Counting total number of stereoisomers of 1,2-dibromo-3,4-dimethylcyclobutane [closed]








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I came across this question in one of my tests.


The answer assumes the major product (the anti markovnikov one) being formed. That is, I wish to determine number of stereoisomers of 1,2-dibromo-3,4-dimethylcyclobutane. I had a hard time figuring this out.


I have found a total of 10 stereoisomers - 2 are meso-compounds and 4 pairs of enantiomers, just by drawing and visualizing the possible 3-d structures.


However, I am quite unsure of this answer. Does anyone have a systematic way of finding the number of stereoisomers of this compound? Can someone confirm that there are 10 isomers only?


Any help would be appreciated. Thanks in advance!




Rishi Shekher: I am in agreement with Mithoron and Martin that the cyclobutadiene shown is a poor chemical example. Nonetheless, it does not preclude addressing the stereochemical question. The choice of 2,3-dimethylcyclohexa-1,3-diene as a substrate.satisfies both problems. At issue here is the recognition that the peroxide effect (Kharasch reaction) is operative and no other regioisomers are to be considered.. All 16 possible permutations for drawing 1,4-dibromo-2,3-dimethylcyclohexane are shown below. Filtering through these structures is tedious. However, there is a more convenient approach to addressing the question at hand. *continued*  



![](https://i.stack.imgur.com/GwAzO.jpg)  



A systematic presentation of the 16 possible descriptors are shown below that follow the coefficients of a binomial expansion for $\pu{2^4}$ (1,4,6,4,1). Owing to the potential symmetry in the molecule, there is ample opportunity for duplication. There are two meso compounds: meso 1 (RSRS = SRSR; red) and meso 2 (RRSS = SSRR; blue). There are four pairs of enantiomers 1 through 4. There is a redundancy of structures for enantiomers 3 (green) and enantiomers 4 (magenta). In total there are 10 stereoisomers for 1,4-dibromo-2,3-dimethylcyclohexane.


![](https://i.stack.imgur.com/0Pig6.jpg)
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