Inversion and Pseudorotation

Trigonal bipyramidal isomers, whether optically active or not, are interconverted by the process known as pseudorotation. In some molecules this process may take place spontaneously, while in others it is inhibited. 

The second type, known as Turnstile Rotation (TR) [30], involves a rotation of a pair of arms (one axial and one equatorial) relative to the remaining trio of arms. Before this rotation takes place, a slight initial distortion of about 9% is necessary in order that the pair and the trio become symmetrically disposed with respect to the turnstile axis. After the relative twist of the pair and the trio in turnstile fashion, a further angular adjustment of 9% takes place to restore the correct angular arrangement of the trigonal bipyramid (3.35). 

The principles of pseudorotation have an important application in the explanation of the reaction mechanisms of many phosphorus compounds (e.g. Chapter 13.3). Because of pseudorotation and pyramidal inversion possibilities, trigonal bipyramidal and pyramidal phosphorus compounds are said to be stereochemicaUy non-rigid. There is evidence that pseudorotation processes occur in arsenic compounds and a few other non-pnictide compounds such as Fe(CO 5. 

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Energy profiles in Figure 14 also reveal that planar furanose forms are often of lower energy than puckered conformers. For example, relative conformational energies determined for 7 with the 3-21G basis set indicate that the planar conformer is more stable than the Eq conformer in 8, the planar conformer is calculated to be more stable than. These observations suggest that the conformational dynamics of some furanose rings may not be completely described by pseudorotation in these cases,conformer interconversion may occur by both inversion and pseudorotational pathways, with the latter being the more preferred route. 

Cycloheptane and cyclooctane data on the thermal properties are also given in Table 3.1 They show little change from the cyclopentane and cyclohexane properties. Again, there is no indication of increasing amounts of conformational entropy in the transition entropies. For cyclooctane in solution H and NMR could prove ring-inversions and pseudorotation among the boat-chair conformations through the twist-boat-chair intermediate to very low temperatures (100 K). Only about 6% of the cydooctane could be found at about 300 K in the other three crown-family... 

Anet and Anet reserve the name pseudorotation for interconversion of the same conformational type and have given a detailed description of ring inversion and pseudorotation in their review. It is likely that the discussion of ring inversion and pseudorotation in any particular case will describe and illustrate the processes being referred to, so the author s meaning will be clear. 

Dioxocane (13a) appears similar to (12) in that n.m.r. coalescence and dipole moment data are consistent with enantiotopic BC(1,3) and BC(1,3 ) conformations. However, replacement of methylene groups by further oxygen atoms is expected to introduce destabilizing transannular repulsions, and for (13b) and (13c) symmetrical crown, twist-BC and twist-CC forms become important.In contrast, tetrathiocane (13d) is assigned, from n.m.r. data, a BC conformation with low barriers to ring inversion and pseudorotation (singlet, — 170°C, 251 MHz), and this conformation persists in the solid state [cf. X-ray data of other heterocyclic systems of type (13) where crown forms are preferred]. Energy barriers for conformational processes within the system (14) have also been reported. ... 

Dynamic NMR shows the presence of two conformations in 1,3,5,7-tetroxocane a crown and a boat-chair. The equilibrium constant is strongly solvent and temperature dependent, with the highly symmetrical crown, which has a high dipole moment, having a lower entropy than the boat chair by about 6 J K-1 mol-1 (72JA1390,1389). Hie interconversion barrier is 50 kJ mol-1, and no ring inversion nor pseudorotation process has been detected in the boat-chair. 

An explanation could be achieved by the consistent application of the mechanistic concepts used to explain data at tetravalent phosphorus compounds (48). Most of the available data on nucleophilic displacements are usually explained by an apical entry of the nucleophile displacement of the leaving group occurs from an apical position (Scheme 3). The first invoked TBP intermediate is the most stable one on the basis of the relative apicophilicity of the groups attached to phosphorus the more electronegative ligands prefer apical positions. Since both inversion and retention can proceed, the retention pathway has been rationalized on the basis of intramolecular ligand exchange by pseudorotation (Scheme 3). 

Independently on the final result the stereochemical course of SPDE catalyzed hydrolysis of argue against the presumption, that "all enzymatic reactions at phosphorus proceed with inversion and that, therefore, they occur without pseudorotation at phosphorus" /18/. 

The extended definitions for ring inversion and (ring) pseudorotation will be used in the present chapter, unless stated to the contrary. These definitions are independent of mechanism, unUke Hendrickson s usage of... 

The dipolar structure (rdipolar interactions without correction for vibrations, but in which slower motions, if present (e.g., the rotation of methyl groups and the interconversion of conformers such as ring inversion or pseudorotation), have been accounted for. 

This situation was presaged by Westheimer (1980), who stated ... that all enzymic reactions at phosphorus proceed with inversion and therefore they occur without pseudorotation at phosphorus. The argument for such a statement is based on two tenets first, the molecular motion caused by pseudorotation may require a conformational change of the enzyme to accommodate this movement secondly, a pseudorotation pathway will require a multistep mechanism. For example, the cyclization step of the reaction catalysed by ribonuclease may be postulated to involve pseudo-... 

The internal symmetry number is defined as the number of different but indistinguishable atomic arrangements that can be obtained by internal rotations around single bonds, or other intramolecular processes such as pyramidal inversion, Berry pseudorotation and ring circumrotation (in the case of catenanes). It is implied that the processes giving rise to the internal symmetry number are fast with respect to the time scale in which the equilibrium in Eq. [34] is attained and measured. For example, staggered... 

Only a few of these populated conformational types are symmetrical and in the absence of all symmetry there will be two sets of n conformations for each type. In each set a labelled CH2 group will occupy successively each of the n different positions in the conformation, and interconversion of the n-members of the set is a pseudorotation. The second pseudorotating set comprises the enantiomers of each member of the first set and the interconversion of the two sets is a different pseudorotation invariably called a ring inversion. The simplification is complicated enough and pseudorotation and ring inversion are discussed further in the next section. 

It is interesting to note that many of the techniques developed in phosphorus chemistry are npw being routinely applied to hypervalent molecules of other elements. For instance, Martin et al. have studied the pseudorotational (Berry) mechanism for the inversion of 10-Si-5-siliconates (1) by 19F n.m.r. and demonstrated a linear correlation between AG for inversion at silicon and the a values of the variable ligand, Y The energy barriers for... 

From the pseudorotating transition state the inversion process proceeds via an intermediate minimum of D2-symmetry (twist-conformation) and across a symmetry-equivalent second pseudorotational transition state to the inverted chair-conformation. The symmetric boat-form of cyclohexane (symmetry C2v) corresponds to a one dimensional partial maximum, i.e. a transition state (imaginary frequency 101.6 cm-1). It links sym-... 

Fig. 18. Top transition coordinates (with symmetry species) of conformational transition states of cyclohexane (top and side views). Hydrogen displacements are omitted. The displacement amplitudes given are towards the C2v-symmetric boat form, and towards >2-symmetric twist forms (from left), respectively. Inversion of these displacements leads to the chair and an equivalent T>2-form, respectively. Displacements of obscured atoms are given as open arrows, obscured displacements as an additional top. See Fig. 17 for perspective conformational drawings. Bottom pseudorotational normal coordinates (with symmetry species) of the Cs- and C2-symmetric transition states. The phases of the displacement amplitudes are chosen such that a mutual interconversion of both forms results. The two conformations are viewed down the CC-bonds around which the ring torsion angles - 7.3 and - 13.1° are calculated (Fig. 17). The displacement components perpendicular to the drawing plane are comparatively small. - See text for further details.

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