# Find the number of geometrical and optical isomers of 1,2,3,6-tetramethyl cyclohex-1,4-diene

The compound given to me is 1,2,3,6-tetramethyl cyclohex-1,4-diene.
The geometrical isomers for the following compounds are:

The isomer on the right can also be an optical isomer with its enantiomer. So does this mean that there are 3 stereoisomers in total with one common geometrical and optical isomer?

Your analysis is in right track. Yet, I would like to point some few points on deciding stereoisomers. The step by step analysis is depicted in following diagram:

The two geometrical isomers are $$3,6$$-$$syn$$- and $$3,6$$-$$anti$$-isomers. The compound has 2 chiral centers, hence $$2^2 = 4$$ maximum stereoisomers possible. However, as shown in the diagram, $$3,6$$-$$syn$$-isomer has a plane of symmetry. Therefore, its mirror immage is the same as indicated by $$(3S,6R)$$- or $$(3R,6S)$$-. In addition, $$3,6$$-$$anti$$-isomer does not has a plane of symmetry, and hence, has two enantiomers (see the diagram).

• I think syn and anti in the diagram should be switched. Differs from text. Apr 28 '20 at 22:59
• Yes, and thank you. Just a mental mistake. :-) Apr 28 '20 at 23:02
• Thanks a lot for your better explanation and clearing my doubt. Apr 29 '20 at 7:40

Given compound has 1 geometrical isomer having methyl groups at trans , given is cis.Given compound has 2 chiral centers, C3,C6. Given structure is meso.C6 has S, C3 has R configuration. There exist its optical isomers having both chiral centers either R or S configuration leading to 2 optical isomers. Both having S configuration is also the trans isomer of given structure. Total 2 optical, 2 geometrical isomers(cis +trans).

• your answer is wrong. There are 2 geometrical isomers not just one. Apr 28 '20 at 9:56
• 1 meant 1 structure other than you had given,cis. For language clarity I had edited other 1 to 2(cis+trans). Apr 29 '20 at 1:18
• There are two geometrical isomers, cia and trans, but three stereoisomers, RS, RR and SS Apr 29 '20 at 1:36