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

A reduced-dimensionality three degrees-of-freedom quantum dynamics calculation 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 highly 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, designated as a tl ans configuration for the purposes of analysis. Here also, R-tc depends on the initial torsional orientation. Analysis of wavepacket density and the time constants for formation of product density indicate that that the contributing mechanisms range from direct, concerted conrotatory motion to more statistical behavior. A 'Boltzmann' average at 695 K of the ratio of 'double' to 'single' rotations, k(12)/k(1), results in k(12)/k(1) = 2R(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.