The most important aspect of a CD curve is the sign of theCotton Effect. Apart from numerous assessments of the sign andmagnitude of the Cotton Effect for particular chromophores, usingmostly MO-based theory, many applications use one of manysemiempirical rules: sector rules for achiral chromophores andhelicity rules for chiral chromophores. These are summarizedbelow.
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Whenever chiroptic atoms or groups are present in a moleculecontaining an achiral chromophore, perturbation of the electronictransitions of the chromophore will be sufficient to generatechiroptical properties (i.e. a Cotton Effect). The name sector rulestems from the division of 3D space surrounding symmetricchromophores into sectors by nodal or symmetry planes as well as bynodal surfaces. Such rules are designed to assess the contributionsof perturbing groups to the sign of the Cotton Effect according totheir positions in one or another sector that surrounds thechromophore. Thus, the sign of the Cotton Effect depends on severalfactors, including the nature of substituents, configuration andconformation. In general, any two of three structural descriptorsconstitution, configuration and conformation must be known if thethird is to be deduced from chiroptical spectra (CD or ORD).Therefore, in general, for chiral molecules having torsionaldegrees of freedom (free rotation), it is not possible to acquireinformation on both configuration and conformation simultaneouslyfrom chiroptical spectra. This is why much work in this area hasbeen concentrated on cyclic systems, often fused systems, astorsional isomerism is limited in these molecules.
Sector rules are widely used in the assignment of configurationby inspection of CD spectra of homologous and analogous compoundsthat have an identical chromophore. It is essential to know thenature of the transition in each case, since only comparabletransitions can be treated in such a way. It is also necessary toknow the transition symmetry properties of the chromophore and whateffect structural features have upon the strength of the CDband.
The octant rule is the most widely applied sector rule. It wasdeveloped from an earlier rule, known as the axial haloketone rule,based on ORD measurements carried out on steroidal ketones that hadbeen (axially) substituted with a halogen atom at the (-carbon.Axial substitution (conformation) is often preferred because of thedipole-dipole repulsions in the equatorial isomer:
It was suggested that prediction of the sign of the CottonEffect is possible if the ketone group is viewed along the O=C bondin the direction of the ring with the carbonyl carbon at the headof the chair (the major conformer in cyclohexane ring systems). Ifthe axial (halogen is found on the right (as in the(S)-enantiomer), then there exists a positive Cotton Effect; if itappears on the left, a negative Cotton effect is observed, as shownbelow.
In the example below, a negative Cotton Effect is seen uponbromination of the cyclic fused ring ketone. Therefore,substitution must have occurred predominantly at the 5 position.The axial nature of bromine atom in the product was deduced from IRspectroscopy.
On chlorination of (R)-(+)-3-methylcyclohexanone, a crystalline2-chloro-5-methyl product is isolated that shows a negative CottonEffect in octane, but a positive one in methanol. The negative CEis consistent only with trans stereochemistry, with independentevidence for axial Cl (in octane).
expected. The 2(-bromo isomer unexpectedly shows a negative CE.This is best explained by supposing the boat conformer issignificant in ring A of this isomer, because of steric hindrancebetween the (axial) methyl groups in the chair conformer.
The axial haloketone rule is a special case of the octant rulefor saturated ketones. A set of left-handed Cartesian coordinatesis drawn through the carbonyl group with its origin at the centerof the bond and with the z axis collinear with the bond, as shownbelow. The coordinate system divides the space around the carbonylgroup into 8 sectors or octants (diagram (a)). The effect on the CEassociated with the n-(* transition of the carbonyl group is givenby the position of a substituent (as a product of its coordinates)in these segments (in practice, the rear segments are moreimportant). Thus, a substituent in the bottom right rear sector(diagram (b)) would have coordinates x, +y, -z and so would give apositive CE.
The octant rule was first applied to fused cyclohexanone ringsystems, such as those in steroids, because of their conformationalrigidity. The cyclohexanone skeleton is placed in the coordinatesystem as shown below, with the 2 and 6 carbon atoms in the yzplane and the carbonyl at the head of the chair (diagram (a)).
Diagram (b) shows the projection of the view along O=C with thesigns of the rear octants. Contributions from hydrogens in thesimple cyclohexanone skeleton are usually ignored, being assumed tomore or less cancel. Substituents at position 4 will have no effecton the CE, since either equatorial or axial groups here in thenodal xz plane. Likewise, equatorial groups at positions 2 and 6will make only small contributions to the CE, because of theirproximity to the yz plane.
The compound (R)-(+)-3-methylcyclohexanone exhibits a positiveCotton Effect. Application of the octant rule to the projections ofthe equatorial and axial conformations (below) indicate clearlythat the preferred conformer is the equatorial one.
When applying the octant rule to ketosteroids, the sector withmost carbons in it will make the biggest contribution to the signof the Cotton Effect. Hence, the octant rule can be used toestimate the relative magnitudes of the CE for isomeric 1-, 2- and3-cholestanones. The three isomers and their octant ruleprojections are shown below, where it can be seen that for the1-keto isomer, the balance of carbons in negative sectors isgreater, indicating a moderate negative CE. The 2-keto isomerprojection shows a majority of carbons in the + sector indicating alarge positive CE, whereas that of the 3-keto isomer has a smallmajority of carbons in the + sector (and many on the xz plane,contributing zero), suggesting a very small positive CottonEffect.
The octant rule is one of the first and arguably the most effective of the several chirality sector rules that connect the cotton effect to organic stereochemistry. It establishes an absolute configuration or stereochemistry from the sign and intensity of the cotton effect and is unquestionably the most well-known and often-utilized rule.
The Octant rule for cyclohexanone is one of the most studied types. The cyclohexanone molecule, with its well-known geometry and fixed conformations, was the first compound in which the octant rule was followed. The cyclohexanone molecule is oriented in the three-dimensional coordinate system, or three orthogonal planes A, B, and C. These planes basically split the carbonyl group into eight sectors in the same way as described above and are shown in the figure below:
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