Double-rotation

The results (Figs. 21-25) show that bond-strengthening and bond-weakening effects of the substituents are also at work here. The most heavily substituted bond is broken most easily. This is specially evident in the case of [13], where Figs. 23—25 show the energetics of the rupture of each of the three bonds. Moreover, the double rotation at the reacting centers is... 

Samoson, A., and Lippmaa, E. (1989) Synchronized double-rotation NMR spectroscopy. Solid State Magn. Reson., 84, 410-416. 

Dynamics calculations have also provided new approaches to the stereochemical modes through which cyclopropanes and trimethylene intermediates may be related. Full quantum dynamics calculations for the trimethylene diradical based on a reduced dimensionality model that followed wave packet densities and time constants for formation of products led to the conclusion that conrotatory and disrotatory double rotations of both terminal methylene groups are favored over a single rotation of just one by a 2.2 1 ratio." °... 

However, quantitative evaluation of the size of this preference depended on knowing the size of the secondary deuterium isotope effect on which C—C bond in 7b cleaves. With the seemingly reasonable assumption of a secondary isotope effect of 1.10 on bond cleavage, the experimental data led to the conclusion that double methylene rotation was favored over single methylene rotation by a factor of 50 in the stereomutation of 7b. Although the error limits on the measurements were large enough to allow the actual ratio to be much smaller, Berson wrote, There is no doubt that the double rotation mechanism predominates by a considerable factor. ... 

Sixteen years later Baldwin and co-workers published the results of even more elegant experiments in which the stereomutation of optically active 7-l- C-l,2,3-was studied. Because a deuterium atom is attached to each of the carbons in this compound, it was unnecessary for Baldwin to assume the size of a secondary deuterium isotope effect on which bond cleaves, in interpreting his kinetic data. The results of his experiments led him to conclude, the double rotation mechanism does not predominate by a substantial factor. ... 

For the cis isomer, the ratio of racemization to epimerization was found to be 107 at 274.5 °C, and the cis isomer was found to undergo racemization 16.2 times faster than the trans isomer. The ratio of racemization to epimerization for the latter was found to be only 6.6 at 274.5 °C. Thus, these experiments confirmed the computational predictions that in 9b and 9c, double methylene rotations are faster than any process that leads to net single methylene rotation, and the preferred mode of double rotation is disrotation, rather than conrotation. ... 

The screw extruder is a hollow chamber of suitable length that contains single or double rotating screws driven by a variable speed drive to transport... 

The reaction was studied theoretically by Hoffmann who concluded that it should involve a double rotation of the methylene groups.81 A study of the kinetics of racemization vs. isomerization of optically active trans-l, 2-dideuteriocyclopropane provided evidence for this process.82 Further experimental studies have made the interpretation of the details of this reaction more difficult.83 The most recent calculations84 have concluded that the conrotatory double rotation is slightly preferred. It is likely that substituents could have a major effect on the course of the reaction. 

The last equation here implies that the directions of a Beltrami field and the direction of its double rotational counterpart form an acute angle. If the A field is solenoidal, V A = 0, then Eq. (93) implies the condition A Vfc = 0 for any kind of k(r, t) function. This results in the fact that current lines and vortex lines are located on surfaces k r, t) = Ct for any given t. 

After we have worked out the characters for all of the new operations, CyR, of the double group, we will then collect them into classes, using the same rule as for simple groups, namely, that all operations having the same characters are in the same class. Thus in general we shall find the following classes in double rotation groups ... 

The barrier for stereomutation is calculated to be close to 61 kcalmoT1 (CISD+Q/TZ + 2py 32,275 Conrotatory double rotation of the methylene groups is about 1 kcal mol-1 more favourable than single rotation of a methylene group. Calculations further reveal that dis-rotatory rotation is also possible with a barrier0.5 kcalmol-1 larger than conrotatory rotation (Figure 27). 

At any rate, by 1984 the kinetic study of l,2-d2-cyclopropanes reported in 1975276 278 became the only unchallenged claim of kinetically favored two-center epimerization and of a predominance of the theoretically predicted double rotation mechanism . 

The 1036 cm 1 absorption band together with the 1041 cm"1 absorption associated with the trans isomer appear to provide a particularly reliable measure of relative cis versus trans concentrations281"12. Only by disregarding the k, value based on the 1036 cm"1 absorption data and by passing over probable systematic errors in the estimation of k, from infrared data at 846 cm 1 was it possible to conclude that kn is very much greater than k and that the double rotation mechanism predominates by a substantial factor. 

Ab initio MRCI calculations showed that the barrier from trimethylene to propene is 7.9kcalmol 1 higher than that from trimethylene to cyclopropane.11 Thus, cyclopropane stereomutation may occur through trimethylene as an intermediate (Chart 3). Trimethylene biradical may cyclize by double rotation of the two C C bonds in conrotatory or disrotatory fashion or successive single rotation. The calculations showed that the PES at the... 

Figure 15.11. Hexamethylbenzene l3C spectra at various spinning speeds. The rotation of the molecule about its sixfold axis imposes axial symmetry on its chemical shift tensors. The double rotation of the methyl group (first about its own C3 axis and then about the molecular D6 axis) averages its chemical shift anisotropy to an exceedingly small value.

Table 6 Character table for the double rotation and wagging in non-planar pyro-catechin.

It is noticeable that the NRG theory developed here furnishes two different groups for the double rotation in planar pyrocatechin (or acetone), and the double rotation and wagging mode in non-planar pyrocatechin (or pyramidal acetone). The group structures, however, are seen to be the same. The Longuet-Higgins theory yields indeed the same Molecular Symmetry Groups for both pyramidal uid planar systems. As a result, the NRG theory is seen to furnish a more det ulled information about the dynamics of the non-rigid systems. 

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