Strain of Cycloalkanes

Introduction

• The structures and energies of cyclic alkanes are highly dependent on the size of their rings
• Small ring strain: a strain associated with ring sizes below six that arises from nonoptimal bond angles (optimal angle is 109.5)
• Cyclic alkanes of 4 carbons or more have rapidly interconverting conformations with varying degrees of torsional strain along their C-C single bonds
  • The bonds can only rotate so far without breaking the ring (rotations limited to certain angles)

Cyclopropane

• Observed bond angles of cyclopropane: 60 (much less than 109.5)
  • This compression causes considerable angle strain
• Since cyclopropane is planar, there are 6 pairs of C-H bonds that are fully eclipsed and introduce torsional strain
• Because of their extreme degree of intramolecular strain, cyclopropane and its derivatives undergo several ring opening reactions not seen with larger cycloalkanes

Cyclobutane

• Nonplanar or puckered conformations are favored in all cycloalkanes bigger than cyclopropane
• If cyclobutane were planar, it's C-C-C bond angles would be 90 and there would be 8 pairs of eclipsed C-H bonds, which would maximize torsional strain
• Rotations along the C-C bonds can slightly relieve strain puckering of the ring alters strain energy in 2 ways
  • It decreases the torsional strain associated with eclipsed interactions
  • It further increases the angle strain caused by the compression of C-C-C bond angles
• Because the decrease in torsional strain is greater than the increase in angle strain, the puckered conformation is more stable than the planar conformation of cyclobutane
• Not static but undergoes interconversions between puckered conformations

Cyclopentane

• If cyclopentane were planar, all C-C-C bond angles would be 108
• Little angle strain but there are 10 pairs of fully eclipsed C-H bonds, creating a lot of torsional strain
• To relieve part of this torsional strain, the ring twists by rotations along the C-C bonds into the envelope conformation
• Envelope conformation: 4 carbons are in the same plane and the fifth one is bent upward (like a flap on an envelope)
• Exists as a dynamic equilibrium of five envelope conformations in which each carbon atoms alternates as the out of plane carbon
• In the envelope conformation, the average C-C-C bond angle is reduced to 105
  • Increases angle strain
  • The number of C-H interactions is reduced which reduces torsional strain

Cyclohexane

• Cyclohexane adopts a number of puckered conformations that interconvert via C-C bonds
  • Most stable is chair conformation
  • all C-C-C bond angles are 110.9 (minimizing angle strain) and all hydrogens on adjacent carbons are staggered with respect to one another (minimizing torsional strain)
  • No 2 atoms are close enough to each other for nonbonded interaction strain to exist
  • Very little strain
  • C-H bonds are orients in 2 ways
    • 6 bonds are axial bonds: a bond to a chair conformation of cyclohexane that extends from the ring parallel to the imaginary axis through the center of the ring; a bond that lies roughly perpendicular to the equator of the ring
    • 3 axial bonds point straight up and the other 3 point straight down
    • Axial bonds alternate first up and then down as you move from one carbon to the next
    • 6 bonds are equatorial bonds: a bond to a chair conformation of cyclohexane that extends from the ring roughly perpendicular to the imaginary axis through the center of the ring; a bond that lies roughly along the equator of the ring
    • Equatorial bonds alternate first slightly up and then slightly down as you move from one carbon to the next
  • If the axial bond on a carbon points upward, the equatorial bond points slightly downward (vice versa)
  • Boat conformation: a nonplanar conformation of a cyclohexane ring in which carbons 1 and 4 of the ring are bent toward each other
  • Considerably less stable than a chair conformation because of the torsional strain associated with 4 pairs of eclipsed C-H interactions and the steric strain between the 2 flagpole hydrogens
  • Twist-boat conformation: a nonplanar conformation of a cyclohexane ring that is twisted from and is slightly more stable than a boat conformation
  • Twisting from a boat conformation to this one relieves some of the strain
  • The 2 chair conformations can be interconverted by first twisting into a boat and then into an alternative chair
  • When this occurs, there's a change in the relative orientations in space of the hydrogen atoms bonded to each carbon
    • All hydrogens axial in one chair become equatorial in another (and vice versa)
  • Diaxial interaction: the steric strain arising from interaction between an axial substituent and an axial hydrogen (or another group) on the same side of a chair conformation of a cyclohexane ring

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