Modeling Photochemical [4 + 4] Cycloadditions: Conical Intersections Located with CASSCF for Butadiene + Butadiene

The [4 + 4] photocycloaddition of butadiene + butadiene has been studied at the CASSCF/4-31G level, as a prototype for a class of photochromic systems. For this model system, minima and transition structures are characterized by analytic frequency calculations, and conical intersections are located. Our results indicate that the standard model for the [4 + 4] addition (based on H 4) needs to be revised. The reorganization of all 8π electrons is crucial (i.e., it is not always the same 4π electrons that are important). Efficient nonradiative decay of butadiene + butadiene can be explained by the presence of two distinct S 1/S 0 conical intersections. The first - the lowest energy point on S 1 overall - is preceded by a barrier for the formation of a new σ bond. The resulting structure is similar to those previously characterized for methyl migration in but-1-ene and the addition of ethylene to benzene. A higher-energy barrier leads to a second crossing which resembles the rhomboidal funnel for the [2 + 2] addition of ethylene + ethylene, but which involves only one double bond from each butadiene. Both reaction paths commence at a true pericyclic minimum, at which the (S 0-S 1) energy gap of ~37 kcal mol -1 prohibits decay.