Conformations and Cycloalkanes
Cyclohexane Chair Conformation Stability: Which One Is Lower Energy?
Last updated: December 13th, 2022 |
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
- A-Values Are A Useful Measure of Bulkiness
- A-Values Are Additive
- Example: Determining The Most Stable Conformation Of cis– And trans- 1,2-Dimethylcyclohexane
- To Determine Chair Conformation Stability, Add Up The A-Values For Each Axial Substituent. The Lower The Number, The More Stable It is.
- Summary: Stability of Cyclohexane Conformations
- (Advanced) References and Further Reading
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.
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:
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, 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.
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.
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. ]
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.
- 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
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.
- 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
This paper uses the additivity of A-values to determine the A-values of -SCH3, -SOCH3, and -SO2CH3 (Table IV).
- The gauche interaction in trans-1,2-dimethylcyclohexane
Muthiah Manoharan and Ernest L. Eliel
Tetrahedron Lett. 1983, 24 (5), 453-456
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.
- 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
Tables V-VII in this paper contain conformation energies of disubstituted cyclohexanes, which can be derived from adding the respective A-values.
- 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
1,2-disubstituted cyclohexanes do not add neatly due to repulsive interactions from the groups being so close to each other.
- Steric Interactions in Organic Chemistry: Spatial Requirements of Substituents
Hans Förster, Prof. Dr. Fritz Vögtle
Angew. Chem. Int. Ed. 1977, 16 (7), 429-441
- Conformational analysis. LXXVIII. The conformation of phenylcyclohexane, and related molecules
L. Allinger and M. T. Tribble
Tet. Lett. 1971, 12 (35), 3259-3262
Oddly enough, in certain phenylcyclohexanes, the phenyl group prefers to be axial, and this paper investigates that using computational methods.
- 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
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.
- 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
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).