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I have many confusions regarding optical isomerism:

What is the use of the R/S nomenclature? I understand that it is used to distinguish between the different spacial arrangements that are possible for a molecule, but i have few questions.

  • I believe R/S nomenclature can only be used for a chiral center. Now, say we have a two chiral center molecule, so there are 4 types of different molecules (because 4 different configurations are possible) are possible, according to me, (R,R), (R,S),(S,S),(S,R). Am i right? Are all these 4 molecules different?

  • I am getting confused when we introduce chirality here. If the molecule is achiral then will some of the above four become the same molecule? If the compound is chiral, will all the above 4 be different from each other?

  • Generalizing, if a molecule has n chiral center, will it always have $2^{n}$ different isomers, irrespective of whether it is chiral or not, or am I wrong in thinking so? Please correct me

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An environment around an atom may be chiral (stereogenic centre, or chiral centre). A molecule including one, or multiple chiral centres may but does not need to be chiral.

You are right that the presence of two chiral centres ($n = 2$) may yield four permutations, namely (R,R), (R,S), (S,R), or (S,S). However, depending on the overall structure of the molecule in question, $2^n$ is the maximum number of different molecules.

Take the example of tartaric acid with two chiral centers and start the permutation of the absolute configuration at C(2) and C(3). The two configurations of (2R,3S) and (2S,3R)-tartaric acid are identical to each other and represent the meso form of tartaric acid. Despite the environment around the atoms is chiral, the molecule of the meso-isomer is not chiral.

enter image description here

(derived from here)

If you have a model kit at hand, build the molecules in question. For each conformation of the mesoisomer, the lower part of the Fischer formula is transferred into the upper part of the Fischer formula by a mirror plane. The presence of either a mirror plane (in the drawing indicated by the horizontal dashed line), or a centre of inversion however is incompatible with the molecule's structure being chiral. The principle identifying the mirror plane is illustrated below:

enter image description here

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