Cyclohexane pseudorotation

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.

Spherical polar coordinates are used for conformational representation of pyranose rings in the C-P system. Unlike the free pseudorotation of cyclopentane, the stable conformations of cyclohexane conformers are in deeper energy wells. Even simong the (less stable) equatorial (6 = 90 ) forms, pseudorotation is somewhat hindered. Substitutions of heteroatoms in the ring and additions of hydroxylic or other exocyclic substituents further stabilize or destabilize other conformers compared to cyclohexane. A conformational analysis of an iduronate ring has been reported based on variation of < ) and 0 (28), and a study of the glucopyranose ring... 

Figure 3. The conformational sphere for pyranoid rings. The perfect chairs are at the north and south poles (0=0 and 180 , respectively). The boat and skew (B and S designations) at the equator permit pseudorotation that is slightly hindered, at least for cyclohexane. The envelopes, E (also called sofas and half-boats), and half-chairs, H, are not observed for rings coiqposed of saturated carbon and oxygen atoms, but are iiqportant forms for rings with unsaturated carbon atoms. The aiqplitude of puckering corresponds to the radius of the sphere.

The value of q3 = (6) V2R (R is the CC bond length) is 0.63 A. Under pseudorotation the equatorial boat-shaped structures B (0 = 90°, = 0, 60°, 120°,.. . ) turn into a twist-boat structure TB (0 = 90°, = 30°, 90°,.. . ). The transitions between the chair and twist boat structures involve the intermediate formation of half boat (HB) and half chair (HC) structures. Quantum chemical calculations carried out by Dixon and Komornicki [1990] show that the axial structure C with symmetry D3d is stable. The energies of structures B and TB are 7.9 and 6.8kcal/mol higher than C. The barrier for transition from C to TB is 12.2-12.4 kcal/ mol. Because of the high barriers for pseudorotation, only thermally activated conformational transitions occur in cyclohexane. 

Note Added in Proofs. There has been additional work on the calculation of conformational energies for cyclohexane, see Section II. Wiberg and Boyd 129) conclude that non-bonded interactions make little contribution to the barrier, the most important component of which is torsional strain, in agreement with earlier work. Quantum mechanical calculations of various conformations which do not by their nature allow a spUtting of energies into Bayer strain, Pitzer strain, and van der Waals strain, have also been made I30,i3i), it has been concluded 12D that transition state conformations 1 and 2 are of similar energies i. e. that there is pseudorotation in the transition state as proposed by Pickett and Strauss 29,30),... 

Ring inversion (when strictly defined) of achiral conformations is nothing more than a pseudorotation. Ring inversion in the cyclohexane chair, for example, leaves the molecule apparently rotated by 60° along the C3 axis. Nevertheless, in order to conform with common usage, we will exclude ring inversion from the definition of ring pseudorotation. 

The symmetric puckered conformations of cyclopentane are the Cs symmetric envelope (E) (10) with four carbon atoms in a plane and the C2 s)mrmetric twist (T) (11) with three carbon atoms in a plane [88]. Unlike cyclohexane, these conformations are of almost equal energy and are separated by barriers of about RT or less [89]. There are ten envelope conformations, each with one of the five carbon atoms out of the plane in one of the two directions, and ten corresponding twist conformations. The individual conformations freely exchange which atom or atoms are out of the plane, a process termed pseudorotation, and the whole sequence of conformations is called the pseudorotational itinerary (O Fig. 9). 

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... 

Cyclic alkanes undergo pseudorotation because rotation by 360° is not possible. Pseudorotation in cyclic alkanes leads to many conformations. Cyclopropane is planar, with relatively weak banana bonds. The lowest energy conformation of cyclobutane is a puckered conformation. The lowest energy conformation of cyclopentane is an envelope conformation. The lowest energy conformation of cyclohexane is an equilibrating mixture of two chair conformations. 

By this analysis, planar cyclopentane should be most stable, then cyclohexane, cyclobutane (which is about the same as cycloheptane), and finally cyclopropane. However, this is not the correct order for the inherent stability of cyclic alkanes. The energy inherent to each ring is shown in Table 8.1. The data in this table clearly show that cyclopropane is the highest in energy, but they also show that cyclohexane is lower in energy than cyclopentane. Indeed, cyclopentane and cyclohexane are the more stable (lowest energy) cyclic alkanes in the series 45-49 because cUc alkanes are not planar. The pseudorotation mentioned before leads to conformations that are lower in energy than... 

Cyclohexane has one more carbon atom than cyclopentane and the greater flexibility allows for significant pseudorotation. Just as with smaller rings, the planar form of cyclohexane (48A) is very high in energy, and it has both Baeyer... 

Two drawings are provided that appear to be different chair conformations 48B and 48F. The Cl and C4 carbon atoms are marked in both structures Cl in 48B is up whereas Cl is down in 48F. Likewise, C4 is down in 48B but up in 48F. Conformations 48B and 48F are identical in structure and shape, and they are identical in energy. Twisting the bonds (pseudorotation) in cyclohexane will interconvert 48C into 48F and back again. In other words, chair conformations 48B and 48F are in equilibrium and because they are of the same energy, the equilibrium constant (K q see Chapter 7, Section 7.10.1) is unity (K q = 1). This means that there is a 50 50 mixture of 48C and 48F. The equilibrium constant (Kgq) for this molecule is defined as K q = [48F]/[48B], where [48C] and [48F] are the molar concentrations of each conformation. 

Make a model of chair cyclohexane 48B, take hold of the up carbon (Cl), and twist it down. Then, take hold of the down carbon (C4) and twist it up. This exercise will generate chair conformation 48F. If the model is held by two adjacent carbon atoms and twisted back and forth in a rotational motion, this action mimics pseudorotation about that bond. This exercise generates both chair conformations, along with many others. 

The chair forms of cyclohexane are the lowest energy conformations and that planar cyclohexane is probably the highest in energy. There are other conformations of cyclohexane and the most important are those that occur during the pseudorotation of one chair to another. 

Previous sections described the relevant conformations of cyclohexane. As the size of the ring in cyclic alkanes increases, there is more conformational flexibility and more conformations must be considered. The focus will be on a few conformations in order to make one or two key points. The larger cavity formed by the seven-membered ring and the extra carbon in the ring (relative to cyclohexane) should lead to great flexibility for pseudorotation. As with cyclohexane. 

This flattening is due to the presence of an odd niimber of carbons in the ring and it means that there will be some torsion strain due to eclipsing bonds and atoms in this form of cycloheptane. Some twisting of the ring can occur to relieve this strain, but such pseudorotation may increase strain elsewhere in the molecule. This increase in strain makes conformations 49A and 49B for cycloheptane higher in energy than the chair conformations of cyclohexane. 

---