Kinetic energy functions for the ring-bending and ring-twisting vibrations of asymmetrically substituted six-membered rings

Vector models were developed for calculating the kinetic energy (reciprocal reduced mass) expressions for the ring-bending and single bond ring-twisting vibrations of six-membered rings with one double bond. These models are valid for asymmetrically substituted rings. A two-dimensional kinetic energy calculation was carried out and the twist-bend cross terms were also calculated. The reduced masses calculated for several oxygen-containing analogs of cyclohexene increase as the ring bends or twists. Kinetic energy expressions as functions of the vibrational coordinates were derived.