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Stereoisomers are molecules with the same chemical bonds but different configurations, which cannot be interconverted without temporarily breaking one or more covalent bonds. Configuration is the spatial arrangement of atoms, and occurs either around double bonds or at single-atom chiral centers; around either these, the substituents can be attached in different orders. The result is stereoisomers which are configurationally different, intuitively acknowledged as not capable of being superimposed.

There are different categories of stereoisomers, categorized according to their structural differences: geometric (cis-trans) isomers; enantiomers, which are mirror images; and diasteromers, which are not mirror images. Given the importance of sterochemistry in biochemistry, there are three conventions for specifying spatial arrangement around a chiral center. Of note, conformational isomers simply involve rotation around a single bond, and are not stereoisomers because they can be interconverted without breaking bonds.

Chiral CenterA chiral center is the atom around which the attached substituents can be arranged differently to create a structural different molecule (ie, the different molecules cannot be superimposed). The number of stereoisomers possible in a molecule with one or more chiral centers is 2n, where n is the number of chiral centers; for instance, a molecule with one chiral (assymetric) carbons will have 2 stereoisomers, while another molecule with two chiral carbons will have 4 stereoisomers.
Chiral MoleculeA chiral molecule can be readily identified as follows: if its reflection in a mirror cannot be superimposed, then the molecule is chiral. The substituents attached to the chiral center(s) can be rearranged to create a stereoisomer. However, the isomers will be related as the right hand is to the left.
Achiral MoleculeAn achiral molecule only has one structure; no matter how the substituents are shifted around a given atom in the structure, the results can always be superimposed on one another.
EnantiomerStereosiomers which are mirror images of one another. They behave nearly identically chemically, but differ in optical rotation. Molecules without chiral centers will not rotate plane-polarized light. However, two enantiomers will rotate polarized light, though in opposite directions. Thus, an equimolar solution of two enantiomers (a racemic mixture) will exhibit no rotation of plane-polarized light.
DiastereomersPairs of stereoisomers that are not mirror images of one another.
Geometric IsomersAlso known as cis-trans isomers, these differ in their orientation of functional groups around two carbons double-bonded to one another as in the example below.

RS System of Notating Stereochemistry

For a chiral center with all single bonds attached, the best notation is the RS system. First, the substituents are assigned priorities based on their atomic number: first by the atom closest to the chiral center (for instance, H would have 1, the lowest priority; C would have 6; and N would have a yet higher priority of 7); if two substituents' closest atom is identical, then the sums of the second atoms on are considered (for instance, -COOH would be higher priority than -COH because 6 + 17 is of higher priority than 6 + 9).

In the RS system, a chiral center's handedness is R (for Latin rectus, right) or S (for Latin sinister, left). To draw out the structure, begin by drawing the lowest priority functional group pointing away from the viewer. The remaining three functional groups all point toward the viewer. The three remaining are drawn in increasing order of priority clockwise in the R orientation, and counter-clockwise in the S orientation. Thus, the RS system specifies stereochemistry by assigning handedness based on a priority system ordered by atomic number.