# Dextrorotation and levorotation

Dextrorotation and levorotation

Dextrorotation and levorotation (also spelled laevorotation)[1] refer, respectively, to the properties of rotating plane polarized light clockwise (for dextrorotation) or counterclockwise (for levorotation), seen by an observer whom the light is approaching. A compound with dextrorotation is called dextrorotatory or dextrorotary[2], while a compound with levorotation is called levorotatory or levorotary[2].

Compounds with these properties are said to have optical activity and consist of chiral molecules. If a chiral molecule is dextrorotary, its enantiomer will be levorotary, and vice-versa. In fact, the enantiomers will rotate polarized light the same number of degrees, but in opposite directions.

It is not possible to determine whether a given chiral molecule will be levorotatory or dextrorotatory directly from its configuration, except via detailed computer modeling.[3] In particular, both "R" and "S" stereocenters have the ability to be dextrorotatory or laevorotatory.

## Chirality prefixes

### The prefixes "(+)-", "(–)-", "d-", "l-", "D-", and "L-"

A dextrorotary compound is often prefixed "(+)-" or "d-". Likewise, a levorotary compound is often prefixed "(–)-" or "l-". These "d-" and "l-" prefixes should not be confused with the "D-" and "L-" prefixes based on the actual configuration of each enantiomer, with the version synthesized from naturally occurring (+)-glyceraldehyde being considered the D- form. For example, nine of the nineteen L-amino acids commonly found in proteins are dextrorotatory (at a wavelength of 589 nm), and D-fructose is also referred to as levulose because it is levorotatory. See the article: Chirality (chemistry).

### The prefixes "(R)-" and "(S)-"

The R and S prefixes are different from the preceding ones in that the labels R and S characterize a specific stereocenter, not 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, and likewise 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 detailed computer modeling[3] or experimental measurements.

## Specific rotation

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

The formula for specific rotation is:

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

where: [α] = specific rotation
α = observed rotation
c = concentration of the solution of an enantiomer
l = length of the tube (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 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 occasionally (but very infrequently) used in English.[4]

## References

1. ^ The first word component dextro- comes from Latin word for dexter "right (as opposed to left)". Laevo- or levo- comes from the Latin for laevus, "left side."
2. ^ a b Solomons, T.W. Graham, and Graig B. Fryhle. Organic Chemistry. 8th. Hoboken: John Wiley & Sons, Inc., 2004.
3. ^ a b See, for example, this paper, "Determination of absolute configuration using ab initio calculation of optical rotation", by Stephens et al.
4. ^ For example: Farnesyltransferase inhibitors in cancer therapy, edited by Sebti and Hamilton, p126

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