Enantiomeric Excess and Optical Purity

Sometimes we deal with mixtures that are neither optically pure (all one enantiomer) nor racemic (equal amounts of two enantiomers). In these cases, we specify the optical purity (o.p.) of the mixture. The optical purity of a mixture is defined as the ratio of its rotation to the rotation of a pure enantiomer. For example, if we have some [mostly (-1-)] 2-butanol with a specific rotation of -1-9.72°, we compare this rotation with the -1-13.5° rotation of the pure (-I-) enantiomer. 

The enantiomeric excess (e.e.) is a similar method for expressing the relative amounts of enantiomers in a mixture. To compute the enantiomeric excess of a mixture, we calculate the excess of the predominant enantiomer as a percentage of the entire mixture. For a chemically pure compound, the calculation of enantiomeric excess generally gives the same result as the calculation of optical purity, and we often use the two terms interchangeably. Algebraically, we use the following formula  

The units cancel out in the calculation of either e.e. or o.p., so these formulas can be used whether the amounts of the enantiomers are expressed in concentrations, grams, or percentages. For the 2-butanol mixture just described, the optical purity of 72% (-I-) implies that d — I = 72%, and we know that d + I = 100%. Adding the equations gives 2d = 172%. We conclude that the mixture contains 86% of the d or (-1-) enantiomer and 14% of the / or (—) enantiomer. 

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Biological Discrimination of Enantiomers 189 5-6 Racemic Mixtures 191 5-7 Enantiomeric Excess and Optical Purity 192 5-8 Chirality of Conformationally Mobile Systems 193 5-9 Chiral Compounds without Asymmetric Atoms 195 5-10 Fischer Projections 197... 

Because the observed specific rotation is positive, we know that the solution contains excess (5)-(+)-2-bromobutane. The enantiomeric excess (ee) tells us how much excess (5)-(+)-2-bromobutane is in the mixture. As long as the compound is chemically pure, enantiomeric excess and optical purity will be the same. 

The unambiguous determination of enantiomeric excess and optical purity is an important task for the characterization and application of nonracemic chiral compounds. There are two different principles available the determination of chiroptical properties such as CD, ORD, or the specific rotation [a]Jor to analyze the diastereomeric interaction with other chiral environments. The enantiomeric excess... 

For example, if a mixture consists of 75% of the R enantiomer and 25% of the S enantiomer, then the enantiomeric excess of the R enantiomer is 50%. Enantiomeric excess and optical purity are numerically identical. 

Enantiomeric excess or % ee (or % optical purity) = [observed specific rotation] divided by [specific rotation of pure enantiomer] X 100. Note that there are examples where the linear relationship between enantiomeric excess and optical rotation fails. A percent enantiomeric excess (% ee) of less than 100% indicates that the compound is contaminated with the other enantiomer. The ratio of enantiomers in a sample of known (measured) optical purity may be calculated as follows fraction of the major isomer = [(% ee) + 0.5 (100 - % ee)]. Thus,... 

Since the early times of stereochemistry, the phenomena related to chirality ( dis-symetrie moleculaire, as originally stated by Pasteur) have been treated or referred to as enantiomericaUy pure compounds. For a long time the measurement of specific rotations has been the only tool to evaluate the enantiomer distribution of an enantioimpure sample hence the expressions optical purity and optical antipodes. The usefulness of chiral assistance (natural products, circularly polarized light, etc.) for the preparation of optically active compounds, by either resolution or asymmetric synthesis, has been recognized by Pasteur, Le Bel, and van t Hoff. The first chiral auxiliaries selected for asymmetric synthesis were alkaloids such as quinine or some terpenes. Natural products with several asymmetric centers are usually enantiopure or close to 100% ee. With the necessity to devise new routes to enantiopure compounds, many simple or complex auxiliaries have been prepared from natural products or from resolved materials. Often the authors tried to get the highest enantiomeric excess values possible for the chiral auxiliaries before using them for asymmetric reactions. When a chiral reagent or catalyst could not be prepared enantiomericaUy pure, the enantiomeric excess (ee) of the product was assumed to be a minimum value or was corrected by the ee of the chiral auxiliary. The experimental data measured by polarimetry or spectroscopic methods are conveniently expressed by enantiomeric excess and enantiomeric... 

What happens for a nonracemic mixture of enantiomers Is it possible to calculate the values of the chiral properties of the solution from knowledge of the properties of the enantiopure compound In principle, yes, on the condition that there is no autoassociation or aggregation in solution. Then, the observed properties will be simply the weighted combination of the properties of two enantiomers. A nice example of where this normal law may be broken was discovered by Horeau in 1967 it is the nonequivalence between enantiomeric excess (ee) and optical purity (op, with op = [a]exi/[ ]max) for 2,2-methylethyl-succinic acid. In chloroform op is inferior to ee, while in methanol op = ee. This was explained by the formation of diastereomeric aggregates in chloroform, while the solvation by methanol suppresses the autoassociation. 

We therefore quickly turned our attention to the ruthenium-catalyzed asymmetric transfer hydrogenation recently reported by Noyori. Without any optimization, 95% yield and 96% e.e. were obtained with 0.25 mol% catalyst and formic acid-triethylamine 5 2 azeotropic mixture (2.5 mL/g) in CH2CI2 at room temperature for 8 h (Scheme 6.17). - Apart from the high yield, enantiomeric excess, and turnover, this procedure is particularly simple to carry out. It also allows an easy recovery of the optically active amine by filtration, as its formiate salt at the end of the reaction, if needed, would offer an additional improvement in optical purity. 

In view of their importance in asymmetric synthesis new routes have been developed to chiral sulphoxides and related species. Sulphinates, useful as precursors of chiral sulphoxides, have been prepared in 40-70% enantiomeric excess and the synthesis and dieno-philic properties of the isomeric sulphinyl acrylates (2l8) and (219) (Ar = 4-MeCgH ) have been described. ( )-Vinyl sulphoxides have been prepared in high optical purity via 1-alkynyl... 

These are given wherever possible, and normally refer to what the Carbohydrates contributor believes to be the best characterised sample of highest chemical and optical purity. Where available an indication of the optical purity (op) or enantiomeric excess (ee) of the sample measured follows the specific rotation value. 

Fill a 0.5-dm polarimeter cell with your chiral hydroxyester (about 2 mL required). You may need to combine your product with material obtained by one other student in order to have enough material to fill the cell. Determine the observed optical rotation for the chiral material. Your instructor will show you how to use the polarimeter. Calculate the specific rotation for your sample using the equation provided in Technique 23. The concentration value, c, in the equation is 1.02 g/mL. Using the published value for the specific rotation of ethyl (S)-(-l-)-3-hydroxybutanoate of [ d ] = +43.5°, calculafe fhe optical purity (enantiomeric excess) for your sample (see Technique 23, Section 23.5). Report the observed rotation, the calculated specific rotation, the optical purity (enantiomeric excess), and the percentages of each of the enantiomers to the instructor. How do the percentages of each of the enantiomers calculated from the polarimeter measurement compare to the values obtained from chiral gas chromatography ... 

Due to the presence of some methylene chloride in the sample of the chiral amine, you may obtain low rotation values from polarimetry. Because of this, your calculated value of the optical purity (enantiomeric excess) and percentages of the enantiomers will be in error. The percentages of the enantiomers obtained from the optional chiral gas chromatography experiment below should provide more accurate percentages of each of the stereoisomers. 

Traditionally and even today, polarimetry is used in many laboratories for control of optical purity. However, this method suffers from some well-known specific drawbacks. Furthermore, often calculation of the enantiomeric excess from optical rotation is impossible, because the specific rotation of the pure enantiomer is not known precisely, or calculated enantiomeric excess values may be wrong owing to impurities. For these reasons direct chromatographic analytical procedures are preferred. 

Although optical and enantiomeric purities are usually equated, this is not necessarily correct. Indeed it was with (1) that the inequivalence of enantiomeric purity and optical purity was first demonstrated unequivocally. If optical rotation does not vary linearly with concentration (and this may occur even in polar solvents) then an alternative method for measuring enantiomeric excess must be sought. 

Several synthetic methods have appeared in which derivatives of amino-acids have been reacted with strong base and then with carbon electrophiles. This process has been used in the a-hydroxymethylation of SchifI bases derived from a-amino-acid esters and good yields of /3-hydroxy-a-amino-acids are obtained. This type of compound is also prepared using the optically active imine (183) the t/trco-product was obtained with selectivity ranging from 58 to 92% and optical purity between 43 and 71% (Scheme 88). The jS-hydroxy-a-amino-acid (185) is a constituent of the antibiotic bleomycin and its preparation from L-rhamnose has been described. Studies on the asymmetric synthesis of amino-acids by alkylation of various lactim ethers (186) have continued. L-Alanine, L-valine, and (S)-0,0-dimethyl-a-methyldopa have been used to prepare the heterocyclic intermediates (186), which give a range of amino-acids in high yield and enantiomeric excess. Earlier work has also been extended to the alkylation of the imidazolone anion (187). ... 

The 2,3-epoxy alcohols are often obtained in high optical purity (90% enantiomeric excess or higher), and are useful intermediates for further transformations. For example by nucleophilic ring opening the epoxide unit may be converted into an alcohol, a /3-hydroxy ether or a vicinal diol. 

The synthesis of 4-alkyl-y-butyrolactones 13 and 5-alkyl-<5-valerolactones 14 can be achieved in high enantiomeric excess by alkylation of ethyl 4-oxobutanoate and ethyl 5-oxopentanoate (11, n = 2, 3). The addition of diethylzinc, as well as dimethylzinc, leads to hydroxy esters 12 in high optical purity. When methyl esters instead of ethyl esters are used as substrates, the enantioselectivity of the addition reaction is somewhat lower. Alkaline hydrolysis of the hydroxy esters 12, followed by spontaneous cyclization upon acidification, leads to the corresponding y-butyro- and -valerolactones32. 

The submitters report obtaining the product in 99% yield. The enantiomeric excess of the Mosher ester of 3 was measured to be 98% using a Chiralcel OD column (40% 2-propanol/hexane). This optical purity measurement substantiated the optical purity assessment made by 111 NMR studies of 3 and racemic 3 prepared using a different method3. Addition of the chiral shift reagent tris[3-(heptafluoropropylhydroxymethylene)-(+)-camphorato]europium (III) resulted in clear resolution of the respective aromatic proton signals for the two enantiomers, which was demonstrated with the racemate. Under similar conditions, NMR analysis of 3 showed that within the detectable limits of the experiment (ca. <3%), there was none of the disfavored enantiomer. 

In an ideal DKR, where the substrate stays racemic throughout the reaction process, the optical purity depends only on the enantiomeric ratio (E) (ee =(E— 1)/ (E +1)), and is independent of the extent of conversion. The enantiomeric excess of the product formed under racemizing conditions is equal to the initial enantiomeric... 

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