Dextrorotation and levorotation

Dextrorotation and levorotation (also spelled laevorotation)[1] are terms used in chemistry and physics to describe the optical rotation of plane-polarized light. From the point of view of the observer, dextrorotation refers to clockwise or right-handed rotation, and levorotation refers to counterclockwise or left-handed rotation.[2][3]

A chemical compound showing dextrorotation in a polarimeter. From the perspective of the observer, the plane is rotated to the right (clockwise).

A chemical compound that causes dextrorotation is called dextrorotatory or dextrorotary, while a compound that causes levorotation is called levorotatory or levorotary.[4] Compounds with these properties consist of chiral molecules and are said to have optical activity. If a chiral molecule is dextrorotary, its enantiomer (geometric mirror image) will be levorotary, and vice versa. Enantiomers rotate plane-polarized light the same number of degrees, but in opposite directions.

Chirality prefixes

(+)-, (−)-, d-, l-, D-, and L-

A dextrorotary compound is often prefixed with "(+)-" or "d-". Likewise, a levorotary compound is often prefixed with "(−)-" or "l-". These lowercase "d-" and "l-" prefixes are distinct from the SMALL CAPS "D-" and "L-" prefixes, which are most often used to distinguish chiral organic compounds in biochemistry and are based on the compound's absolute configuration relative to (+)-glyceraldehyde, which is the D-form by definition. The prefix used to indicate absolute configuration does not necessarily imply the prefix used to indicate chirality in the same molecule. For example, nine of the nineteen L-amino acids naturally occurring in proteins are, despite the L- prefix, actually dextrorotary (at a wavelength of 589 nm), and D-fructose is sometimes called "levulose" because it is levorotary.

(R)- and (S)-

The (R)- and (S)- prefixes from the Cahn–Ingold–Prelog priority rules are different from the preceding ones in that the R and S labels characterize the absolute configuration of a specific stereocenter, rather than of a whole molecule. A molecule with just one stereocenter can be labeled R or S, but a molecule with multiple stereocenters needs more than one label, for example (2R,3S).

If there is a pair of enantiomers, each with one stereocenter, then one enantiomer is R and the other is S; one enantiomer is levorotary and the other is dextrorotary. However, there is no general correlation between these two labels. In some cases the (R)-enantiomer is the dextrorotary enantiomer, and in other cases the (R)-enantiomer is the levorotary enantiomer. The relationship can only be determined on a case-by-case basis with experimental measurements or detailed computer modeling.[5]

Specific rotation

A standard measure of the degree to which a compound is dextrorotary or levorotary is the quantity [α], known as the specific rotation. Dextrorotary compounds have a positive specific rotation, while levorotary compounds have a negative specific rotation. Any pair of enantiomers have equal but opposite specific rotations.

The formula for specific rotation, [α], is

[\alpha ]={\frac {\alpha }{c\cdot l}},

where:

α = observed rotation (in degrees),

c = concentration of the solution of an enantiomer (in g/ml),

l = length of the polarimeter tube (in decimeters).

The degree of rotation of plane-polarized light depends on the number of chiral molecules that it encounters on its way through the tube of the polarimeter (thus, the length of the tube and concentration of the enantiomer). In many cases, it also depends on the temperature and the wavelength of light that is employed.

Other terminology

The equivalent French terms are dextrogyre and levogyre. These are used infrequently in English.[6]

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References

The first word component dextro- comes from the Latin word dexter, meaning "right" (as opposed to left). Laevo- or levo- comes from the Latin laevus, meaning "left side".
LibreTexts Chemistry – Polarimetry
"Determination of optical rotation and specific rotation" (PDF). The International Pharmacopoeia. World Health Organization. 2017. ISBN 9789241550031.
Solomons, T.W. Graham; Fryhle, Graig B. (2004). Organic Chemistry (8th ed.). Hoboken: John Wiley & Sons, Inc.
See, for example,Stephens, P. J.; Devlin, F. J.; Cheeseman, J. R.; Frisch, M. J.; Bortolini, O.; Besse, P. (2003). "Determination of absolute configuration using calculation of optical rotation". Chirality. 15: S57–64. doi:10.1002/chir.10270. PMID 12884375.
For example: Sebti; Hamilton, eds. (2001). Farnesyltransferase inhibitors in cancer therapy. p. 126. ISBN 9780896036291. Retrieved 2015-10-18.

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[word-1] The first word component dextro- comes from the Latin word dexter, meaning "right" (as opposed to left). Laevo- or levo- comes from the Latin laevus, meaning "left side".

[2] LibreTexts Chemistry – Polarimetry

[3] "Determination of optical rotation and specific rotation" (PDF). The International Pharmacopoeia. World Health Organization. 2017. ISBN 9789241550031.

[Solomons,_T.W._Graham_2004-4] Solomons, T.W. Graham; Fryhle, Graig B. (2004). Organic Chemistry (8th ed.). Hoboken: John Wiley & Sons, Inc.

[Stephens-5] See, for example,Stephens, P. J.; Devlin, F. J.; Cheeseman, J. R.; Frisch, M. J.; Bortolini, O.; Besse, P. (2003). "Determination of absolute configuration using calculation of optical rotation". Chirality. 15: S57–64. doi:10.1002/chir.10270. PMID 12884375.

[6] For example: Sebti; Hamilton, eds. (2001). Farnesyltransferase inhibitors in cancer therapy. p. 126. ISBN 9780896036291. Retrieved 2015-10-18.