On the barriers to planarity and the isotope effect in cyclobutane and cyclobutane-d8

The infrared and Raman data on the ring-puckering vibration in cyclobutane and cyclobutane-d₈ have been reexamined including the coordinate dependence of the reduced mass in the Hamiltonian. This was done for the purpose of estimating the importance of these small terms in the determination of barrier heights for four-membered rings and also on the determination of the dihedral angle corresponding to the potential minimum.The conclusions reached are that there is an isotopic dependence of the barriers to planarity in cyclobutane and cyclobutane-d₈ yielding a difference of ～14 cm^?1, but the precise value of the difference in barrier heights is ill determined. The higher-order kinetic energy terms in the Hamiltonian can account for a spread of ～3 cm^?1 in each of the barriers derived for cyclobutane and cyclobutane-d₈, depending on the details of the model used for the vibration, but not a difference of 14 cm^?1, which undoubtedly indicates the effects of coupling with other vibrational modes. It is also found that the derived values of the dihedral angles are quite sensitive to the details of the vibrational model, in fact, much more so than to the uncertainties in the bond distances and bond angles. A relationship between the potential constants derived for cyclobutane and cyclobutane-d₈ assuming an effective constant reduced mass and those derived for a semirigid model is demonstrated.