Conformational energy of the 5-membered ring. Implication of geometric and energetic properties in the conformational characteristics

In a previous article (8) a geometrical study of the five-membered ring showed that: a) for the case of the 20 symmetrical C2 and Cs conformations, the pseudorotation formulae for the torsion angles are a geometrical property of the ring; b) geometrical considerations alone are unable to define the puckering amplitude, the bond angle values, and the pathway between two symmetrical conformations. Here we examine how the energy equations enable us to define the deformation amplitude χm, establish the bond angles expressions and check the energy invariability along the pseudorotation circuit. The problem is next developed fully in the case where the bond and torsional energy only are considered: the literal expression1 of χm is then given as a function of the bond angle Ω which cancels out the bond angle energy. A numerical application is carried out on cyclopentane and the values of the parameters Kt, K1 and Ω used in the Conformational energy calculations are considered.