What is Angle Strain?

Angle strain is a phenomenon experienced in cyclic structures due to the deviation in bond angle caused by the ring size. A very classic example is cyclopropane. The carbon-carbon bond angle is ideally 109° (tetrahedral structure) but in the case of the three membered ring system, cyclopropane, the carbon-carbon bond angle is 60° which causes angle strain in the molecule. The molecule experiences increased potential energy due to angle strain. The conformation of such a molecule is generally planar. A similar example to cyclopropane is cyclobutene with 90° carbon-carbon bond angle and planar conformation. 

What is von Baeyer’s Theory of Angle Strain?

In 1885 when structural theory was developing rapidly, a German chemist reported about strain in molecules which is popularly known as the strain theory. He had suggested that the small membered rings are less stable due to their deviation from the ideal bond angle. The stability of the molecule under study is inversely proportional to the strain experienced by the molecule due to the change in the bond angle. The assumption of all the cyclic structures to be having planar conformation caused him to conclude that cyclic rings, apart from the 5-membered cyclopentane, are highly strained structures since the closest bond angle to the ideal value was in the cyclopentane ring. The carbon-carbon bond angle for cyclopentane is 108°, closest to 109°.

Although the ideas put forth by Von Baeyer were partially correct, the fact that cyclic rings can relieve their strain through puckering was not introduced yet. Therefore, his theory was not applicable for the ring systems with more than four members. Based on his theory, he concluded that synthesis of large ring systems is not feasible. This theory failed to stand when the practical stability of a cyclohexane was found to be more than that of a cyclopentane.

The Von Baeyer theory was extended by H. Sachse, another German chemist who brought the ideology of changing conformation to relieve the molecule of this angle strain. Thus, the chair and boat conformation were introduced. The chair conformation of cyclohexane and the envelope conformation of the cyclopentane introduced relaxation in the angle strain for these molecules.

What Affects Angle Strain?

Angle strain causes a molecule to possess internal energy and thereby cause it to be unstable. Due to this energy present in the molecule, it is generally more reactive than a molecule with less/no angle strain. In cycloalkanes angle strain causes the molecule to undergo ring opening reactions that could relieve the molecule of this strain. Thus, it can be said that ring opening reactions affect the angle strain in a molecule. Another way of relieving the angle strain is by adopting a different configuration. For example, the cyclohexane angle strain is less when the molecule adopts a chair conformation. Therefore, the most stable conformation of cyclohexane is the chair form. In general terms, the larger cyclic systems undergo puckering to reduce the angle strain and attain stability. The cyclopentane forms the envelope conformation in which there is pseudo-rotation of the carbon atoms to gain more stability than the planar structure.

Comparison of Molecules Using Strain Energy

For a molecule, the strain energy is calculated using the heat of formation ΔH_f and it is compared to a molecule that is assumed to be strain-less.

For instance, the strain free model chosen is the cyclohexane, the heat of formation is$-29.5\text{ kcal/mol}$that accounts per methylene group to possess$-4.92\text{ kcal/mol}$. Based on this calculation the expected heat of formation for cyclopropane is$-14.75\text{ kcal/mol}$since there are three methylene groups but the observed value is$+12.73\text{ kcal/mol}$. Therefore, the strain energy is the difference between these values$27.5\text{ kcal/mol}$.

Similarly, the expected calculation for cyclobutene will be$-19.7\text{ kcal/mol}$ and observed value for the heat of formation is$+6.8\text{ kcal/mol}$. Thus, the strain energy for cyclobutene will be$26.5\text{ kcal/mol}$.

The most strained molecule is the cyclopropane with a large value of heat of formation. Thus, the cyclopropane readily reacts to form a much stable structure. Epoxides are also under the class of cyclopropanes with an oxygen atom that are reactive in nature. After cyclopropane, cyclobutene is considered to be the least stable due to its angle strain. Cyclobutene’s are not formed readily due to this angle strain. Only cyclobutene intermediates are readily generated as a driving force for the reaction.

Note: The values presented are not precise since cyclohexane is not completely strain free.

Factors Contributing to Strain in Molecules

The quantitative analysis of strain for a molecule is contributed by various factors such as steric strain, torsional strain, bond length distortion and bond angle distortion. Of these, the highly contributing factors are torsional strain and steric strain. Torsional strain is caused due to a close approach between atoms that are not directly bonded to each other. For example, in a cis molecule the two molecules are on the same plane and therefore can cause torsional strain in the molecule. This phenomenon is generally seen with the equatorial conformations. Torsional strain can be avoided by approaching towards a staggered configuration since the atoms are maximum distanced in a staggered conformation.

Steric strain is caused due to the bulkiness of one or more substituent. This leads to crowding of the molecule at a particular site and thereby disturbing the stability of the molecule as a whole. In order to avoid such bulkiness stereochemistry in introduced into the molecule by using chiral auxiliary. This enables the molecule to change the planes for bulky components and thereby increase their stability

Strain: Chemical consequence

It is expected that when the strain of a molecule is increased the reactivity of the molecule is also increased however this did not stand true at all times. When the cycloalkanes were subjected to electrophilic reaction and the strain energy relief was equally it was observed that cyclobutene’s were not as reactive as cyclopropanes. This is because the activated complex that plays a major role in the reactivity of a reaction must be considered for its location. Since the resemblance of the activated complex with the reactants could cause the rate determining step to experience a release in the strain energy and thereby the rate would be accelerated. Also, the reaction is accelerated through the driving force by the strained products or intermediates.

Context and Applications

This topic is significant in the professional exams for both undergraduate and graduate courses, especially for  

Bachelors and Masters Genetics, Biochemistry and Molecular biology  

Ecology and Evolutionary biology  

Biological science  

Masters in Biotechnology