Pure Pseudorotation

Gwinn and co-workers34 have given an excellent exposition of the theory appropriate to treating hindered pseudorotation, with particular attention to the use of an angular Hamiltonian for small-barrier cases. For the special case of pure pseudo- 

Ikeda et al.35 considered solutions of Eqs. (3.34) and (3.35) by the variation method with two-dimensional harmonic oscillator functions in Cartesian and polar coordinates, respectively, as basis functions. Some of the eigenvalues are plotted in Fig. 3.4 as a function of the parameter B. The case of pure pseudorotation corresponds to large negative values of B on the right hand side of the figure. 

It was found from numerical solution of Eqs. (3.34) and (3.35) that the calculated pseudorotational frequencies exhibited curvature rather than a strict linear dependence on quantum number as in Eq. (3.38). This is shown in Fig. 3.5. Such curvature had been experimentally observed for 1,3-dioxolane and tetrahydrofuran35 and was also noted by Davis and Warsop37, who used it to estimate the barrier to planarity. 

Consideration of approximate solutions to Eq. (3.35) by obtaining an effective Hamiltonian by a 2nd order Van Vleck transformation led to an expression35 for /- /+ 1 transitions given by 

The pseudocentrifugal distortion constant, D, accounts for the curvature of the frequencies (Fig. 3.5) and Eq. (3.40) gives the variation of pseudorotational constants with vibrational state. 

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Figure 3.3 gives a potential energy contour diagram appropriate for pure pseudorotation. 

B. Molecules Treated by Two-Dimensional Hamiltonians 1 Pure Pseudorotation... 

C5H10 1 1 CH2CH2CH2CH2CH2 Cyclopentane MIR, R Essentially pure pseudorotation. Barrier to planarity = 1824 cm-1. Isotopic species studied 7, 97, 188, 189)... 

From (8.23) and (8.24) one can see two special cases when the potential becomes separable. In the first case c12 = 0, we have two independent anharmonic modes, each having two equilibrium positions. In the second case, the angular part of the potential (8.23) Vr is zero, and the motion breaks up into radial vibration in the double well V0(q) and a free rotation, i.e. propagation of the waves of transverse displacements along the ring. The latter case is called free pseudorotation. Since the displacements of atomic groups in the wave are purely transverse, they do not contribute to the total angular momentum. 

The first observation is in contrast to the studies on phosphoranes (14, 15, 16) for which the equatorial cycle is highly unfavorable owing to the non-cyclic equatorial C-P-C angle of 120°. The non-cyclic C-S-C bond angle is presumably in the vicinity of the 102° F-S-F angle of SF4. [For relevant data see Table VI of Reference (17).] Also trimethylene-sulfide is a known compound. This is an example of the diflFerence between the pure p-bond picture of sulfuranes and the -hybridized picture of phosphoranes. The only evidence relative to the second observation is the lack of pseudorotation in solvolysis sulfurane intermediates (16) although some authors seem intuitively to believe pseudorotation likely in these compounds (18). 

Hall and Inch therefore synthesized the optically pure enantiomers of [13a,b,c,d] and examined the stereochemistry of the alcoholysis products. The monochloro derivative undergoes methanolysis by predominant P—S bond cleavage with 70% inversion of configuration. P—O bond cleavage is competitive, accounting for 15% of products. Both the stereochemistry and product distribution demonstrate that in this system there remains a barrier to pseudorotation. 

Further calculations on transition states with fixed TBP and SP geometry demonstrate that the energy difference between pure TBP (6.82 Real mol ), pure SP (7.03 Real moP ) and the 50% distorted transition state (6.38 Real moP ) is surprisingly small. Calculations on a number of transition-state structures allows assessment of pseudorotational barriers involved in adjacent displacement mechanisms. From these data, the following significant conclusions can be drawn. 

Reaction of optically pure 104 with organolithiums to form 105 occurs with preponderant P-0 bond cleavage and retention of configuration (de>90%), exactly like in the modern Juge-Stephan method, but at that time those observations were unexpected. The retention of configuration in the ring opening of 104 was explained by the sequence formation of a pentacoordinated intermediate-pseudorotation-apical elimination. Acidolysis of 105 produced the desired phosphinothioic acids 106 in ee values better than 90%. This step is also directly comparable to the acidic methanolysis in the modern method. 

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