# Dextrorotation and levorotation

Dextrorotation

Dextrorotation and levorotation (also spelled as laevorotation)[1] are terms used to describe the rotation of plane-polarized light. From the point of view of the observer, dextrorotation refers to clockwise rotation while levorotation refers to counterclockwise rotation.[2][3]

A 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 are said to have optical activity and consist of chiral molecules. If a chiral molecule is dextrorotary, its enantiomer (geometric mirror image) will be levorotary, and vice versa. The enantiomers will 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 "(+)-" or "d-". Likewise, a levorotary compound is often prefixed "(−)-" or "l-". These lowercase "d-" and "l-" prefixes are distinct from the SMALL CAPS "D-" and "L-" prefixes, which are based on the absolute configuration relative to (+)-glyceraldehyde, which is defined as 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 sometimes called "levulose" because it is levorotatory.

### (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, 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; 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 called the specific rotation [α]. Dextrorotary compounds have a positive specific rotation, while levorotary compounds have negative. Any pair of two enantiomers have equal but opposite specific rotations.

The formula for specific rotation, [α], is

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

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 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 infrequently used in English.[6]