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92 Stereochemistry

including NMR in a chiral solvent or with a chiral com- been superseded by the simpler to interpret CD (Nakanishi
plexing agent, or by chromatography of unmodified enan- et al., 2000). While it might appear that plane-polarized
tiomers on a chiral stationary phase. The methods just light is achiral, it may actually be considered to be a su-
described provide the mole fractions of each individual perposition of right- and left-circularly polarized light in
enantiomer, which may be expressed as an enantiomer which the sense of polarization changes as a right-handed
ratio (n + /n − or n − /n + ). However, because optical pu- or left-handed helix along the direction of propagation of
rity had been used in the past, it is more common to the light beam. If the right- and left-circularly polarized
use an expression for “enantiomeric excess” (e.e.): e.e. = beams proceed at the same speed, the result is light polar-
|(n + − n − )|/(n + + n − ). Since this represents the mole ized in an unchanging plane, but if one of the two generat-
fraction of the major enantiomer diminished by that of the ing beams moves faster than the other, the plane of polar-
minor one, it is equal to the above-defined optical purity. ization will keep turning as the light propagates, i.e., there
Although there is no direct relation between sign of will be optical rotation. Since the speed of light depends
rotation and configuration, it may now become possible on the refractive index of the medium it traverses, the
to infer configuration from optical rotation data (Kondra, polarization is thus caused by unequal refractive indices
Wipf, and Beratan, 1998). The method is based on van’t for right- and left-circularly polarized light. There are de-
Hoff’s “optical superposition” rule, which says that in a vices that can produce right- and left-circularly polarized
molecule containing several chiral centers, the total molar light beams separate from each other. Using such beams,
rotation ( = 100α/MW) is the sum of the contributions it is found that not only the refractive indices, but also
of each chiral center. As originally proposed the rule had the absorption coefficients for the two beams differ. The
several shortcomings, including (1) that it would require phenomenon resulting from this difference in absorption
model compounds of known absolute configuration to de- is called “circular dichroism” and manifests itself in what
termine the contribution of a given chiral center and (2) looks similar to an absorption curve in the UV, except that
it does not hold when the centers are close to each other it is signed. (In fact its maximum or minimum occurs at
and thus influence each other’s contributions. This second the wavelength of the UV maximum.) Comparison of CD
limitation means that for closely connected chiral centers, absorption spectra can be used to infer configuration sim-
it is necessary to determine the contribution of a segment ilarly as was the case for ORD; however, CD spectra are
containing all of these centers. The first problem is being better resolved than ORD spectra since there is less band
attacked by performing a priori computations of the mo- overlap resulting from multiple UV absorption maxima.
lar rotation contribution of individual chiral centers or ap- CD is also very useful in throwing light on confor-
propriate groupings thereof (Kondra, Wipf, and Beratan, mation. Thus the (weak) CD absorption spectrum of a
1998). This is becoming possible due to the advances in random-coil polypeptide chain is essentially a superposi-
quantum chemical calculations (e.g., by density functional tion of the spectra of the individual constituting amino
methods) and the increasing power of computers to handle acids. However, when secondary structure comes into
computationally demanding problems. play, as in an α helix of β-pleated sheet, a large and char-
Other chiroptical techniques to infer configuration are acteristic increase in CD absorption is observed, which, in
optical rotatory dispersion (ORD) and circular dichroism turn, allows one to infer the nature of the secondary struc-
(CD). ORD relates to the change in optical rotation with ture, if any. CD is used to infer not only protein but also
the wavelength of the light employed in the measure- nucleic acid and polysaccharide conformation (Fasman,
ment. Normally the absolute value of rotation increases 1996).
as wavelength becomes shorter; observation at shorter
wavelengths is thus a convenient way to increase rota- XIV. PROCHIRALITY
tion (and thereby the accuracy of measuring it) when α D
is small. However, as the wavelength approaches that of a The phenomenon of prochirality (Mislow and Raban,
UV absorption band (e.g., of C O in a ketone), its abso- 1967) is important both in NMR spectroscopy and in
lute value (whether positive or negative) suddenly drops enzyme chemistry. An atomic center (e.g., a tetrahedral
precipitously, passes through zero near the UV absorp- carbon atom) in a molecule is considered “prochiral” if
tion maximum, reverses sign rapidly approaching another replacing one of two identical ligands at the center by a
extremum (of opposite sign to the first), and then gradu- different one not previously attached to that center pro-
ally declines. This phenomenon of rapid change at the UV duces a chiral center. Thus the carbon atom in CH 2 ClBr
maximumiscalledthe“Cottoneffect”aftertheFrenchsci- is prochiral since hypothetical replacement of one of the
entist who discovered it. Similarity in Cotton effects of re- hydrogen atoms by deuterium yields CHDClBr, which
lated compounds, one of known and one of unknown con- is chiral. The apparently identical (or “homomorphous,”
figuration, can sometimes be used to assign the configura- from Greek “homos,” same, and “morphe,” form) hy-
tion of the unknown. However the use of ORD has largely drogen atoms in CH 2 ClBr are in fact distinct; they are