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              Stereochemistry                                                                              91

                                                                conformations of which the envelope (four carbon atoms
                                                                in a plane, one out of plane) and the half-chair (three ad-
                                                                jacent carbons in a plane, the fourth above that plane and
                                                                the fifth below) are the most symmetrical. The barrier be-
                                                                tween these conformations is very low; thus their rapid
                                                                interconversion, which involves up-and-down motions of
                                                                successive adjacent carbon atoms, has the appearance of
                    FIGURE 14  Conformation of 3β-cholestanol.
                                                                a bulge moving around the rings; this process has there-
                                                                fore been named “pseudorotation.” Higher cycloalkanes
                                                                from C(7) on display families of conformations which
              about 42 kJ/mole and interconversion of the two conform-
                                                                are separated by barriers similar to those in cyclohexane,
              ers is extremely rapid at room temperature. Thus chloro-
                                                                but within a given family there may be several individual
              cyclohexane (Fig. 15, X = Cl) exists in rapid equilibrium
                                                                members interconverted by pseudorotation. This subject
              between axial and equatorial conformers which differ in
                                                                is discussed in detail in Eliel and Wilen (1994).
              free energy by only about 25 kJ/mole, corresponding to
                                                        ◦
              74% of the equatorial and 26% of the axial isomer at 25 C.
              As expected, in the infrared spectrum there are two C−Cl
              stretch frequencies, but in the laboratory, chlorocyclohex-  XIII. CHIROPTICAL PROPERTIES.
              ane, even though a mixture of two conformers, appears as a  ENANTIOMERIC PURITY
              homogeneous substance with the average properties (such
              as chemical shifts in NMR) of the two conformers. When  By “chiroptical properties” are meant optical properties
                                         ◦
              one cools the substance to ca. −60 C (the exact tempera-  that differ between enantiomers and can be used to char-
              ture required depends on the operational frequency of the  acterize them. They comprise optical rotation, optical ro-
              NMR instrument), however, two different NMR spectra  tatory dispersion (ORD), and circular dichroism (CD).
              begin to emerge, and at −150 C the equatorial conformer  Optical rotation has already been discussed. Because
                                     ◦
                                                                of its critical dependence on solvent (including cosol-
              has actually been crystallized from trideuteriovinyl chlo-
                                                                vents, such as ethanol in chloroform), temperature, con-
              ride solution, with concomitant enrichment of the axial
                                                                centration, and the potential presence of impurities, es-
              isomer in solution.
                                                                pecially chiral impurities, in the sample, experimental
                Equilibria for a large number of monosubstituted cyclo-
                                                                determination of [α] requires considerable care and many
              hexanes have been determined and tabulated; they were
              mostly determined by low-temperature  13 C NMR spec-  of the values given in the literature cannot be trusted. This
                                                                is unfortunate since it is often desirable to determine the
              troscopy (Eliel and Wilen, 1994).
                                                                “enantiomeric purity” of a sample to see whether the de-
                The conformations of piperidine (azacyclohexane) and
                                                                sired enantiomer is obtained free of the other. (For exam-
              tetrahydropyran (oxacyclohexane) are qualitatively simi-
                                                                ple, in pharmaceutical chemistry one wants to obtain the
              lar to those of cyclohexane. (Some quantitative differences
                                                                pure eutomer free of the distomer; see above.) Since in all
              are seen, for example, in the equatorial preferences of
                                                                but a few cases optical rotation is proportional to the frac-
              some substituents resulting from dipolar interactions with
                                                                tion of the major enantiomer in the total substance, one
              the ring hetero atom and from the fact that C–N and C–O
                                                                might expect enantiomeric or optical purity to be equal to
              distances are shorter than C–C in cyclohexane.) These
              ring systems are important, being found in alkaloids and  100[α obs ]/[α max ]%, where [α max ] is the (presumed known)
              hexose sugars, respectively.                      specificrotationofanenantiomericallypuresample.How-
                Because of torsional (eclipsing) strain, cyclobutane and  ever, this is true only if both values have been accurately
              cyclopentane are not planar. Cyclobutane is wing-shaped;  determined under exactly the same conditions (solvent,
              cyclopentane oscillates among a number of low-energy  temperature, etc.).
                                                                  Because of this difficulty, other, more reliable methods
                                                                of determining enantiomeric purity (now no longer called
                                                                “optical purity”) have been developed. Basically these de-
                                                                pend on converting the enantiomers into diastereomers,
                                                                either by covalent chemical bonding or by complexing
                                                                in some fashion, with another, usually enantiomerically
                                                                pure chiral auxiliary. (For some methods the auxiliary
              FIGURE 15 Conformational inversion of substituted cyclohex-
              ane.  [Reprinted  with  permission  from  Eliel,  E.  L.,  and  Wilen,  need not even be enantiomerically pure.) Once the enan-
              S.  H.  (1994).  “Stereochemistry of Organic  Compounds,”  Wiley,  tiomers have been converted into diastereomers, their ratio
              New York.]                                        can be determined by NMR or chromatographic methods,
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