Quantum dynamics of the trimethylene biradical - Stereomutation of cyclopropane and unimolecular decay

A reduced-dimensionality three degrees-of-freedom quantum dynamics calculat ion of the stereomutation of cyclopropane has been performed. In one set of calculations, wavepackets are initiated centered around stationary points on the conrotatory, disrotatory and single rotation (cis/trans conversion) pathways. The ratio of trans to cis isomer formed, R-tc, is shown to be hig hly dependent on the location, and average energy of the initial wavepacket as well as the initial orientation of the terminal methylene torsions. In a second set of calculations, wavepackets are initiated as 'highly excited cyclopropane', in one of the four possible isomeric configurations, designa ted as a tl ans configuration for the purposes of analysis. Here also, R-tc depends on the initial torsional orientation. Analysis of wavepacket densi ty and the time constants for formation of product density indicate that th at the contributing mechanisms range from direct, concerted conrotatory mot ion to more statistical behavior. A 'Boltzmann' average at 695 K of the rat io of 'double' to 'single' rotations, k(12)/k(1), results in k(12)/k(1) = 2 R(tc) = 2.2. Wavepacket density is shown to orient preferentially along the conrotatory and disrotatory pathways rather than the higher energy single rotation(cis/trans conversion) pathway.