A sample of a compound in which all the molecules are of the same enantiomer is now
“optically pure,” although the terms “enantiopure” and “homochiral” are still encoun- tered.33 A sample of a compound containing more of one enantiomer than the other is now
“enantiomerically enriched.” It is still most usual to describe such compounds in terms of the enantiomeric excess, ee, although a case has now been made for “enantiomer ratio,”
er, in its place.34 This is gaining in popularity. The enantiomeric excess of a compound is defined as the ratio of the specific rotation of the sample to the maximum specific rotation of the same compound, where the specific rotation is
α α
[ ]λ5 cl
T for solids, [ ]αλT5lαρ and for liquids,
where α is the observed rotation, is the path length in dm, c is the concentration of the solute in g mL–1, and ρ is the density of a pure liquid in g mL–1. Because the behavior or the specific rotation is not necessarily linear with concentration, it is important to note the concentration of the sample. This corresponds to the difference between the fractions of the two enantiomers in the sample or to the amount of one enantiomer present in excess of the racemate:
Optical purity = {[ ]αTλ(obs)/ [ ]αλT(max)} × 100% = {(% major enantiomer) – (% enantiomer)} = major enantiomer in total – % racemate in total
33. (a) Review: Raban, M.; Mislow, K. Top. Stereochem. 1967, 2, 199. (b) For a discussion of the use and abuse of stereochemical terms, see Eliel, E.E. Chirality 1997, 9, 428.
34. Gawley, R.E. J. Org. Chem. 2006 71, 2411.
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For example, optically pure (+) glyceraldehyde has a specific rotation of +14°. Thus, a sample of glyceraldehyde with a specific rotation of +7.0° is (7.0/14) 100 = 50% optically pure. It may be viewed as consisting of a mixture of 50% (+) glyceraldehyde and 50% (±) glyceraldehyde, or 75% (+) glyceraldehyde and 25% (–) glyceraldehyde.35 The optical purity of a compound can be measured by a variety of methods, of which NMR spectroscopy36 and chromatography on a chiral stationary phase37 have become the most widely used. The use of these techniques, which provide the ratio of the enantiomers (or diastereoisomers) directly, prompted a reevaluation of the use of the terms enantiomeric excess (e.e.) and diastereoisomeric excess (d.e.)38 as well as the suggestion that the e.e. be replaced by the enantiomer ratio (e.r.) as a more useful measure of the composition of a mixture of enantiomers.
Before we proceed further, we need to discuss the nature of plane-polarized light, which is responsive to chirality, in more detail. In plane-polarized light, the electric vector of the radiation oscillates in a single plane, but its chiral nature may be viewed as arising from the superimposition of two waves of circularly polarized light, one left- handed, and one right-handed (Figure 2.7). In circularly polarized light, the electric vector describes a helix along the direction of propagation of the wave. If the two circu- larly polarized waves are passed through an achiral medium, they emerge unchanged at the end, and the plane of polarization remains unchanged. If the same plane-polarized wave is passed through a chiral medium, however, the two circularly polarized waves will interact differently with the medium. If the medium has different refractive indices for right and left circularly polarized light, for example, the wave emerging from the medium will again be plane polarized, but the plane of polarization will have been rotated by an amount proportional to the difference between the two refractive indices. The angle of rotation per unit path length is α π
λ
( )
5 nL2nR , where nL and nR are the refractive indices for the left and right circularly polarized light, respectively, and λ is the wavelength of the light.39 Just as the refractive indices of right circularly and left circularly polarized light
35. This method does require that be independent of concentration: Horeau, A. Tetrahedron Lett. 1969, 3121.
36. (a) Raban, M.; Mislow, K. Tetrahedron Lett. 1965, 4249; 1966, 3961. (b) Jacobus, J.; Raban, M. J. Chem.
Educ. 1969, 46, 351. (c) Tokles, M.; Snyder, J.K. Tetrahedron Lett. 1988, 29, 6063. (z) Review: Parker, D. Chem.
Rev. 1991, 91, 1441.
37. Gas chromatography: (a) Halpern, B.; Westley, J.W. Chem. Commun. 1965, 246. (b) Vitt, S.V.; Sapor- ovskaya, M.B.; Gudkova, I.P.; Belikov, V.M. Tetrahedron Lett. 1965, 2575. (c) Guett, J.; Horeau, A. Tetrahedron Lett. 1965, 3049. (d) Westley, J.W.; Halpern, B. J. Org. Chem. 1968, 33, 3978.
High-performance liquid chromatography: Pirkle, W.H.; Finn, J. In Morrison, J.D., Ed. Asymmetric Synthe- sis, Vol. 1 (Academic Press: New York, 1983), p. 87.
38. (a) Selke, R.; Facklam, C.; Foken, H.; Heller, D. Tetrahedron: Asymmetry 1993, 4, 369. (b) Seebach, D.;
Beck, A.K.; Schmidt, B.; Wang, Y.M. Tetrahedron 1994, 50, 4363. (c) Gallagher, D.; Du, H.; Long, S.A.; Beak, P.
J. Am. Chem. Soc. 1996, 118, 11391.
39. Fresnel, A. Ann. chim. phys. [2] 1825, 28, 147.
Figure 2.7 Differential refraction of waves of circularly polarized light leads to observed rotation of the plane of plane-polarized light.
polarizationleft right
polarization nL > nR
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are different in a chiral medium, so, too, are their extinction coefficients for absorption.
This results in plane-polarized light becoming elliptically polarized on passing through a chiral medium. The measurement of differential absorption of right and left circularly polarized light is the basis of the technique of circular dichroism (CD). CD is expressed in terms of the molar ellipticity, θ, which is related to the difference in absorbance (∆A) for right and left circularly polarized light by θ = 3238(∆A). The tangent of the ellipticity, tan θ, is related directly to ∆A. CD is especially important in biochemistry, where it is used to probe the conformations of biological molecules such as nucleic acids and proteins. The CD spectrum of (1R)-camphor-10-sulfonic acid (1 mg/mL in water) is shown in Figure 2.8.
The specific rotation of a substance depends both on the temperature and wave- length at which the measurement is made. Most measurements are made using the sodium D line (589.0 nm). This sharp, bright line in the sodium atomic spectrum has long been easy to obtain. The measurement of the specific rotation over the range of wavelengths from the visible to the ultraviolet (UV) gives a spectrum known as the optical rotatory dispersion (ORD) curve. ORD spectra of a group of four steroids40 are shown in Figure 2.9.
In a plain ORD curve, the specific rotation changes monotonically with wavelength.
In ORD curves with an anomalous Cotton effect, the magnitude of the rotation initially increases as the wavelength becomes shorter, and it then changes sign, passing through another maximum (or minimum).41 Typical examples of the anomalous Cotton effect are provided by the ORD spectra shown in Figure 2.9. Enantiomers exhibit mirror image ORD curves (i.e., if the ORD curve of one enantiomer exhibits a positive Cotton effect, the ORD curve of other will exhibit a negative Cotton effect).
The use of ORD curves in studying the chiroptical properties of chiral ketones led to the development of the octant rule.42 This empirical rule, which was originally devel- oped to allow the prediction of the sign of the Cotton effect from a known absolute configuration, can also be applied in the corollary sense, to determine absolute
40. Djerassi, C.; Closson, W.; Lippman, A.E. J. Am. Chem. Soc. 1956, 78, 3163.
41. (a) Cotton, A. Ann chim. phys. [7] 1896, 8. 347. (b) Mitchell, S. The Cotton Effect (G. Bell & Sons) 42. (a) Moffitt, W.; Woodward, R.B.; Moscowitz, A.; Klyne, W.; Djerassi, C. J. Am. Chem. Soc. 1961, 83, 4013.
(b) Mislow, K.; Glass, M.A.W.; Moscowitz, A.; Djerassi, C. J. Am. Chem. Soc. 1961, 83, 2771.
Figure 2.8 Circular dichro- ism spectrum of camphor- sulfonic acid (1 mg mL–1).
The vertical scale is specified as millidegrees, which is a reasonable approximation for small values of θ because tan θ ≈ θ when θ is small.
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O
H O H
H H
H O H
H H AcO
H H
H HO H O
H H
H H
O
(V) (VI)
(VIII) (IX)
(a)
300 400 500
-1000
-2000 +2000
+1000
0
-3000 +3000
Specific Rotation
Wavelength (nm)
IX
VIII
V
VI VII
IX
(b)
Figure 2.9 Optical rotatory dispersion spectra of a series of steroidal ketones
configuration of a known structure from the sign of the Cotton effect. To apply the rule, the carbonyl group of the ketone is oriented as if to draw the Newman projection with the carbonyl oxygen atom toward the observer (Figure 2.10). The middle of the C = O bond is the origin, with the plane of the sp2 orbitals and the plane perpendicular to it and containing the C = O bond (the two lines in Figure 2.10) as the first two planes. The plane perpendicular to the C = O bond is the third plane. These three planes divide the
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Figure 2.10 Octant rule for cyclohexanone derivatives
region about the C = O group into eight octants: four rear octants and four front octants.
The four rear octants make positive (lower right and upper left) and negative (lower left and upper right) contributions to the observed Cotton effect, with the corresponding front octants making the opposite contributions. However, because groups in the front octants must necessarily project forward beyond the carbonyl oxygen, they are seldom involved.43
When one examines the cyclohexanone ring using these rules, one can make some fairly straightforward predictions. Thus, by numbering the carbonyl carbon 1 and then proceeding in clockwise order around the cyclohexane ring (so that the α carbon to the left becomes position 2, and the α carbon to the right becomes position 6), one predicts that:
1. Substituents at position 3 make a positive contribution to the Cotton effect and that substituents at position 5 make a negative contribution
2. Substituents at position 4 make a minimal contribution to the Cotton effect
3. Equatorial substituents at positions 2 and 6 make a minimal contribution to the Cotton effect
4. Axial substituents at position 2 make a negative contribution to the Cotton effect, and axial substituents at position 6 make a positive contribution
Exciton Chirality and Absolute Configuration
In the early 1980s, a method known as exciton chirality method was developed for deter- mining the absolute configuration of cyclic 1,2-diols where the two OH groups are gauche to each other. It involves measuring the CD spectra of derivatives that have a groups that can absorb UV-visible light (a chromophore).44 The derivatives are defined to have positive or negative chirality based on the dihedral angle between the two chromophores, as illus- trated by structures 2.26 and 2.27 in Figure 2.11. When the dihedral angle from front to back is clockwise, the chirality is defined as positive. The technique can be used on very small scale (micro to nanomolar). The diol is esterified with an achiral aromatic acid (p-aminobenzoate esters have been especially popular), and the CD spectrum of the resulting diester (which need not even be purified) is then measured. The spectrum shows two Cotton effects near the maximum absorbance of the ester, one positive and one
43. Review of chiroptical spectroscopy: Kirk, D.N. Tetrahedron, 1986, 42, 777.
44 Monograph: Harada, N.; Nakanishi, K. Circular Dichroic Spectroscopy. Exciton Coupling in Organic Ste- reochemistry (University Science Books: Mill Valley, CA, 1983).
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negative. For molecules with “positive chirality,” the longer wavelength Cotton effect is positive, and the shorter wavelength Cotton effect is negative. The reverse is true for molecules with negative chirality (Figure 2.12).
Problems
2-13 What is the relationship (enantiomers, diastereoisomers, constitutional isomers) between the two molecules in each of the following pairs of compounds?
(d) Me Et H H MeEt (e) H Me
Et H
Me Et Et
H
Me Et
Me H (f) Me H
Et Me
H Et Et
H
Me H
Me Et
(a) Me
Pr H
Et Me
Pr H
Et (b) Me H
Et Et
Me H
Me H
Me Me
Me H (c) Me H
Et Et
Me H
Et H
Et Me
Me H
2-14 What is the relationship (enantiomers, diastereoisomers, epimers, anomers, con- stitutional isomers) between the two molecules in the following pairs of
compounds?
O O
NMe2
OO Me2N
counterclockwise: negative (2.26)
O O NMe2
OO
NMe2
clockwise: positive (2.27)
Figure 2.11 Defining positive and negative chirality
A
A
λ
positive chirality negative chirality
Figure 2.12 Predicted Cotton effects in chirality exciton method
(a) (b)
H
HO H
HO
OH HO
OH Cl
OH Cl
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(c) O (d)
HO
HO OHOH
O HO
HO OH OH OH
OH
Me Br Br
Me Br Me
Br Me
(e) (f)
OO
CHO OO
CHO
N O
Me
OHOH N
O Me
HOHO
2-15 Define the sign of the chirality of each of the following 1,2-diols as needed to pre- dict the Cotton effects in the CD spectra of their bis-p-dimethylaminobenzoate derivatives. Note that a single OH group distant from the diol has little effect on the Cotton effects.