# Is cis-1,2-dimethylcyclohexane a meso compound?

I was watching a video lecture today on hydrocarbons and came across this. The instructor says that, as there is a plane of symmetry, cis-1,2-dimethylcyclohexane is a meso-compound:

However, the cyclohexane ring is never planar as it adopts a chair conformation. I cannot find any plane of symmetry in chair form. Like this:

Is the compound meso or not?

cis-1,2-Dimethylcyclohexane is achiral, not because there is a plane of symmetry, but because it consists of two enantiomeric conformations which interconvert rapidly via ring flipping at normal temperatures.

This is exactly the same case as amine inversion. "Chiral nitrogens" such as that in $$\ce{NHMeEt}$$ do not lead to chirality or optical activity because of rapid inversion of configuration at the nitrogen atom, leading to interconversion of the two enantiomeric forms 1a and 1b.

Likewise, the ring flip in cis-1,2-dimethylcyclohexane leads to two different conformers. I have deliberately chosen to depict the ring flip in the following fashion, to make the mirror image relationship more obvious. The green methyl group, equatorial in conformer 2a, is changed into an axial methyl group in conformer 2b. Likewise, the blue methyl group goes from axial to equatorial. The 1,2-cis relationship between the two methyl groups is retained in both conformers.

Each individual conformer can be said to be chiral, but just like how the amine is considered achiral, cis-1,2-dimethylcyclohexane as a whole is considered achiral.

Is the compound meso? According to the IUPAC Gold Book, a meso-compound is defined as:

A term for the achiral member(s) of a set of diastereoisomers which also includes one or more chiral members.

1,2-Dimethylcyclohexane possesses two diastereomers, one cis and one trans form. The trans form is chiral, but the cis form is achiral, as explained above. Therefore, the cis form satisfies the above definition and is considered a meso-compound.

• Can we get it cold enough to freeze the enantiomers long enough to detect them? Can we see evidence of non-racemization in an optically active environment? – Oscar Lanzi Jan 14 '18 at 14:46
• @OscarLanzi I don't know. I presume it is possible, but for all intents and purposes it's achiral. – orthocresol Jan 14 '18 at 14:51
• Sir, I'd like to ask one thing, suppose we have the compound 1-(chloromethyl)-3,5-dimethylcyclohexane in which all three substituents (the 2 methyl and one chloromethyl) are coming out of the plane, is this compound meso? Due to the same reason as explained in this answer (flipping of ring)? It does have two stereogenic centres (the 3,5 positions)... – Harry Potter Jan 23 at 19:50
• @LightYagami Yes, it is the same thing. – orthocresol Jan 23 at 20:36
• Is it wrong then to see "plane of symmetry" at all in the rings? Because that is not how in reality it exists, but is it a conicidence that if we answer according to the 2D picture (using POS idea), the answer still comes out to be the same. I am also not able to see why the same argument for the trans form cannot be applied in this case. – Harry Potter Feb 12 at 3:51

I'd like to add a few points definition wise from the IUPAC goldbook.
(Because recently the original website seems to be broken I am using links via the internet archive.)

meso
A prefix to indicate the presence of a symmetry element of the second kind (see chirality) in a chemical species which is usually one of a set of diastereoisomers that also includes a chiral member.

However, there is a more general definition, too:

meso-compound
A term for the achiral member(s) of a set of diastereoisomers which also includes one or more chiral members.

The first part clearly does not apply to the cis-isomer, (1R,2S)-1,2-dimethylcyclohexane, the second does because of the definition of chirality.

chirality
The geometric property of a rigid object (or spatial arrangement of points or atoms) of being non-superposable on its mirror image; such an object has no symmetry elements of the second kind (a mirror plane, σ = S1, a centre of inversion, i = S2, a rotation-reflection axis, S2n). If the object is superposable on its mirror image the object is described as being achiral.

I think the key point of this definition is in this case, that the object needs to be rigid, which (1R,2S)-1,2-dimethylcyclohexane is not at room temperature. If you cool down the solution, inhibiting the ring flip, you would probably be able to find both configurations; that is a racemic mixture of them.

Since (1R,2R)-1,2-dimethylcyclohexane and (1S,2S)-1,2-dimethylcyclohexane, the trans-conformers, are both chiral (and enantiomers), the remaining member of the set (1R,2S)-1,2-dimethylcyclohexane can be considered a meso-compound, since it is achiral.