Cyclohexane Chair Conformation Stability: Which One Is Lower Energy?

Finding The Most Stable Conformation Of A Cyclohexane Chair

You’re given a structure with two or more substituents on a cyclohexane ring, and you’re asked to draw the most stable conformation. How do you do that? That’s what this post is about.

Table of Contents

1. A-Values Are A Useful Measure of Bulkiness
2. A-Values Are Additive
3. Example: Determining The Most Stable Conformation Of cis– And trans- 1,2-Dimethylcyclohexane
4. To Determine Chair Conformation Stability, Add Up The A-Values For Each Axial Substituent. The Lower The Number, The More Stable It is. 
5. Summary: Stability of Cyclohexane Conformations
6. Notes
7. (Advanced) References and Further Reading

1. A-Values Are A Useful Measure Of Bulkiness

In the last post, we introduced A values and said they were a useful tool for determining which groups are “bulkiest” on a cyclohexane ring. (See post: Ranking the Bulkiness Of Substituents On Cyclohexane Rings With A-Values)

The greater the A-value (bulk), the more favoured the equatorial conformer will be (versus axial). We saw that hydroxyl groups (OH) have a relatively low A-value (0.87), methyl groups are higher (1.70) and the t-butyl group is one of the highest of all (>4.5) .

We also saw that by knowing the A value (which is essentially the energy difference in kcal/mol) we could figure out the % of axial and equatorial conformers in solution using the formula ΔG = –RT ln K

In this post we’re going to extend this concept and see what happens when we have MORE than one group on a cyclohexane ring.

2. A-Values Are Additive

The nice thing about A values is that they are additive. We can make the (safe) assumption that groups on adjacent carbons don’t bump into one another [Note 1] so figuring out the torsional strain of a cyclohexane chair is simply a matter of adding up the A values of the axial groups in any chair conformation.

We can apply this to cyclohexanes with two, three, or even more substituents.

Here are some examples:

3. Example: Determining The Most Stable Conformation Of cis- And trans– 1,2-Dimethylcyclohexane

That’s nice, you might say, but when might we ever want to do that? The key example is when we are examining two chair conformers of the same molecule. A-values are essential in helping us figure out which one is most stable.

Here’s an example of the type of question we might be asked: draw the two chair conformations of cis-1,2-dimethylcyclohexane and trans-1,2-dimethylcyclohexane, and determine which is most stable.

• Here, I’ve started by drawing the conformer of trans-1,2-dimethylcyclohexane where both CH₃ groups are axial (remember – it’s trans because one group is up and one group is down).
• The two axial methyl groups give a total of 3.4 kcal/mol of torsional strain.
• A chair flip converts all axial groups to equatorial and vice versa (but all “up” groups remain “up” and all “down” groups remain “down”! ) giving us a conformer where both methyl groups are now equatorial (and therefore do not contribute any strain).
• Therefore the di-equatorial conformer is favoured by 3.4 kcal/mol. [If we wanted to, we could also figure out the equilibrium constant here: K is about 340,  giving a ratio  99.6: 1 in favour of the di-equatorial conformer.]
• In the case of cis-1,2-dimethylcyclohexane, I’ve started by drawing an axial CH₃ at C-1 and an equatorial CH₃ at C-2 (note that my designation of C-1 and C-2 is completely arbitrary). This has a strain energy of 1.70 kcal/mol due to the single axial CH₃.
• When we do the chair flip, we convert all axial groups to equatorial and all equatorial to axial, giving us…. a new chair which still has one methyl group equatorial and one axial! The same energy, in other words (1.70 kcal/mol). [The equilibrium constant here is 1, giving a 50:50 ratio]

4. To Determine Chair Conformation Stability, Add Up The A-Values For Each Axial Substituent. The Lower The Number The More Stable It Is

Now that we’ve drawn all four possibilities, we can rank them in order of stability if we want, and then determine that for the two isomers of 1,2-dimethylcylohexane, the di-equatorial conformer of trans-1,2-dimethylcyclohexane is the most stable.

5. Summary: Chair Conformation Stability

In the next post we’re going to talk about fused cyclohexane rings, and ask how we can apply what we’ve already learned to understand more about the stability of the conformers of these molecules.

Notes

Note 1. One key exception to the “A values are additive” assumption is 1,2-di-t-butyl cyclohexane, in which the trans form is actually less stable than the cis despite the fact that both groups are equatorial in the trans. That’s because the two t-butyl groups are held together so closely in space that there is significant “1,2” strain (Van der Waals strain). [Note: it turns out in the trans isomer, the diaxial conformation is favored by 6.2 kcal/mol ! see the References section. ]

Another exception is the amino alcohol below. What force might be responsible for the fact that the axial conformer is favoured in equilibrium conditions?

(Advanced) References and Further Reading

This is a topic commonly taught to undergraduates in Organic Chemistry. A-values are empirically derived and denote the thermodynamic preference for a substituent to be in the axial or equatorial position in cyclohexane. A-values can be added, and the total energy thus derived gives the difference in free energy between the all-axial and all-equatorial conformations.

1. Neighboring Carbon and Hydrogen. XIX. t-Butylcyclohexyl Derivatives. Quantitative Conformational Analysis
   S. Winstein and N. J. Holness
   Journal of the American Chemical Society 1955, 77 (21), 5562-5578
   DOI: 10.1021/ja01626a037
   An early paper on the determination of A-values (see Table XII) through kinetic (solvolytic) measurements, which is what Prof. Winstein was well known for. The introduction features a nice summary of how A-values are determined, and later on, Prof. Winstein states “The energy quantity by which a t-butyl group favors the equatorial position is sufficiently large to guarantee conformational homogeneity to most 4-t-butylcyclohexyl derivatives”, in agreement with what is commonly taught in organic chemistry classes today.
2. Conformational analysis. 32. Conformational energies of methyl sulfide, methyl sulfoxide, and methyl sulfone groups
   Ernest L. Eliel and Duraisamy Kandasamy
   The Journal of Organic Chemistry 1976, 41 (24), 3899-3904
   DOI: 1021/jo00886a026
   This paper uses the additivity of A-values to determine the A-values of -SCH₃, -SOCH₃, and -SO₂CH₃ (Table IV).
3. The gauche interaction in trans-1,2-dimethylcyclohexane
   Muthiah Manoharan and Ernest L. Eliel
   Tetrahedron Lett. 1983, 24 (5), 453-456
   DOI: 10.1016/S0040-4039(00)81435-5
   Although this is generally not covered in introductory organic chemistry, one complication with employing A-values is that  groups are on adjacent carbons (as in 1,2-dimethylcyclohexane) can undergo steric repulsion through so-called “gauche interactions”. In this paper, the gauche interaction in trans-1,2-dimethylcyclohexane is calculated to be 0.74 kcal/mol.
4. Conformational analysis. LVII. The calculation of the conformational structures of hydrocarbons by the Westheimer-Hendrickson-Wiberg method
   Norman L. Allinger, Mary Ann Miller, Frederic A. Van Catledge, and Jerry A. Hirsch
   Journal of the American Chemical Society 1967, 89 (17), 4345-4357
   DOI: 1021/ja00993a017
   Tables V-VII in this paper contain conformation energies of disubstituted cyclohexanes, which can be derived from adding the respective A-values.
5. Conformational Studies. VII.1 p-Menthane-2,5-diols and the Relative “Size” of the Isopropyl Group
   Robert D. Stolow
   Journal of the American Chemical Society 1964, 86 (11), 2170-2173
   DOI: 1021/ja01065a013
   1,2-disubstituted cyclohexanes do not add neatly due to repulsive interactions from the groups being so close to each other.
6. Steric Interactions in Organic Chemistry: Spatial Requirements of Substituents
   Hans Förster, Prof. Dr. Fritz Vögtle
   Angew. Chem. Int. Ed. 1977, 16 (7), 429-441
   DOI: 10.1002/anie.197704291
7. Conformational analysis. LXXVIII. The conformation of phenylcyclohexane, and related molecules
   L. Allinger and M. T. Tribble
   Tet. Lett. 1971, 12 (35), 3259-3262
   DOI: 10.1016/S0040-4039(01)97150-3
   Oddly enough, in certain phenylcyclohexanes, the phenyl group prefers to be axial, and this paper investigates that using computational methods.
8. Janus face all‐cis 1,2,4,5‐tetrakis(trifluoromethyl)‐ and all‐cis 1,2,3,4,5,6‐hexakis(trifluoromethyl)‐ cyclohexanes
   David O’Hagan, Cihang Yu, Agnes Kütt, Gerd-Volker Röschenthaler, Tomas Lebl, David B. Cordes, Alexandra M. Z. Slawin, Michael Bűhl
   Angew Chem. Int. Ed. 2020, Accepted Article
   DOI: 10.1002/anie.202008662
   This recently published paper is on the synthesis of 1,2,3,4,5,6-hexakis(trifluoromethyl)-cyclohexane. Computational analysis shows that it has a barrier to interconversion of approx. 27.1 kcal/mol.
9. Conformational Study of cis-1,4-Di-tert-butylcyclohexane by Dynamic NMR Spectroscopy and Computational Methods.
   Gurvinder Gill, Diwakar M. Pawar, and Eric A. Noe
   J. Org. Chem. 2005, 70, 10726-10731
   DOI: 10.1021/jo051654z
   Although mainly a study of 1,4-Di-t-butylcyclohexane, this paper also presents calculations for comparing the energies of diaxial and diequatorial trans-1,2-Di-t-butylcyclohexane, and finds that the diaxial conformer is more stable than the diequatorial conformer by about 6.2 kcal/mol! Interestingly the twist-boat conformer of this molecule is only slightly lower in energy (0.5 kcal/mol).