Stereochemistry and Conformational Analysis

Stereospecific reactions and stereoisomer relationships

A stereospecific reaction is one in which different stereoisomers of the starting material give different stereoisomers of the product, whereas a stereoselective reaction merely favours one product among several possible ones. The key principle is that the spatial course of bond breaking and bond making fixes the geometry of the product. In an anti-periplanar elimination, the leaving groups depart from opposite faces, so the relative configuration of the two stereocentres decides whether the new double bond is E or Z. Acid-promoted Peterson olefination proceeds by anti elimination, and the diastereomers that have like descriptors give the Z-alkene in that case. Base-promoted Peterson olefination is syn elimination, so the same diastereomer gives the opposite alkene. Addition reactions follow the same logic. Syn addition of OsO4 to a cis alkene gives a meso diol, while syn addition to a trans alkene gives a racemic (dl) pair. Anti addition, as in the Prévost reaction, reverses this outcome, so anti addition to a trans alkene gives the meso diol.

The same stereochemical reasoning applies to substituted cyclohexanes. An axial leaving group is displaced by an S_N2 nucleophile faster than an equatorial one, and an axial alcohol is oxidized faster by chromic acid, whereas an equatorial hydroxyl group is less hindered toward acylation or tosylation. Enantiomeric substrates give enantiomeric products in a stereospecific reaction, and diastereomeric substrates give diastereomeric products. For example, cis-2-butene gives meso-2,3-butanediol on syn dihydroxylation, while trans-2-butene gives the racemic pair.

1H NMR signal count from symmetry

The number of {}^1H NMR signals equals the number of symmetry-distinct sets of protons. Protons that are related by a proper rotation are homotopic, and they are always equivalent in NMR. Protons that are related only by a mirror plane or an improper axis are enantiotopic, and they are equivalent in an achiral solvent. Protons that are not related by any symmetry operation are diastereotopic, and they give separate signals. Aromatic protons related by a mirror plane give one signal, and each set of equivalent methyl groups gives one singlet. For example, p-xylene shows two signals, one for the four aromatic protons and one for the six methyl protons.

Diastereotopic protons, most often the two protons of a CH_2 group next to a stereocentre, are chemically non-equivalent. They couple to each other and give an AB pattern rather than a singlet. A CH_2 group in an achiral, symmetric environment is enantiotopic, so its two protons appear as one sharp singlet.

Gauche-butane interaction counting

A gauche-butane interaction is a steric interaction between two non-hydrogen substituents on adjacent carbons that are staggered with a dihedral angle of about 60^\circ. In a cyclohexane chair, an axial substituent is gauche to the two ring carbons that lie two positions away from its attachment point, so each axial substituent gives two gauche interactions. An equatorial substituent is anti to those ring carbons and gives none. This is the origin of the preference for equatorial positions.

When two substituents are on adjacent carbons, a gauche relationship between them also counts. In the trans-1,2-dimethylcyclohexane case, the diequatorial conformer has one gauche methyl–methyl interaction, while the diaxial conformer has four gauche interactions, one for each axial methyl with the two ring carbons, and the two axial methyls are anti to each other. The difference between the two conformers is therefore three gauche interactions. The same counting logic applies to ring-fused systems. A fusion methyl group that is axial to one ring but not the other adds gauche interactions, and the cis-fused arrangement therefore carries more gauche interactions than the trans-fused one.

Topicity of diastereotopic and enantiotopic protons

Topicity describes the symmetry relationship between two identical ligands or protons on a molecule. The test is to replace one of the two protons with a dummy group, such as D, and then compare the resulting species. If the two products are identical, the protons are homotopic. If they are enantiomers, the protons are enantiotopic. If they are diastereomers, the protons are diastereotopic.

Homotopic protons are interchanged by a proper rotation, typically a C_2 axis. In a chiral molecule with a C_2 axis, the two methine protons on the carbons bearing the hydroxyl groups are homotopic. In the meso isomer of the same diacid, the two protons are instead related by a mirror plane and are enantiotopic. Enantiotopic protons are also found in a bicyclic framework where a mirror plane relates one proton to another across a bridge, whereas a proton on the other side of the molecule is related to neither and is therefore diastereotopic. In an allene, the two terminal hydrogens are enantiotopic, and replacing either one with deuterium gives opposite axial configurations. A proton that is related to a second proton by a proper rotation is homotopic, and those two protons are exchangeable without changing the molecule.

Fischer projections and sugar anomers

In a Fischer projection, the vertical bonds point away from the viewer and the horizontal bonds point toward the viewer. A carbon whose hydroxyl group is on the right is R-configured in the D series, and the configuration of the highest-numbered stereocentre defines D or L. Converting an open-chain sugar to its cyclic hemiacetal creates a new stereocentre at the anomeric carbon. The α anomer has its anomeric oxygen on the opposite face of the ring from the reference group in a Haworth projection, whereas the β anomer has it on the same face as the reference group. Fructose cyclizes to a furanose, and the ring-closing oxygen is attached to the ketone carbon, which becomes the anomeric centre.

A sugar with a free anomeric hydroxyl group can open to the open-chain aldehyde or ketone form, so its specific rotation changes over time. This change is called mutarotation, and the sugar is a reducing sugar. A disaccharide in which both anomeric carbons are tied up in the glycosidic bond cannot open and does not mutarotate. Sucrose is such a non-reducing disaccharide, and acid hydrolysis gives two different monosaccharides, glucose and fructose. Trehalose is also non-reducing, but its two units are identical, so hydrolysis gives only one monosaccharide.