Torsional Strain: Examples and Applications

Torsional strain is the destabilization of a molecule caused by the eclipsing of groups present on the adjacent atoms. It is the difference in the energy between a staggered and eclipsed conformation. This is a structural feature that affects the stability of a compound. In other words, it is the repulsion between two groups in a Newman projection.

Conformational analysis of Ethane

Ethane has many possible conformations. Two of which have been shown in the figure below.

newman projection of ethane

Stability among such conformations

The two Newman projections of ethane have a difference in the C-C bond. If the carbon atoms are placed in front of the eye in such a way both are aligned horizontally, we get this picture. If C at the back (large circle) is rotated and the front carbon (dot) is held fixed, the torsional angle between adjacent hydrogens can be increased from 0-180o.

At the dihedral or torsional angle of 0 degrees (eclipsed conformation), the greatest torsional strain is observed whereas, at 60 degrees (staggered conformation), the minimum repulsion is experienced by nearby hydrogen hence it becomes the most stable one. However, all eclipsed conformations, as well as all staggered conformations of ethane, are degenerate.

torsional strain

High Stability of Staggered Conformation

From the calculation, it has been observed that staggered conformation has 12 KJ/mol less energy than the eclipsed one. It has also been revealed from the quantum mechanical approach, that the stability of staggered conformation is because it is the most favorable interaction between HOMO (highest occupied molecular orbitals) and LUMO (lowest unoccupied molecular orbitals). This interaction has the lowest angular and steric strains as well.

Torsional strain: stability of ethane

Some other examples of Torsional strain

Propane

On conformational analysis of propane, it has been noted that the eclipsed conformation form is 2 KJ/mol more unstable than ethane. This can be calculated by the difference between total energy and the energy of 2 dihedral atoms.

Butane

The Newmann projections and possible conformations have now a new term ‘gauche’ when the carbon number gets to four. This conformation, “Gauch conformation” has less energy than a fully eclipsed molecule, even lesser than a staggered one.

In cyclic compounds

Cyclopropane has max steric strains hence the most unstable of all the cyclic compounds. On moving toward higher members, strain decreases such that cyclohexane is the most stable of all. After cyclohexane, the torsional strain is again observed to rise because hydrogen eclipsing cannot be further avoided. The torsional energy versus no of carbon atoms (CH2) is given in the graph below.

torsional strain energy bar

This graph shows that cyclohexane is the most stable among cycloalkanes. It is due to a stable configuration geometry having no (very less) torsional and angular strain.

Cyclopropane

Torsional strain is also present in cyclic compounds with severe angular strain. This torsional strain shown in the figure is due to the eclipsing of H atoms.

cyclopropane

Cyclobutane

Cyclobutane has even more torsional strain than cyclopropane because 4 pairs of hydrogen atoms are available here to increase the possibility of eclipsing. To reduce this additional strain and gain stability, cyclobutane adapts puckered shape.

cyclobutane

Cyclopentane

Cyclopentane has much less strain than cyclopropane and cyclobutane. Moreover, it adopts an envelope shape to alleviate the torsional and angle strain.

Cyclohexane

Cyclohexane, the most stable of all, can arrange itself into a number of conformations. Such as chair, half chair, twist boat, and boat shape. The most common of them are boat and chair conformations. Both these conformations possess no angle strain because, each carbon exhibits hybridization geometry of tetrahedron with an angle of 109, as expected.

cyclohexane

Boat and Chair conformations of Cyclohexane

The main difference in the energies of chair and boat conformations is due to the difference in their torsional strains. Chair conformation has no such strain because there exists no eclipsing of H atoms. This can be best explained through its Newman projections. In boat conformation, some H atoms are eclipsed, by flagpole interaction which causes a slight torsional strain.

boat conformation strainTherefore, cyclohexane is mostly found in its chair form. Actually, there are two chair conformations it is found in. These are interchangeable depending upon the energy.

cyclohexane

Due to these energy differences, many examples are there like that glucose exists in alpha and beta forms.

Effects of torsional strain on reactivity

The most remarkable reactivity of epoxides is due to the strain that results from eclipsing of bonds torsional and ring strain. Simple open chains are inert in some reactions and epoxides react rapidly to release this strain. These reactions are known as ring-opening reactions

For example, an acid-catalyzed ring-opening reaction of epoxides with nucleophiles gives alcohol as a product.

ring opening reaction

Concepts Berg

What are steric strain and torsional strain?

Steric strain is the sum of all the possible strains in a molecule such as a ring strain, angular strain, and torsional strain whereas, torsional strain is the repulsion between H bonds in a molecule that causes destabilization.

What is a torsional strain in DNA replication?

Deoxyribonucleic acid (DNA) is the double strand of a macromolecule with a phosphate backbone. The two strands are connected through hydrogen bonding. Dihedra bonds (adjacent hydrogens) may eclipse and cause the deformation of the shape of DNA.

What causes torsional strain? How can it be avoided?

The major cause of torsional strain is eclipsing of bonds or bonded atoms. That can be minimized by setting these repulsive groups at the maximum possible distance. It is possible only when the single bond is present (as it allows the rotation). The structures with different orientations in space thus formed are known as conformers.

How do you reduce torsional strain?

Molecules arrange themselves in such a way as to minimize their strains. To reduce torsional strain, molecules rotate to remain in minimum energy conformation.

What is the torsional strain in cycloalkanes?

In cycloalkenes, it is caused by the overlapping of hydrogen atoms with other groups bonded at adjacent carbon atoms.

Is torsional stress a type of shear stress?

Torsional strain is observed in a molecule due to the overlapping bonding of molecular orbitals, mostly by adjacent carbon atoms that have eclipsing hydrogen atoms. On the other hand, shear stress is the term used in mechanics when a force is applied to a cylinder when one end is fixed and the other is twisted, causing stress known as shear stress.

What is the difference between angle strain and steric strain?

Angle strain

It appears in a molecule when the expected angle as per its hybridization is different from the actual one. For example, Cyclopropane has all sp3 hybridized carbon atoms. Its angle in bonding should be 109o. On the contrary, it is 60o as it gets a triangular shape. This difference in angle decreases the stability of a given molecule, which is called angle strain.

Steric strain

The destabilization caused by the repulsion of bonded and non bonded electrons in a molecule is known as steric strain. This strain cannot be reduced by rotation within a molecule.

What is a torsional strain example?

Torsional strain destabilizes the eclipsed ethane conformer up to 12 kJ/mol. Similarly, propane eclipsed conformation strain is up to 14 kJ/mol.

Reference Books

  • Organic Chemistry (4th edition), By Francis A. Carey (University of Virginia)
  • Organic chemistry (9th edition) By T. W. G. Solomons (Department of Chemistry, University of South Florida) & C. B. Fryhle (Chair and Professor of Chemistry at Pacific Lutheran University)
  • Chemistry (IB Diploma Programme): Second edition By Christopher TalbotRichard Hardwood, and Christopher Coates
  • Organic chemistry By David R. Klien (Johns Hopkins University)

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