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# Enantiomeric excess

Enantiomeric excess exists where one enantiomer is present more than the other in a chemical substance.

Such a mixture of two enantiomers, unlike a racemic mixture, will show a net optical rotation. It is possible to determine the specific rotation of the mixture and with knowledge of the specific rotation of the pure enantiomer the enantiomeric excess $\ ee$ can be determined.

$\ ee = ([\alpha]_{obs}/[\alpha]_{max})*100%$ (1)

The enantiomeric excess can be determined in another way if we know the amount of each enantiomer produced. If one knows the moles of each enantiomer produced then:

$\ ee = ((R-S)/(R+S))*100%$ (2)[1]

$\ R$ and $\ S$ are the respective fractions of enantiomers in a mixture such that

$\ R + S = 1$

For example, in a sample with 40% ee in R, the remaining 60% is racemic with 30% of R and 30% of S, so that the total amount of R is 70%. Direct determination of these quantities is possible with NMR spectroscopy and chiral column chromatography.

For mixtures of diastereomers the same treatment leads to diastereomeric excess.

The term enantiomeric excess was introduced in 1971 by Morrison and Mosher in their publication Asymmetric Organic Reactions. Many practical observations challenge the supposed relationship and equality of equations 1 and 2:

• the specific rotation of (S)-2-ethyl-2-methyl succinic acid is found to be dependent on concentration
• in what is known as the Horeau effect the relationship between mole based ee and optical rotation based ee can be non-linear i.d. in the succinic acid example the optical activity at 50% ee is lower than expected.
• the specific rotation of enantiopure 1-phenylethanol can be enhanced by the addition of achiral acetophenone as an impurity.

The use of enantiomeric excess has established itself because of its historic ties with optical rotation. It has been suggested that the concept of ee should be replaced by that of er which stands for enantiomeric ratio or er (S:R) [2] or q (S/R) because determination of optical purity has been replaced by other techniques which directly measure R and S and because it simplifies many mathematical treatments. The same arguments are valid for changing diastereomeric excess (de) to diastereomeric ratio (dr).

## References

1. ^ According to http://www.iupac.org/goldbook/E02070.pdf, the pattern (2) is incorrect. ee cannot reach the negative values, so the absolute value of (R-S) must be taken.
2. ^ Do the Terms "% ee" and "% de" Make Sense as Expressions of Stereoisomer Composition or Stereoselectivity? Robert E. Gawley J. Org. Chem.; 2006; 71(6) pp 2411 - 2416; doi:10.1021/jo052554w