Angle strain

Angle strain, also called Baeyer strain in cyclic molecules, is the resistance associated with bond angle compression or bond angle expansion.^[1] 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°.^[1] But angle strain occurs when the carbon-carbon bonds can't be at 109.5° in cycloalkanes.^[1] 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.^[1] 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.^[1]

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.^[1] These measurements commonly use heat of combustion.^[1]

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.^[1]

The reference value is 658.6 kJ per mole of methylene group.^[1] The reference value was obtained from an unstrained long-chain alkane.^[1]

In cyclohexane the total ring strain is 0 kJ.^[1]

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.^[2] The intense angle strain leads to nonlinear orbital overlap of its sp³ orbitals.^[1] Because of the bond's instability, cyclopropane is more reactive than other alkanes.^[1] Since any three points make a plane and cyclopropane has only three carbons, cyclopropane is planar.^[2] The H-C-H bond angle is 115° whereas 106° is expected as in the CH₂ groups of propane.^[2]
• cyclobutane, C₄H₈ — if it was completely square planar its bond angles would be 90° whereas tetrahedral 109.5° bond angles are expected.^[1] 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.^[1] The high strain energy of cyclobutane is primarily from angle strain.^[2]
• cyclopentane, C₅H₁₀ — if it was completely rectangular planar pentagon its bond angles would be 108° whereas tetrahedral 109.5° bond angles are expected.^[1] However, it has an unfixed puckered shape that undulates up and down.^[1] The unstable half-chair conformation has angle strain in the C-C-C angles which range from 109.86° to 119.07°.^[3]
• ethylene oxide, CH₂OCH₂
• cubane, C₈H₈

See also

• Alkane stereochemistry
• Torsional strain
• Ring strain

References