Statistical effects in the skeletal inversion of bicyclo(2.1.0) pentane

Abstract

A semiempirical potential-energy surface for bicyclo(2.1.0) pentane which includes bond stretching, bending, and torsional terms is reported. The bond dissociation energies have been estimated using the available thermochemical data and results of ab initio molecular orbital calculations performed at the fourth order Mo/ller–Plesset (MP4) perturbation theory level using a 6-31G** basis set. The predicted equilibrium geometry of bicyclo(2.1.0) pentane and of the 1,3-cyclopentanediyl radical, the barrier for the ring inversion, and the fundamental frequencies of bicyclo(2.1.0) pentane are in fair-to-good agreement with the measured and ab initio calculated values. Using a projection method of the instantaneous Cartesian velocities onto the normal mode vectors and classical trajectory calculations, the skeletal inversion and the intramolecular energy flow in bicyclo(2.1.0) pentane are studied for different types of excitation. For random energization of the vibrational modes, the results of trajectory calculations agree with the predictions of statistical unimolecular theory. The same statistical behavior is supported by the results of power spectra calculated at different energization levels. The significant broadening and overlapping of the spectral bands, together with the disappearance of characteristic spectral features in the power spectra of the flap angle, indicate high intramolecular vibrational redistribution rates and global statistical behavior. The total intramolecular vibrational relaxation rates for the energy flow from the flap mode have been extracted from the time dependence of the average total normal-mode energy in this mode. For initial excitation of the flap mode in the range 30–60 kcal/mol, the calculated total intramolecular vibrational relaxation rates are found to be significantly larger than the microcanonical ring inversion rates. This result further supports the statistical character of the ring inversion in bicyclo(2.1.0) pentane.