parameter using the model-free approach, as has been applied for the interpretation of CCR rates by Carlomagno et al. [46]. 

In organic solids the determination of rotating frame relaxation is severely complicated by the presence of the strongly interacting proton spin system. Spin-spin fluctuations compete with spin-lattice fluctuations to produce an effective relaxation time large rf field amplitudes are mandated to discriminate against the spin-spin event. The burden of proof lies with the experimenter to establish that a rotating frame relaxation rate actually reflects a motional effect seen by the carbon nuclei. 

Application to hexacyanobenzene indicates an improved fit to the 120 K experimental data (Druck and Kotuglu 1984). But interpretation of the results is not straightforward, because such a model does not deconvolute charge density and thermal motions effects, and is not well suited for comparison with theory and derivation of electrostatic properties. 

Johnson CK (1969) Addition of higher cumulants to the crystallographic structure-factor equation a generalized treatment for thermal-motion effects. Acta Crystallogr A 25 187-194... 

Ihese adverse motion effects can be satisfactorily resolved with plate baffle systems for rc a tively small marine vessel motions (less than three degrees of pitch and six degrees of roll, double amplitude), where high oil and water quality Is net required from the process equipment. However, In the case of more severe marine vessel motions and/or... 

Brownian motion effects are weak, then we may transit from the statistical description to the dynamical one. In such a situation the particle rotation is determined simply by the balance of viscous and field-induced torques and thus is governed by the equation... 

Least motion effects are often energetically small and vary in importance with the nature of the transition state they are frequently overridden by other factors. Therefore, even though the predictions of ALPH and PLNM are equivalent, the fact that ALPH/PLNM fails implies that the physical basis of the observed effects is not a supposedly fundamental electronic dogma like ALPH. 

Hine (1966a) also addressed the question of the physical origin of least motion effects. He considered them to arise from bond stretches and deformations in the substrate molecule, and treated the energetic consequences of these stretches and deformations in terms of intersecting Morse curves which could be approximated by parabolas. PLNM could thus be recast in terms of energetics. The energy required for a molecular deformation was considered to vary as the square of the displacement from a stable equilibrium geometry, be it reactant or product. As a consequence, reactions with very early or very late transition states were anticipated to show only small least motion effects, which should be most pronounced in reactions with central transition states. 

This feature of PLNM immediately explains why least motion effects are not observed in cleavage of acetals, but are observed in cleavage of orthoesters and other substrates at the acyl level of oxidation the transition state for acetal cleavage is late, whereas that for orthoester hydrolysis is more central (Sinnott, 1984 Cordes and Bull, 1974). 

It seems to the author that consideration of least motion effects in this fine detail with respect to the substrate is unlikely to give worthwhile insight into reactions in solution, particularly in solution in highly polar, and hence highly structured solvents. It is precisely in these solvents that many of the heterolytic reactions whose stereochemical outcome is held to support ALPH have been carried out. Most of these reactions are formally either the reaction of a delocalised carbocation with a nucleophile, or its microscopic reverse. The reactions of delocalized carbocations with nucleophiles have been studied extensively by Ritchie and co-workers, and the main conclusions of their work are particularly germane to considerations of least nuclear motion. 

If a major contributor to least motion effects in. solution is the varying degrees of solvent reorganisation required for varying degrees of nuclear motion, then it is not clear what function of atomic displacements should be minimised to determine the least motion path. Following Hine (1966a), the square of the atomic displacement has been minimised, but if solvation forces are involved, this will be accurate only for small displacements. 

If indeed solvent disruption is a major contributor to least motion effects, then its importance should be minimal in reactions with late transition states, since at the transition state the solvent shell will be already disrupted. 

A tetrahedral intermediate in which the central carbon atom is substituted by two oxygen atoms and a nitrogen atom can also be generated by the addition of water or hydroxide to an imidate salt. Least motion considerations can then affect the two possible modes of decomposition of this intermediate, to ester and amine or to amide and, alcohol. The balance between these two modes of fragmentation will depend on protonation-deprotonation processes as well as any least motion effects. However, despite attempts to rationalise results with various acyclic imidates in terms of interplay between steric and stereoelectronic interactions (Deslongchamps, 1983, pp. 118-147), it is quite clear from the incisive work of... 

Whatever the physical origin of least motion effects in R—C=N—O... 

In fact, although in some radical reactions there appear to be antiperiplanar lone pair effects, they are always modest, and, where they are not equally well considered as least motion effects, they arise from the intrinsic bias of the system examined. In this section systems supposedly giving rise to ALPH effects will be treated in order of increasing complexity. 

When the glycopyranosyl radical adopts a B2 5 conformation then the preference for axial coupling products is readily understood on the basis of well-known steric interactions. Approach of a reagent from the P-face is significantly sterically hindered, particularly by the substituent at C(3), whereas attack from the a-face is less so. If ease of approach to position-2 of the norbornyl system [145] is taken as a model for ease of approach to C(l) of a pyranose ring in the B2 5 conformation, then the favoured approach to the carbohydrate corresponds to the favoured exo-approach to the norbornyl system. If the glycopyranosyl radical adopts the 4H3 conformation, then axial reaction is favoured by the least motion effects set out in Scheme 13. 

In the case of the epimeric pairs [146], [147], and [34], the experiments are open to the objection that the thermodynamically most stable epimer is the slowest to react, as would be expected anyway. This is not the case with epimeric pair [148], where abstraction of axial hydrogen by (CH3)3CO is still preferred despite the epimer with the axial methyl group being the less stable (Beckwith and Easton, 1981). However, since the electron —13C coupling constants indicate that dialkoxy radicals are not completely tetrahedral, it follows that there will be some least motion effects favouring axial hydrogen abstraction, as there will with the epimeric pairs [146] and [147]. 

Most studies of magnetic relaxation in polymers have dealt with solid or melted polymers (73)] however, Odajima (20) has studied proton relaxation in solutions of polystyrene and polyisobutylene. It is desirable to extend and refine such measurements. In concentrated solution, some insight into the motional effects of polymer-solvent interactions should be obtainable and if, despite low sensitivity, reliable 7 values can be obtained for polymers in dilute solutions, valuable information concerning the detailed motional behavior of isolated polymer molecules may be provided. 

Dynamical effects of a two-axis 3-by-2-site jump process as can be observed in DMS-d6 were investigated by both QCPMG and MAS simulations. Besides rather interesting line broadening effects when both rate constants were in the intermediate regime, it was observed that the QCPMG experiment is more sensitive towards motional effects than MAS if either of the two rate constants is in the fast regime. 

Most NMR-groups exploring effects of molecular motion tend to develop their own software to simulate these effects. Recently the simulation program EXPRESS developed by Void and Hoatson69 was presented. By this program, effects of dynamics can be simulated (see Table 1 in Ref. 69 for details) but so far effects of finite rf-pulses and the motional effects on satellite transitions in half-integer quadrupolar nuclei are not included. 

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