Theoretical study of geometric phase effects in the hydrogen-exchange reaction

The crossing of two electronic potential surfaces (a conical intersection) should result in geometric phase effects even for molecular processes confined to the lower surface. However, recent quantum simulations of the hydrogen exchange reaction (H + H2 --> H2 + H) have predicted a cancellation in such effects when product distributions are integrated over all scattering angles. We used a simple topological argument to extract reaction paths with different senses from a nuclear wave function that encircles a conical intersection. In the hydrogen-exchange reaction, these senses correspond to paths that cross one or two transition states. These two sets of paths scatter their products into different regions of space, which causes the cancellation in geometric phase effects. The analysis should generalize to other direct reactions.