the dihedral angle of this chain goes through zero. Switching the signs of the two chains sequentially in this way minimizes the maximum energy state along the way (at the half-chair state) — having the dihedral angles of both four-atom chains switch sign simultaneously would mean going through a conformation of even higher energy due to angle strain at carbons 1 and 4. The detailed mechanism of the chair-to-chair interconversion has been the subject of much study and debate. The half-chair state (D, in figure below) is the key transition state in the interconversion between the chair and twist-boat conformations. The half-chair has C2 symmetry. The interconversion between the two chair conformations involves the following sequence: chair → half-chair → twist-boat → half-chair′ → chair′. Twist-boat to twist-boat The boat conformation (C, below) is a transition state, allowing the interconversion between two different twist-boat conformations. While the boat conformation is not necessary for interconversion between the two chair conformations of cyclohexane, it is often included in the reaction coordinate diagram used to describe this interconversion because its energy is considerably lower than that of the half-chair, so any molecule with enough energy to go from twist-boat to chair also has enough energy to go from twist-boat to boat. Thus, there are multiple pathways by which a molecule of cyclohexane in the twist-boat conformation can achieve the chair conformation again. Substituted derivatives In cyclohexane, the two chair conformations have the same energy. The situation becomes more complex with substituted derivatives. Monosubstituted cyclohexanes A monosubstituted cyclohexane is one in which there is one non-hydrogen substituent in the cyclohexane ring. The most energetically favorable conformation for a monosubstituted cyclohexane is the chair conformation with the non-hydrogen substituent in the equatorial position because it prevents high steric strain from 1,3 diaxial interactions. In methylcyclohexane the two chair conformers are not isoenergetic. The methyl group prefers the equatorial orientation. The preference of a substituent towards the equatorial conformation is measured in terms of its A value, which is the Gibbs free energy difference between the two chair conformations. A positive A value indicates preference towards the equatorial position. The magnitude of the A values ranges from nearly zero for very small substituents such as deuterium, to about 5 kcal/mol (21 kJ/mol) for very bulky substituents such as the tert-butyl group. Thus, the magnitude of the A value will also correspond to the preference for the