Patai S., Rappoport Z. 1997 The chemistry of functional groups. The chemistry of double-bonded functional groups / 0155 260

American Chemical Society]

tert-butyladamantan-2-one, gives relatively stronger Cotton effects (Figure 8)21. Application of the octant rule places the perturbers in an upper left (or lower right) negative front octant. Although an axial methyl perturber sometimes makes a negative contribution and sometimes a positive at 25 °C, the Cotton effects are uniformly strongly negative at low temperatures21. The temperature and solvent effects seen for the ˇ-axial-methyl group, which lies close to the third nodal surface, have been ascribed to restricted rotation and solvent perturbation of the CDO chromophore or vibronic effects21.

D. Octant Consignate and Dissignate Perturbations

Kirk and Klyne assigned the term octant ‘consignate’ to apply to those groups or locations obeying the octant rule, and octant ‘dissignate’ where the octant rule is not obeyed44. Following an extensive analysis of decalones and analogues43, they also proposed a somewhat different model to use in predicting Cotton effect signs and magnitudes, adopting the view espoused by Hudec and colleagues45 48 that interactions from the hydrocarbon chains outside the chromophore (rather than direct perturbative action on the carbonyl group) dominate the contributions to Cotton effect. They believed that the ‘through-bond’ interactions are quite sensitive to chain conformations and reach appreciable values only when a planar (W-zig-zag) path can be traced along the bonds from the carbonyl group to the dissymmetrically placed substituent. Using this approach, Kirk and Klyne integrated

FIGURE 9. Carbon W-coupling (zigzag) paths shown in heavy lines for octant consignate perturbers: CH3 of (a) and C-6, C-7, C-8 of (b). Octant dissignate perturbers [the angular CH3 of (c) and axial CH3 of (d)] do not lie on a primary zigzag coupling path. [Modified from Figure 10.11 in D. A. Lightner, Chap. 10 in Reference 15. Reproduced by permission of VCH Publishers, Inc., Deerfield Beach, FL]

data for cis- and trans-decalones and the ‘anti-octant’ compounds of Snatzke22,36 into a single empirical scheme, but the shape of the third nodal surface was more difficult to assess49.

Perturbers lying on a primary zig-zag (Figure 9) are said to make octant consignate contributions to the ketone n ! Ł Cotton effect and obey the octant rule43,49. Perturbers not lying on a primary zig-zag make octant dissignate contributions and give front octant or ‘anti-octant’ effects. This analysis places considerable importance on bond couplings in the framework and a lesser importance on octant ‘perturbers’ and therefore offers a complementary perspective to that expressed in the octant rule. Recently a qualitative MO analysis was developed to explain both the enhancement of magnitude and the bathochromic shift of n ! Ł transitions of carbonyl compounds which adopt a planar zig-zag as ‘W’ conformation50.

E. Qualitative Completeness

One of the basic tenets of the octant rule is that atoms or groups lying in the symmetry planes do not contribute to the Cotton effect. Among the problems recognized quite early by Moffitt and colleagues16 in applying the rule included the undefined shape of the third nodal surface (approximated as a plane) and the effect of unforeseen distortions from the ‘idealized’ geometries typically employed. The shape of the nonsymmetry-derived third nodal surface was described by theory20 and experiment51 as concave and cutting behind the carbonyl carbon (B, Figure 1) a surface which divides quadrant space into octant space and explains many previously noted dissignate (or ‘anti-octant’) contributions of normal perturbers. Problems associated with distortion from the ‘idealized’ geometry were less well recognized or investigated. For example, it may be noted that the octant symmetry planes (XZ and YZ, Figures 1 and 4) are derived from the local symmetry (C2v) of the CDO chromophore and are therefore only approximations when the molecular symmetry does not coincide with the local symmetry of the chromophore. Thus, for chair cyclohexanone only the XZ octant plane coincides with both a CDO local symmetry plane and the molecular symmetry plane. In contrast, the YZ octant plane is no longer a molecular symmetry plane. Consequently, the CDO local symmetry breaks and the YZ surface is only approximately a plane. In 3(e)-methylcyclohexanone, which has no planes of symmetry (and therefore no molecular symmetry coincident with the local symmetry of the CDO group), the XZ octant surface is also only approximately a plane (Figure 2). In fact, distortion from planarity of the CDO local symmetry-derived octant surfaces (XZ and YZ, Figures 1 and 4) will follow for all chiral molecules; yet the octant rule still works because most perturbers lie far from the octant ‘planes’. However, when a perturber lies close to an octant surface, anomalous behavior may be anticipated51. A good example is (1S,5S)-dimethyladamantan-2-one (Figure 10), which has both methyl

FIGURE 10. (a) (1S,5S)-Dimethyladamantan-2-one and its octant projection diagram. (b) CD spectra in cyclopentane ( ) and 2,2,2-trifluoroethanol (- - - - -) at 18 °C; the ε D 0 baseline is the CD of the racemic ketone. Data are corrected to 100% e.e. [Modified from Figure 10.17 in D. A. Lightner, Chap. 10 in Reference 15. Reproduced by permission of VCH Publishers, Inc., Deerfield Beach, FL]

perturbers lying in octant symmetry planes. Although optically active, the n ! Ł Cotton effect predicted by the octant rule is zero52,53. Despite the octant rule prediction, the CD data clearly reveal a weak monosignate negative Cotton effect. The Cotton effect remains negative, and its intensity is essentially invariant down to 150 °C.

The apparent discrepancy with the octant rule predictions was anticipated ten years previously in a theoretical paper of Yeh and Richardson54, who explained how a dimethyladamantanone CD might be reconciled with the octant rule. Although the one-electron perturbation model of n ! Ł optical activity in chiral ketones provides the simplest and most direct rationalization for the octant rule, it may be insufficient to account for optical activity when carried out only to first order. That is, in first-order perturbation only (additive) pairwise interactions between the CDO group and dissymmetric perturbers are considered. At this level the octant rule lacks qualitative completeness, but when the one-electron model is carried to higher-order perturbation, multiplicative terms contribute to the n ! Ł Cotton effect. Thus, a ketone such as the dimethyladamantanone of Figure 10 are predicted in first-order one-electron perturbation theory (octant rule) to have zero optical activity. However, it is predicted to be optically active in second-order perturbation, which accounts for three-way interactions among the two CH3 perturbers and the CDO chromophore. Qualitatively, this means that each CH3 group of the dimethyladamantanone destroys each of the two planes of symmetry (octant symmetry planes) in the C2v local symmetry of the CDO chromophore. One way to understand the octant or quadrant symmetry planes is that they are only approximately planes, except for molecules with C2v symmetry, e.g. adamantanone. Any deviation from planarity will depend on the nature and location of the perturbing group. And while such deviations are not important for more qualitative applications of the octant rule, they can in fact be detected and analyzed in carefully chosen molecules.

168 Stefan E. Boiadjiev and David A. Lightner

F. Isotopic Perturbers

Prior to about 20 years ago, there were very few examples where the octant rule had been applied to interpret the n ! Ł Cotton effects of chiral ketones with isotopic perturbers. Then for a period of about 10 years a significant effort was brought to bear on this aspect of isotopic stereochemistry. By the mid-1980s research efforts in this area essentially ceased but left behind a large body of CD data55. The first attempt to study the influence of isotopic substitution focussed on deuterium as a perturber of the ketone carbonyl n ! Ł Cotton effect56; however, no difference could be detected between the ORD spectra of 3ˇ-acetoxy-6ˇ-deuteriocholestan-7-one and its protio analogue. (Results derived by difference measurements of large values are not entirely satisfactory, especially since the two systems measured must be of the same concentration and optical purity, and they must have identical geometries.) Subsequently, Djerassi and Tursch57 attempted the first direct measurement of a ketone Cotton effect where chirality was due to a single deuterium perturber, viz. where the protio analogue is achiral. They prepared (3S)-deuteriocyclopentanone of known absolute configuration and measured its ORD spectrum but found no rotation (<42°) down to 280 nm. Subsequently, Meyer and Lobo58 determined that (C)-camphor-9,9,9-d3 had a molecular amplitude 3% smaller than that of the protio analogue. From this observation and the fact that deuterium has an atomic refractivity less than hydrogen, the authors concluded that deuterium, like fluorine24,59, makes an octant-dissignate contribution.

The first monoketone n ! Ł Cotton effect due solely to deuterium was observed in a later reinvestigation of (3R)-deuteriocyclopentanone which showed it to have a weak

ε302 D 0.021 ( 196 °C) . This result indicated that deuterium is an octant-dissignate

perturber and led to a flowering of interest in the CD Cotton effects of conformationally mobile61 63 and locked64 cyclic deuterio ketones. In those papers, deuterium was typically but not always64,65 found to exhibit an octant-dissignate effect and also to prefer the more hindered (axial) configuration relative to hydrogen62.

Investigations of the CD of ˛-axial and ˛-equatorial deuteriocyclohexanones on the chair conformation anchored by a 4-isopropyl group (Table 2) indicate that an ˛-axial D is a dissignate perturber and an ˛-equatorial D is a consignate octant perturber55. Although both are very weak perturbers, the magnitude of the octant contribution from an ˛-axial deuterium is an order of magnitude larger than that from an ˛-equatorial.

Similarly, studies on ˛-axial and ˇ-equatorial deuteriocyclohexanones couched in the rigid adamantanone framework (Table 2)21,66 indicate that a ˇ-equatorial deuterium makes an octant-dissignate contribution. A ˇ-axial deuterium is found to be an octant-dissignate perturber, with reference to the original octant rule. CD data on the deuterioadamantanones were confirmed in endo-and exo-deuterio-7-norbornanones67 (Table 2). Endo- and exo- deuterium atoms in norbornanones lie in octant positions very similar to those occupied by ˇ-equatorial and ˇ-axial deuterium atoms (respectively) in adamantanone. The octant dissignate contribution from ˇ-equatorial deuterium was confirmed in 4-tert- butylcyclohexanone. However, opposite to that of adamantanones, a ˇ-axial deuterium behaves as a weak consignate octant perturber in 4-tert-butylcyclohexanone64,68. A ˇ- equatorial or endo deuterium gave a much larger octant contribution than ˇ-axial or exo, and a theoretical explanation for the dissignate contributions has been offered67. Although deuterium is generally a dissignate octant perturber, the most notable exception to this trend is the consignate contribution of an ˛-equatorial deuterium55,68, which is located close to an octant nodal plane, a region of sign change. These investigations of deuterium octant contributions in conformationally immobile ketones provided reliable estimates of the sign and magnitude of the perturber’s contribution to the n ! Ł CD

Cotton effect for deuterium ˛ and ˇ positions of chair cyclohexanone. And application of those data to conformationally mobile systems led to the interesting stereochemical conclusion that deuterium prefers the more sterically crowded axial configuration in 3- deuteriocyclohexanone55,69.

Octant contributions from an ˛-deuterium were explored further in conformationally rigid, symmetric ketones: bicyclo[3.2.1]octan-3-one and bicyclo[3.1.1]heptan-3-one. Substitution of ring hydrogen by deuterium is not expected to lead to skeletal distortions from their Cs symmetry. Thus the deuterium atom may be viewed as the lone dissymmetric octant perturber that controls the sign and magnitude of the CD Cotton effect. ˛-Axial deuterioketones (entries 6 and 7) show negative n ! Ł Cotton effects (Table 3). Even a quasi-axial deuterium (entry 5) lying in an upper left or lower right back octant makes an octant-dissignate contribution, albeit with a smaller magnitude. Similarly, in entry 4 where the deuterium perturber lies in a negative back octant, an octant-dissignate positive CD is observed. Even as the ˛-deuterium tilts toward an equatorial location (as in entry 3)72, it still makes an octant-dissignate contribution. However, as the D C˛ CDO torsion angle closes to 20° (entry 2)71 and adopts the characteristic smaller angle associated with an equatorial position, the deuterium perturber becomes octant consignate. Therefore, it would appear that an ‘equatorial’ deuterium is an octant-consignate perturber up to D C˛ CDO torsion angles lying between 20° and 37°, at which point it becomes an octant-dissignate perturber. The reason for this is not entirely clear.

G. Applications of the Octant Rule

The octant rule has been invaluable to the determination of absolute configuration3 15. Illustrations of its utility may be found in a wide variety of ketones, from monocyclic to polycyclic. In the following, applications to decalones illustrate its usefulness and the concept of additivity of octant contributions. For example, (5S)-trans-1-decalone, (a) of Table 4, is predicted to have a negative n ! Ł CD Cotton effect. According to its octant projection diagram, carbons 1, 2, 4, 8, 9 and 10 all lie on carbonyl symmetry planes (Figure 1), and carbons 3 and 5 lie equally disposed across a symmetry plane. These atoms are predicted by the octant rule to make no contribution to the Cotton effect, leaving atoms 6 and 7 to determine its sign. Since both lie in an upper right (or lower left) negative octant, a net negative Cotton effect is predicted in agreement with that observed ( ε ' 1.0). The presence of an angular methyl at C (10), as in (b) of Table 4, leads to a positive Cotton effect. Since the ring atoms of decalone (b) make the same contribution as in those of (a), it is the angular methyl group that causes the sign reversal. The angular methyl is close to the carbonyl group, much closer than carbons 6 or 7, and in an ˛-axial position. It can therefore be expected to act as a stronger octant perturber. An ˛-axial methyl group on cyclohexanone probably contributes ε ' C1.7 when the ˛-axial methyl lies in a positive octant, as in (b).

Octant projection diagrams for the 2- and 3-ketodecalins, (c) and (d) of Table 4, are very similar. The octant locations of the ring atoms are identical, with carbons 7, 8 and 9 in (c) and carbons 6, 7 and 8 in (d) lying in a positive back octant. Since the other ring atoms lie on octant planes, or have counterparts across an octant plane, they make no contribution to the Cotton effect. One would therefore expect a net positive n ! Ł CD coming from both carbocyclic skeletons. The methyl perturbers either lie in an octant plane, as in the angular methyl of (d); or they lie (barely) in a front octant, as in the angular methyl of (c); or they lie distant from the CDO but still in a positive back octant, as in the C(9) methyl of (c). Thus the net CD Cotton effect contributions in decalones (c) and (d) are positive and nearly identical in magnitude, as is observed.

The ring carbons of the trans-4-oxodecalin, (e) of Table 4, lie in the same back octants as those of trans-1-decalone (a): These perturbers should thus sum to a negative CD. The

TABLE 3. Reduced rotatory strengths [R] and D C˛ CDO torsion angles for the n ! Ł transition of ˛-deuterioketones

O

a [R] D rotatory strength ð 1.08 ð 10 40, corrected to 100% ee. and ˛ 100% D and measured at 25 °C.

b Values from Reference 69.

c Measured in isooctane solvent. d Value from Reference 71.

e Value from Reference 70.

f Measured in CF3CH2OH solvent.

g Measured in EPA (ether:isopentane:ethanol, 5:5:2, v/v/v) solvent.

h The value in EPA ( 0.3) is thought to be low due to H exchange for D occurring during isolation (Reference 64).

only difference between (e) and (a) is the presence of a ˇ-axial methyl in the former. ˇ-Axial methyls are known from earlier work on adamantanones to be weak dissignate perturbers. Consequently, the Cotton effect in (e) is predicted to have the same negative sign as (a), with a slightly smaller magnitude. The observed CD Cotton effect of (e) is negative and only slightly smaller than that of (a).