Ab Initio Study of Cyclobutane:  Molecular Structure, Ring-Puckering Potential, and Origin of the Inversion Barrier

The structure and ring-puckering properties of cyclobutane and its perdeuterated isotopomer are studied using high-level ab initio methods and complete basis set extrapolations. Calculations reveal significant coupling between the ring-puckering (θ) and CH2-rocking (α) motions, with equilibrium angles (θeq = 29.59° and αeq = 5.67°) that are within the range of experimentally determined values. Our best estimate of the inversion barrier is 482 cm-1, in excellent agreement with recent experimental determinations. Ring-inversion transition frequencies are evaluated from the eigenstates of the intrinsic reaction coordinate potentials for cyclobutane and cyclobutane-d 8. Natural bond orbital analysis shows that σCC → σCH* and σCH → σCH* hyperconjugative interactions are strengthened as cyclobutane puckers, thereby suggesting that inversion barriers in four-membered ring systems are a consequence of electronic delocalization rather than torsional strain.