Ranking The Bulkiness Of Substituents On Cyclohexanes: “A-Values”

“A-Values” For Substituted Cyclohexanes

“A-Values” are a numerical way of rating the bulkiness of substituents on a cyclohexane ring. The “A-Value” represents the difference in energy (in kcal/mol) between the cyclohexane conformation bearing the group in the equatorial position (more favored) and the cyclohexane conformation bearing the group in the axial position.  The greater the “A-value” the higher the energetic preference for the equatorial position, and the more “bulky” the group is considered.

Table of Contents

1. A Numerical Ranking of “Bulkiness” For Cyclohexane Substituents
2. Ethyl (1.75 kcal/mol)
3. Hydroxyl (OH) (0.87 kcal/mol)
4. Br (0.43 kcal/mol)
5. Isopropyl (2.15 kcal/mol)
6. tert-Butyl (4.9 kcal/mol)
7. Summary: “A-Values”
8. Notes
9. (Advanced) References and Further Reading

1. A Numerical Ranking Of “Bulkiness” For Cyclohexane Substituents

In the last post we saw that adding a methyl group to cyclohexane results in two chair conformers that are unequal in energy. We saw that the conformer where the methyl group was equatorial is the most stable, since it avoids destabilizing diaxial interactions (technically, gauche interactions) that are present in the conformer when the methyl group is axial.

We also said that experiments tell us that 1-methylcyclohexane exists as a 95:5 ratio of conformers at room temperature (favouring the more stable equatorial conformer) and by using the equation ΔG = –RT ln K we can calculate the energy difference, which turns out to be 1.70 kcal/mol.

The next logical question is this. What’s the energy difference for other groups? For example, what happens when we substitute ethyl (CH₂CH₃) for methyl ? Or OH ? Or Br ? Or tert-butyl ? How is the equilibrium affected?

In order to find this out, it’s necessary to set up some experiments that allow us to measure these numbers. However, it’s all been done for us, so we can now present the results.

2. Ethyl (1.75 kcal/mol)

An ethyl group is one carbon larger than a methyl group. Naively, we might think that since it’s twice as long, it has twice as much steric hindrance, and the energy difference would be twice as big.  However, the difference in energy is only 1.75 kcal/mol (compare to methyl at 1.70 kcal/mol).  This is because the only significant diaxial interactions are with the CH₂ group. The ethyl group can rotate such that the CH₃ points away from the ring, where it does not lead to any significant increase in strain.

3. Hydroxyl (OH) (0.87 kcal/mol)

Given that oxygen has a larger atomic number than carbon, it’s not unreasonable to think that the OH group might be “bulkier” than carbon. When you think about the source of strain in CH₃, however, you realize that it’s not necessarily the size of the carbon atom itself but the hydrogens of CH₃ interacting with the axial hydrogens on the ring that lead to strain. Oxygen, having only one hydrogen, can always rotate such that the H is pointing away from the cyclohexane, thereby leading to very little in the way of diaxial interactions with the ring.

The value for OCH₃ is even less (0.6 kcal/mol).

4. Br (0.43 kcal/mol)

Along similar lines one could be forgiven for thinking that Br, being such a heavy and large atom, might exert a large destabilizing influence when in the axial position. However, the difference is only 0.43 kcal/mol, less than that for OH. Why might this be? The answer here is bond length. The average C-Br bond is about 193 picometers in length (1.93 Angstroms) – compare this to 1.50 for the bond between C and CH₃ in cyclohexane. The Br, being farther away, will thus have less interaction with the axial hydrogens. [Note – this A value of 0.43 is the average of two experimentally determined values [0.38 and 0.48].  ]

Interestingly, despite their great difference in size, the A values for Cl, Br, and I are all roughly similar (about 0.43 or so). This is because the increased size is balanced by the increased bond length – the halogens might be increasing in size along Cl <Br < I  – but they are also getting farther away.

5. Isopropyl [-CH(CH3)₂] (2.15 kcal/mol)

In contrast to ethyl, which has a secondary carbon attached to the ring, the isopropyl group represents a tertiary carbon attached to the cyclohexane. There is a relatively small but significant increase in strain to 2.15 kcal/mol . This is because the isopropyl group can still adopt a conformation where the C-H bond lies over the cyclohexane ring, which does not bring it into significant contact with the axial C-H bonds.

6. tert-butyl [-C(CH₃)₃] (4.9 kcal/mol)

This is the biggie. Look at the huge difference in energy between t-butyl (4.9 kcal/mol) and isopropyl (2.15 kcal/mol). What might account for that extra 2.7 kcal/mol in strain energy.

It helps to look at a figure.

Notice how there’s no way to rotate the t-butyl group such that the methyl group is NOT pointing over the ring. A diaxial interaction between one of the methyl groups and an axial C-H is unavoidable. Axial t-butyl groups are strongly disfavoured.

What is the consequence of that value of 4.9 kcal/mol ? If we calculate the equilibrium constant K , it gives us a ratio of about 10,000 : 1 [accounting for only 2 significant figures here].

In other words,  the concentration of axial t-butyl is 1/10,000 of that of equatorial t-butyl.

This value is so small that we often think of the t-butyl group as “locking” the cyclohexane ring in a position where the t-butyl is equatorial.

As we’ll see, this will have very important consequences for future reactions you’ll learn such as substitution and elimination, which can be sensitive to stereochemistry.

7. Summary: “A Values”

It’s nice to have some shorthand. For a mono-substituted cyclohexane, the energy difference between axial and equatorial conformers with a given substituent is known as its A-value.

For example, the A value of methyl is 1.70 , ethyl is 1.75, OH is 0.87, Br is 0.43, i-Pr is 2.15, and t-Bu is 4.9 .

A-values are useful because they are additive. We can use them to figure out the energy differences between di- and trisubstituted cyclohexanes, which is what we’ll talk about in the next post.

Notes

Note 1.  Here is a brief table of relevant A-values for introductory organic chemistry. These are taken from Hans Reich’s awesome website. Values might differ from Wikipedia because figures are averaged. [Note – these values are only valid for six-membered rings! but they do give you an idea of relative bulkiness of the substituents that can be applied to other ring sizes]

(Advanced) References and Further Reading

A-Values

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.

1. Electron Diffraction Investigations of Molecular Structures. II. Results Obtained by the Rotating Sector Method.
   Hassel, O.; Viervoll, H.
   Acta Chem. Scand. 1947, 1, 149-168
   DOI: 3891/acta.chem.scand.01-0149
2. The Structure of Molecules Containing Cyclohexane or Pyranose Rings.
   Hassel, O.; Ottar, B.
   Acta Chem. Scand. 1947, 1, 929-943
   DOI: 3891/acta.chem.scand.01-0929
   Odd Hassel first confirmed that cyclohexane exists in the now commonly accepted chair confirmation. He also proposed that substituents can take two different types of positions on the ring, which he called c- and e-bonds. He also showed that the conformational analysis of cyclohexanes can be extended to other unsaturated 6-membered rings, such as the pyranoses commonly found in carbohydrates. Odd Hassel later shared the Nobel Prize in Chemistry with Prof. D. H. R. Barton for his work on conformational analysis.
3. The Thermodynamic Properties and Molecular Structure of Cyclohexane, Methylcyclohexane, Ethylcyclohexane and the Seven Dimethylcyclohexanes
   Charles W. Beckett, Kenneth S. Pitzer, and Ralph Spitzer
   Journal of the American Chemical Society 1947, 69 (10), 2488-2495
   DOI: 1021/ja01202a070
   This paper first proposes the terms ‘polar’ and ‘equatorial’ for the two types of positions substituents can take in cyclohexane.
4. Nomenclature of cycloHexane Bonds
   BARTON, D., HASSEL, O., PITZER, K., PRELOG, V.
   Nature 1953, 172, 1096–1097
   DOI: 1038/1721096b0
   This is the first instance of the terms ‘axial’ and ‘equatorial’ being used to denote the two positions substituents can take in cyclohexane.
5. 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.
6. Table of Conformational Energies—1967
   Jerry A. Hirsch
   Topics in Stereochemistry 1967, 1, 199-222
   DOI: 1002/9780470147108.ch4
   This paper contains a detailed list of various types of functional groups with A-values, including references to the original sources and details on measurement methods.
7. A Values
   This page in Prof. Hans Reich’s (U Wisconsin-Madison) website contains a handy list of A-values, with references.
8. The experimental determination of the conformational free energy, enthalpy, and entropy differences for alkyl groups in alkylcyclohexanes by low temperature carbon-13 magnetic resonance spectroscopy
   Harold Booth and Jeremy R. Everett
   Chem. Soc., Perkin Trans. 2, 1980, 255-259
   DOI: 10.1039/P29800000255
   This paper covers the use of NMR methods to determine the free energy differences between axial- and equatorial-subtituted alkylcyclohexanes (in essence, A-values).
9. The conformational preference (a value) of deuterium in monodeuteriocyclohexane from deuteron integration at low temperatures
   Frank A. L Anet, Daniel J. O’Leary
   Tetrahedron Lett. 1989, 30 (9), 1059-1062
   DOI: 10.1016/S0040-4039(01)80358-0
   This paper describes an NMR study to determine the A-value of the deuterium substituent in cyclohexane-D₁.
10. The conformational equilibrium of the amino group
    L. Eliel, E. W. Della, T. H. Williams
    Tet. Lett. 1963, 4 (13), 831-835
    DOI: 10.1016/S0040-4039(01)90724-5
    This paper describes a study on measuring the A-value for the amino group in neutral and acidic media (where it would be -NH₃⁺).