Chiral Molecules with Two Stereogenic Centers How many stereoisomers when a particular molecule contains two stereogenic centers?

2,3-Dihydroxybutanoic acid What are all the possible R and S combinations of the two stereogenic centers in this molecule? O CH 3 CHCHCOH HOOH 2 3

2,3-Dihydroxybutanoic acid What are all the possible R and S combinations of the two stereogenic centers in this molecule? O CH 3 CHCHCOH HOOH 2 3 Carbon-2RRSS Carbon-3RSRS

2,3-Dihydroxybutanoic acid 4 Combinations = 4 Stereoisomers O CH 3 CHCHCOH HOOH 2 3 Carbon-2RRSS Carbon-3RSRS

2,3-Dihydroxybutanoic acid 4 Combinations = 4 Stereoisomers What is the relationship between these stereoisomers? O CH 3 CHCHCOH HOOH 2 3 Carbon-2RRSS Carbon-3RSRS

2,3-Dihydroxybutanoic acid O CH 3 CHCHCOH HOOH 2 3 Carbon-2RRSS Carbon-3RSRS enantiomers:2R,3R and 2S,3S 2R,3S and 2S,3R

HO CO 2 H CH 3 H OH H R R CO 2 H CH 3 H H HO OH S S enantiomersenantiomers CO 2 H H CH 3 HO H HO R S CO 2 H CH 3 H OH OH H R S enantiomersenantiomers [  ] = -9.5° [  ] = +9.5° [  ] = -17.8° [  ] = +17.8°

2,3-Dihydroxybutanoic acid O CH 3 CHCHCOH HOOH 2 3 Carbon-2RRSS Carbon-3RSRS but not all relationships are enantiomeric stereoisomers that are not enantiomers are diastereomers

Isomers stereoisomers constitutionalisomers diastereomers enantiomers

HO CO 2 H CH 3 H OH H R R CO 2 H CH 3 H H HO OH S S enantiomersenantiomers CO 2 H H CH 3 HO H HO R S diastereomersdiastereomers CO 2 H CH 3 H OH OH H R S enantiomersenantiomers [  ] = -9.5° [  ] = +9.5° [  ] = -17.8° [  ] = +17.8°

Achiral Molecules with Two Stereogenic Centers It is possible for a molecule to have stereogenic centers yet be achiral.

2,3-Butanediol Consider a molecule with two equivalently substituted stereogenic centers such as 2,3-butanediol. CH 3 CHCHCH 3 HOOH 3 2

Three stereoisomers of 2,3-butanediol 2R,3R 2S,3S 2R,3S chiralchiralachiral

Three stereoisomers of 2,3-butanediol 2R,3R 2S,3S chiralchiral these two are enantiomers

Three stereoisomers of 2,3-butanediol 2R,3S achiral the third structure is superposable on its mirror image

Three stereoisomers of 2,3-butanediol 2R,3S achiral therefore, this structure and its mirror image are the same it is called a meso form a meso form is an achiral molecule that has stereogenic centers

Three stereoisomers of 2,3-butanediol 2R,3S achiral meso forms have a plane of symmetry and/or a center of symmetry plane of symmetry is most common case top half of molecule is mirror image of bottom half

Molecules with Multiple Stereogenic Centers

maximum number of stereoisomers = 2 n where n = number of structural units capable of stereochemical variation structural units include stereogenic centers and cis and/or trans double bonds number is reduced to less than 2 n if meso forms are possible How many stereoisomers?

Example 4 stereogenic centers 16 stereoisomers O HOCH 2 CH—CH—CH—CHCH OHOHOHOH

HO OH H H HO H3CH3CH3CH3C H H CH 2 CH 2 CO 2 H CH 3 H 11 stereogenic centers 2 11 = 2048 stereoisomers one is "natural" cholic acid a second is the enantiomer of natural cholic acid 2046 are diastereomers of cholic acid Cholic acid

maximum number of stereoisomers = 2 n where n = number of structural units capable of stereochemical variation structural units include stereogenic centers and cis and/or trans double bonds number is reduced to less than 2 n if meso forms are possible How many stereoisomers?

Stereochemistry Consider 1,3-dibromocyclopentane. Since it has two stereogenic centers, it has a maximum of four stereoisomers. Disubstituted Cycloalkanes Recall that a disubstituted cycloalkane can have two substituents on the same side of the ring (cis isomer, A) or on opposite sides of the ring (trans isomer, B). These compounds are stereoisomers but not mirror images.

Stereochemistry To find the other two stereoisomers if they exist, draw the mirror images of each compound and determine whether the compound and its mirror image are superimposable. Disubstituted Cycloalkanes The cis isomer is superimposable on its mirror image, making the images identical. Thus, A is an achiral meso compound.

Stereochemistry The trans isomer is not superimposable on its mirror image, labeled C, making B and C different compounds. B and C are enantiomers. Disubstituted Cycloalkanes Because one stereoisomer of 1,3-dibromocyclopentane is superimposable on its mirror image, there are only three stereoisomers, not four.