Cycloalkanes – Ring Strain In Cyclopropane And Cyclobutane

Ring Strain In Cyclopropane and Cyclobutane

In the last post we saw that cyclopropane and cyclobutane have an unusually high “ring strain” of 27 kcal/mol and 26 kcal/mol respectively.  We determined this by comparing heats of combustion from rings of various sizes, and saw that the ΔH_combustion per CH₂ was essentially constant as ring sizes went above 12.

Based on these calcuations, we saw that cyclopropane and cyclobutane are much more unstable  than we might naively expect for an “unstrained” ring of that size. In addition, the C-C bond strength in cyclopropane is considerably weaker (65 kcal/mol) than we observe for a typical C-C bond (80-85 kcal/mol).

Therefore,  there must be some structural feature of cyclopropane and cyclobutane which leads to this additional strain.

What might that be?  Let’s take a look.

Table of Contents

1. Angle Strain In Cyclopropane and Cyclobutane
2. Torsional Strain In Cyclopropane 
3. Torsional Strain In Cyclobutane – Some Puckering Is Possible
4. Summary: Ring Strain In Cyclopropane and Cyclobutane
5. Notes
6. (Advanced) References and Further Reading

1. Angle Strain In Cyclopropane And Cyclobutane

The first thing to notice about cyclopropane and cyclobutane is the non-ideal bond angles. The ideal bond angle in tetrahedral carbon is 109 degrees (See post: How Do We Know Methane Is Tetrahedral)

However, constrained to a triangle and a square, the interior angles of cyclopropane (60°) and cyclobutane (90°) are considerably less than the ideal angle.

This means that the electron clouds surrounding each atom will be considerably closer together than ideal, and since like charges repel, this will be energetically less favorable than for a straight-chain alkane.

The additional instability caused by this constraint is called angle strain or Von Baeyer strain.

[ Note – although the atoms of cyclopropane do form a triangle, the electron clouds between each atom do not necessarily follow the “lines” of it.  The nature of the bonding in cyclopropane is a deep topic – Mike Evans put together a video on it here.]

So is it that simple? Is angle strain all there is to talk about? Not quite – there’s one more factor to consider.

2. Torsional Strain In Cyclopropane

From earlier chapters on conformations, you may recall the concept of “Torsional Strain” (aka “twisting strain) (See Article: Staggered vs. Eclipsed Conformations of Ethane).

Although those two words often generate confusion in students’ minds, the concept is very simple: strain generated through simple rotation.

 Have you ever flown a toy plane with a wind-up propeller? As you twist the propeller, you will progressively encounter more and more resistance from the elastic bands.

When wind-up is complete, you can really feel that propeller digging into your finger! The elastic bands in this case are under a lot of torsional strain. Releasing the propeller results in untwisting of the elastic bands, which is the driving force for propelling the plane.

It is much the same with molecules.

In ethane, for example, rotation about the C-C single bond results in two major conformations: the “eclipsed” conformation, where the two CH₃ groups are directly aligned with each other along the C-C axis, and the more favorable “staggered” conformation where they are offset by 60 degrees.

The difference in energy between these two forms is about 3 kcal/mol (actually 2.8 kcal/mol).

Therefore ethane in the eclipsed conformation feels a torsional strain (driving force for rotation) of about 3 kcal/mol.

 In cyclopropane, the adjcent CH₂ groups are also eclipsed. Unlike in ethane, this strain cannot be relieved through rotation (the ring is too rigid).

In other words, the CH₂ groups are locked in the eclipsed conformation, which results in torsional strain – much like a propeller that has been wound up but held in position. Much like wound-up propellers, it’s common to think of cyclopropanes as being “spring loaded” – later on we will see some examples of reactions where release of ring strain is a significant driving force!

3. Torsional Strain In Cyclobutane: Some Puckering Is Possible

What about cyclobutane? If cyclobutane were completely flat, we would expect eclipsing interactions between four CH₂ groups.

In reality, cyclobutane has a little bit of wiggle room.  The result is that there are three carbons in one plane with the fourth appearing like a “flap” slightly out of plane.

Any one of the four carbon atoms can be the “flap” – in solution, there is interconversion between different conformers, and on average, each carbon spends an equal amount of time as the “flap”. The fact that cyclobutane rings can “pucker” like this leads to a small reduction in torsional strain.

4. Summary: Ring Strain In Cyclopropane and Cyclobutane

Both cyclopropane and cyclobutane have large ring strain due to a mixture of angle strain and torsional strain.

Be on the lookout for future reactions that have “relief of ring strain” as a driving force.

In the next post we’ll talk about 5 and 6 membered rings.

Here’s a puzzle for you: the interior angles of a pentagon are 108° whereas those of a hexagon are 120°.

Based on that alone, you might expect cyclopentane to be less strained than cyclohexane, since the angle is closer to the ideal angle of tetrahedral carbon.

In fact the exact opposite is the case. Why? Answer in the next post.

Next post: Ring Strain of Cyclopentane and Cyclohexane

Notes

(Advanced) References and Further Reading

Because cyclopropane and cyclobutane are small, rigid molecules, they possess high reactivity due to their inherent strain, because the orbitals involved in bonding are forced to deviate from the ideal sp³ tetrahedral angle of 109.5°.

1. Ueber Polyacetylenverbindungen
   Adolf Baeyer
   Ber. 1885, 18 (2), 2269-2281
   DOI: 10.1002/cber.18850180296
   The original paper on ring strain by the German chemist Adolf von Baeyer. Even though this paper is titled on a completely different topic, ring strain is discussed at the very end of the paper.
2. Evaluation of strain in hydrocarbons. The strain in adamantane and its origin
   Paul von R. Schleyer, James Earl Williams, and Blanchard K. R.
   Journal of the American Chemical Society 1970, 92 (8), 2377-2386
   DOI: 1021/ja00711a030
   An early paper by Prof. P. v. R. Schleyer before he moved to Germany in the 1970’s. Adamantane was a pet topic of his, as one of his most highly-cited papers is a 1-page communication in JACS on the simple synthesis of adamantane. Table VII in this paper has a large collection of strain energies of various hydrocarbons, including cyclopropane and cyclobutane (28.13 and 26.90 kcal/mol, respectively).
3. Theoretical analysis of hydrocarbon properties. 1. Bonds, structures, charge concentrations, and charge relaxations
   Kenneth B. Wiberg, Richard F. W. Bader, and Clement D. H. Lau
   Journal of the American Chemical Society 1987, 109 (4), 985-1001
   DOI: 1021/ja00238a004
   Changes in hybridization are associated with changes in electronegativity. The greater the s character of a particular carbon orbital, the greater its electronegativity. As a result, carbon atoms that are part of strained rings are more electronegative than normal towards hydrogen.
4. Nuclear magnetic resonance spectroscopy. Carbon-carbon coupling in cyclopropane derivatives
   Frank J. Weigert and John D. Roberts
   Journal of the American Chemical Society 1967, 89 (23), 5962-5963
   DOI: 1021/ja00999a046
   On the basis of NMR experiments, values of 33% and 17% have been suggested for the s-character of C-H and C-C bonds of cyclopropane, respectively. The late Prof. J. D. (Jack) Roberts was a giant in Physical Organic Chemistry, and spent almost his entire career at Caltech. He was active in research well into his 90’s!
5. Bonding Properties of Cyclopropane and Their Chemical Consequences
   Dr. Armin de Meijere
   Angew. Chem. Int. Ed. 1979, 18 (11), 809-826
   DOI: 10.1002/anie.197908093
   A review by Prof. Armin de Meijere, who has carried out a lot of research on cyclopropanes and other alicyclic hydrocarbons in his career.
6. Theoretical determination of molecular structure and conformation. 20. Reevaluation of the strain energies of cyclopropane and cyclobutane carbon-carbon and carbon-hydrogen bond energies, 1,3 interactions, and .sigma.-aromaticity
   Dieter Cremer and Juergen Gauss
   Journal of the American Chemical Society 1986, 108 (24), 7467-7477
   DOI: 1021/ja00284a004
   Theoretical methods are ideally suited to study ring strain, and this paper studies why the strain energies of cyclopropane and cyclobutane are so close.
7. Stereochemistry of Cyclobutane and Heterocyclic Analogs
   Robert M. Moriarty
   Topics in Stereochemistry 1974, 8
   DOI: 10.1002/9780470147177.ch4
8. Molecular structure and puckering potential function of cyclobutane studied by gas electron diffraction and infrared spectroscopy
   Toru Egawa, Tsutomu Fukuyama, Satoshi Yamamoto, Fujiko Takabayashi, Hideki Kambara, Toyotoshi Ueda, and Kozo Kuchitsu
   J. Chem. Phys. 1987, 86, 6018
   DOI: 10.1063/1.452489
   The authors use FT-IR to show how cyclobutane can ‘pucker’ to alleviate the ring strain a little.