Is there a clear cut rule between the two? For example, is R always (+), or is S always (-), or is there no relationship? And if so, why? Wouldn't it make sense that plane polarized light would rotate in the direction ascribed to chiral molecules?
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4$\begingroup$ You have to remember that (R) and (S) are essentially arbitrary rules that are created by humans. There is no way for nature to assign the Cahn-Ingold-Prelog priority of substituents because nature doesn't know what the priority rules even are and even if she did, she wouldn't have a way to evaluate them. IUPAC could create an entirely new arbitrary naming system under which we would label chiral molecules as (A) and (B) and that would make absolutely no difference whatsoever to the (+)/(-) optical rotation of the molecules. $\endgroup$– orthocresolCommented Dec 10, 2015 at 8:31
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There is no general correlation between the the rectus (R) and sinister (S) prefixes and dextro/levorotation. In some cases the (R)-enantiomer is the dextrorotary enantiomer (as in the case of D-alanine), and in other cases the (R)-enantiomer is the levorotary enantiomer (as in the case of L-cysteine). The relationship can only be determined on a case-by-case basis with experimental measurements or detailed computer modeling.
For a really detailed explanation of exactly how chiral molecules rotate planes of polarized light, I recommend you check out this physics post, but to answer your other question, no it doesn't make sense for planes of polarized light to rotate according the Cahn–Ingold–Prelog Priority Rules. This system only takes into consideration the atomic number and number of bonds to atoms of a higher atomic number. Even though $\ce{-Cl}$ might rank higher than $\ce{-C(CH)3}$, wouldn't it make sense for the two groups to have different effects on rotation, in the cases of both direction and magnitude? This is why dextro/levorotation must be determined experimentally.
