Angle strain

Angle strain, also called Baeyer strain in cyclic molecules, is the resistance associated with bond angle compression or bond angle expansion. It occurs when bond angles deviate from the ideal bond angles to achieve maximum bond strength in a specific chemical conformation. Angle strain typically affects cyclic molecules because non-cyclic molecules will thermodynamically conform to the most favorable stable state.

Angle strain is subdivided into two categories: small angle strain and large angle strain.

In cycloalkanes, optimum overlap of atomic orbitals is achieved at 109.5°. But angle strain occurs when the carbon-carbon bonds can't be at 109.5° in cycloalkanes. Having higher angle strain makes a molecule more unstable and reactive. Maximum bond strength results from effective overlap of atomic orbitals in a chemical bond.

History

The most common cyclic compounds have five or six carbons in their ring. Adolf von Baeyer received a Nobel Prize in 1905 for the discovery of the Baeyer strain theory, which was an explanation of the relative stabilities of cyclic molecules.

Measurement of angle strain

A quantitative measure for angle strain is strain energy. Angle strain and torsional strain combine to create ring strain that affects cyclic molecules. These measurements commonly use heat of combustion.

C_nH_2n + 3/2 n O₂ → n CO₂ + n H₂O + n X

where X is the heat of combustion for a CH₂ group (energy per CH₂).

Normalized energies that allow comparison of ring strains are obtained by measuring per methylene group (CH₂) of the molar heat of combustion in the cycloalkanes.

$\binom{heat\ of\ combustion}{per\ CH_2\ group} - \binom{reference\ value}{per\ CH_2\ group} = \binom{ring\ strain}{per\ CH_2\ group}$

The reference value is 658.6 kJ per mole of methylene group. The reference value was obtained from an unstrained long-chain alkane.

In cyclohexane the total ring strain is 0 kJ.

Examples

In cycloalkanes, each carbon is bonded nonpolar covalently to two carbons and two hydrogen. The carbons have sp³ hybrization and should have ideal bond angles of 109.5°. Due to the limitations of cyclic structure, however, the ideal angle is only achieved in a six carbon ring — cyclohexane in chair conformation. For other cycloalkanes, the bond angles deviate from ideal. In cyclopropanes (3 carbons) and cyclobutanes (4 carbons) the C-C bonds are 60° and ~90° respectively.

Examples of molecules with angle strain include cycloalkanes, cyclophanes, platonic hydrocarbons and pyramidal alkenes.

Some specific examples are:

• cyclopropane, C₃H₆ — the C-C-C bond angles are 60° whereas tetrahedral 109.5° bond angles are expected. The intense angle strain leads to nonlinear orbital overlap of its sp³ orbitals. Because of the bond's instability, cyclopropane is more reactive than other alkanes. Since any three points make a plane and cyclopropane has only three carbons, cyclopropane is planar. The H-C-H bond angle is 115° whereas 106° is expected as in the CH₂ groups of propane.
• cyclobutane, C₄H₈ — if it was completely square planar its bond angles would be 90° whereas tetrahedral 109.5° bond angles are expected. However, the actual C-C-C bond angle is 88° because it has a slightly folded form to relieve some torsional strain at the expense of slightly more angle strain. The high strain energy of cyclobutane is primarily from angle strain.
• cyclopentane, C₅H₁₀ — if it was completely rectangular planar pentagon its bond angles would be 108° whereas tetrahedral 109.5° bond angles are expected. However, it has an unfixed puckered shape that undulates up and down. The unstable half-chair conformation has angle strain in the C-C-C angles which range from 109.86° to 119.07°.
• ethylene oxide, CH₂OCH₂
• cubane, C₈H₈

See also

• Alkane stereochemistry
• Torsional strain
• Ring strain