Number of diastereomer pairs of 1,3-dichloro-1,2,3-triphenylpropane

[![1,1',1''-(1,3-dichloropropane-1,2,3-triyl)tribenzene](https://i.stack.imgur.com/WMhlb.png)](https://i.stack.imgur.com/WMhlb.png)


How can I determine the number of possible pairs of diastereomers here?


My first guess was two: RR with RS and SS with RS. But what about the potential chirality center middle carbon? There are two identical branches attached to it; however, those two branches can change R/S. So, is it a chirality center?




I basically agree with Ron's answer, but had to draw all of the possible structures to confirm it. The complication is that carbon-2 is *[non-stereogenic](http://goldbook.iupac.org/S05980.html)* but it may be *[chirotopic](http://goldbook.iupac.org/C01065.html)* depending on the configuration of the neighboring atoms. The IUPAC Gold Book calls this a [pseudo-asymmetric carbon atom](http://goldbook.iupac.org/P04921.html). Carbon-2 is not a stereocenter, because it does not have four different "things" attached to it. However, its configuration is important relative to carbons-1 and -3. Below are all of the possible combinations.


![enter image description here](https://i.stack.imgur.com/RVRNX.png)


Out of the eight possibilities, we see there are only four unique compounds (names generated in ChemDraw):


A: (1​*R*,2​*s*,3​*S*)-1,3-dichloro-1,2,3-triphenylpropane


B: (1​*S*,3​*S*)-1,3-dichloro-1,2,3-triphenylpropane


C: (1​*R*,2​*r*,3​*S*)-1,3-dichloro-1,2,3-triphenylpropane


F: (1​*R*,3​*R*)-1,3-dichloro-1,2,3-triphenylpropane


The small *r* and *s* are essentially used to indicate the stereochemistry at carbon-2 relative to carbons-1 and -3. Note that in compounds B and F, the stereochemistry at carbon-2 is inconsequential as in both cases the phenyl group is syn to one chloride and anti to another chloride. I haven't been able to find an adequate explanation of assigning the *r*/*s* designations, but I believe that the *R* configured substituent receives higher priority than the *S* configured substituent, and Cahn–Ingold–Prelog system is followed from there.


 18

Let's number the 3 aliphatic carbons to make our discussion clearer.


![enter image description here](https://i.stack.imgur.com/o3ADQ.jpg)


Using the definition of a chiral carbon as a carbon that has 4 different substituents, carbons 1, 2 and 3 are all capable of being chiral. Carbons 1 and 3 are relatively straightforward chiral carbons, it's easy to see the 4 different substituents and assign "*R*" or "*S*" configurations. However carbon 2 is problematic.


If we assign *R*- and *S*- configurations to carbons 1 and 3 respectively, then there are 4 different groups attached to carbon 2, but the difference in 2 of the groups is just "*R*" or "*S*". In fact, in this situation there is actually a plane of symmetry bisecting the molecule and the molecule is achiral - it is a *meso*-isomer. The plane of symmetry contains carbon 2 and the hydrogen and phenyl group attached to carbon 2, and, as expected, the *R*- and *S*-substituents are enantiomeric. In such cases it is correct to say that carbon 2 is [*pseudo*-asymmetric](https://goldbook.iupac.org/html/P/P04921.html) (thanks to @GaurangTandon for pointing this out!). The Cahn–Ingold–Prelog priority rules can still be used to describe carbon 2, the *R* substituent is given priority over the *S* substituent and lowercase "*r*" and "*s*" are used to describe carbon 2, the *pseudo*-asymmetric carbon.


In the case where we assign *R*- and *R*- (or *S*- and *S*-) configurations to carbons 1 and 3 respectively, then there is no longer a plane of symmetry bisecting the molecule. Carbon 2 is now [prochiral](http://en.wikipedia.org/wiki/Prochirality) (this means changing one substituent is all that is required to make carbon 2 chiral), but the molecule as a whole is now chiral.


Going in the order carbon 1-2-3 here are the various possibilities:


1. 1*R*,3*R* is chiral and it has an enantiomer 1*S*,3*S*
2. 1*R*,2*r*,3*S* is an achiral (there is a plane of symmetry bisecting the molecule), *meso*-compound and a diastereomer of 1*R*,3*R*;
3. 1*R*,2*s*,3*S* is a second achiral, *meso*-compound.


So there are 3 diastereomers; one is chiral and exists as a *d,l* pair and the two other diastereomers are achiral, *meso*-compounds.


 13

I don't think it is hindered enough to prevent rotation around the central carbon, so I think it only has two stereogenic centres, leading to four possible stereocentre combinations as you have identified: RR, SS, SR, RS


This results in more than two pairs of diastereomers though:


1) RR with SR  

2) RR with RS  

3) SS with SR  

4) SS with RS


 -1