William S. Murphy
The Octant Rule
University College
Cork, Ireland
Its place in organic stereochemistry
The chiroptical techniques, optical rotatory dispersion (0.r.d.) and circular dichroism (c.d.) are increasingly finding a place as routine tools in organic chemistry ( I ) , particularly for natural products. Although recognized for many years (2), spectropolarimetry aroused little interest until 1953. Within a few years, C. Djerassi and his collaborators a t Stanford University had investigated the 0.r.d. of more substances than in the preceding 140 years (3). In 1961 a commercial c.d. instrument became available ( 4 ) and both techniques were then developed conjointly.
(A)
(8)
Optical Rotatory Dispersion and Circular Dlchroism
Plane polarized light can be considered the resultant of in-phase mixing of right-handed and left-handed circularly polarized light of equal wavelength and intensity (5).Passage of plane polarized light through an optically active medium results in one circularly polarized component travelling faster than the other. The two components therefore emerge out of phase. The result is that the emergent plane polarized light will have its plane rotated through an angle a (observed rotation) relative to the incident plane polarized light. This effect is called circular birefringence. An 0.r.d. curve is obtained by measuring the rotation ([a] or [a])'of the sample as a function of wavelength. I t is found, however, that not only do the two circularly polarized components travel with different velocities in an optically active medium, but they also are absorbed unequally. The emergent light is not plane polarized hut elliptically polarized. The medium is said to exhibit circular dichroism. The differential dichroic absorption Ae is expressed by the equation Ar = E L
- t~
where CR and e~ are the molecular extinction coefficients for the right- and left-handed circularly polarized light. A c.d. curve is obtained by measuring A6 or the molecular ellipticity [%I2 as a function of wavelength. Any medium that exhibits circular birefringence will also show circular dichroism. Both effects are simultaneous. However, the magnitude of circular dicbroism is small except, as will now be discussed, in the immediate vicinity of the uv absorption band. The Cotton Effect and the Octant Rule
If the optically active substance adsorbs in the uv region under investigation, the substance will not only exhibit
Figure 2. A, m b i l and B, r'arbital nodal plane surfaces for saturated carbonyls.
(B)
(A)
Figure 3. A, The eight octants of space around a cyclohexanone molecule. B. The "octant projection" of cyclohexanone.
measurable c.d. but also a so-called anomalous 0.r.d. curve (Fig. 1).The substance thus exhibits a Cotton effect (6). The c.d. is characterized by the sign, Ac,.. or [O],, A,., and fine structure of the curve. The 0.r.d. curve is similarly characterized although its magnitude is called the amplitude a.3 Saturated carbonyl compounds have been investigated in great detail. They absorb weakly a t about 300 nm due to an u* transition. The n-orbital (Fig. 2 (A)) has a nodal n plane coincident with the ( x , z ) plane. The u* orbital (Fig. 2 ( B ) ) has two nodal surfaces coincident with the ( x , y)' and (z, y) planes. The three surfaces divide the space around the ketone, e.g. cyclohexanone, into eight octants (Fig. 3). The molecule is viewed from the 0 atom toward the C atom of the carbonyl group with the molecule oriented so that the remainder of the ring resides above the horizontal ( 2 , y ) plane (Fig. 3 (A)). The ring is now resident in the four rear octants. An "octant projection" of cyclohexa3 (. B..) ) .Substituents which make the none is shown (Fie. . molecule dissymmetric have the effect of perturbing the inherently symmetric carbonyl chromophore by coulomb in-
-
-
'
Figure 1. Curves A and B a r e the superimposed 0.r.d. and c.d. curves. respectively, of a substance exhibiting a positive Conon effect. Curves Cand D cOrreSDOnd to a substance with a neaative Cmon effect. The Ar,, and 0.r.d. point of inflection have the same wavelength as the uu ..A,
774 / Journal of Chemical Education
At a specified temperature and wavelength, the specific rotstion [a]= 100 a (observed rotation)/l (dm) C (g1100 ml); the molecular rotation [a] = [rr] molecular weight1100. [8] = 3300 Ar. J a = [a],,, - [~],j,/lOO. 'The e x a d nature and location of this contour remains to be discerned (7,31).
teractions of the incompletely screened nuclei of the molecule (3). The octant rule. which was emniricallv derived hut now has a theoretical basis (a), states (g) (see Pig. 3)
image relationship t o that of 4a-ethylcholestan-3-one (VI). I t was deduced that (V) and hence cafestol (IV) was enantiomeric (with respect to rings A and B) with (VI). Hydrogenation of mexicanin I (VII) (24) yielded the dihydro-de-
1) Substituents5residing in rear upper left and rear Lower right oc-
tants make positive contributions to the Cotton effect. 2) Substituentssresiding in rear unver right and rear lower left oc-
tants make negative c&ntributi&s to &e Cotton effect. 3) Substituents residing in any of the planes dividing the oetants make no contribution6to the Cotton effect. 4) Substituents residing in front oetants make contributions opposite to those outlined in rules (1)and (2).
Applications of the Octanl Rule
0.r.d. and c.d.' are the only two physical techniques which permit the study of chirality. If the conformation of the saturated ketone is established, aoolication of the octant rule leads to assignment of sb&te configuration. Conversely, if the absolute configuration is known its conformation-can he determined. -
IYIII
(VIIII
(1x1
rivative (VIII). The 0.r.d. of (VIII) had an amplitude a = +I26 which in all respects was very similar to that of androstan-17-one (IX). This provided strong evidence for the configurations of C-5 and C-6 in (VIII) and (VII). Position of Functb~nalGroups
The bromination of 2,3-seco-5a-cholestan-6-one-2,3-dioic acid led to an axial monobromination (ir and uv) product (X) (25). The location of the bromine was readily
Absolute Configuration
We shall limit our discussion. for the sake of hrevitv. .,to a small numher of examples. Of the two enantiomers of trans-l-decalone (18)the one with a neeative Cotton effect must have the absolute configuration The only atoms
h.
1x1
assigned to C-5 by the observation that (X) showed a strongly negative Cotton effect. The octant rule predicts a negative Cotton effect for a Sa-hromo- and a positive one for a la-bromo-derivative of (X). Conformational Stodies
making a significant contribution to the Cotton effect are C-5 and C-6 which lie in the rear upper right octant. The amplitude of the 0.r.d. is dependent on the relative preponderance of substituents in the positive relative to those in the negative octants. This was clearly illustrated during the determination (9) of the absolute configuration of 5a-cholestan-2-one (11) and 5n-cholestan-3-one (111). Each exhib-
(Ill
0
Although temperature dependence studies of the Cotton effect may sometimes he necessary, the preferred conformation can often he deduced from investigations a t room temperature. iso-Menthone (XI) unexpectedly exhibited a
* a
ited a positive Cotton effect from which their configurations were deduced. Comparison of the octant projections shows a high preponderance of suhstituents on (11) in a nositive octant unlike (111). This is reflected bv the ratio of the 0.r.d. amplitudes (121:55) (9). Steroidal kktones, studied in great detail, have been critically reviewed (12). Cyclohutanones (19), cyclopeutanones (20), cycloheptanones (21), and even some acyclic systems (22) also obey the octant rule. Examples of the less direct application of the octant rule are provided by the determination of the absolute configuration of two complex terpenes cafestol (IV) and
mexicanin I (VII). In order to attack the absolute configuration of cafestol (IV) (23) it was degraded to the ketone (V). I t was noted that the 0.r.d. curve of (V) bore a mirror
positive Cotton effect a t room temperature. Initially this result was considered (26) to he compatible only with a predominance of conformation (XIa). Further consideration (27) led t o the new concept and suggested involvement of the twist-boat conformation (XIc). The use of c.d. evidence for the existence of flattened chair conformations in the A-ring of 4.4-dimethyl-3-ketosteroids(XII) and tri-
terpenoids is discussed by Ourisson (28). The effects of solvent polarity (12, 29) and temperature (30)on conformaFluorine (10) and certain other electron withdrawing groups (11) show the opposite effect (12) ("anti-oetant" behavior). True only for making qualitative predictions (13). Equatorial bromine (131, methyl ( l 4 ) , isapropyl (15),and t-butyl (16) on earbons alpha to the earbonyl make small but definite contributions to the Cotton effect. The relative merits of 0.r.d. and cd. have been discussed in detail (17). Volume 52. Number 12, December 1975 / 775
tional equilibria studies by means of c.d. and 0.r.d. have been investigated in considerable detail. Recent Results and Developments
Experimental proof for the concept of front octants is now available (31). These results refute the theoretical calculations which led t o a quadrant rule (32). A recent detailed analysis (12) of the c.d. of cis- and trans-decalones and their analogues has not only clarified apparently anomolous chiroptical behavior (33) but now permits calculations of Ac and [8]. The octant rule has been extended with modifications to other chromophore~.~ With improved inv* transition strumentation (43) the chirality of the n (12) among others (44) is being investigated. Magnetic optical rotatory dispersion (m.0.r.d.) and circular dichroism (m.c.d.) are developing new areas (45).While these techniques have as yet had only limited applicability to organic stereochemistry (461, i t should be noted that they are not dependent on a chiral structure.
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