Mixed state `on the flyʹ non-adiabatic dynamics: the role of the conical intersection topology

An algorithm is presented for non-adiabatic `on the flyʹ dynamics simulations using a valence bond wavefunction that arises in the molecular mechanics valence bond method. The electronic wavefunction is propagated using time-dependent quantum mechanics in synchronisation with nuclear propagation using classical mechanics. Some representative computations for the radiationless decay of all-trans-hexa-1,3,5-triene and azulene at a conical intersection channel are presented. In the dynamics studies one observes almost pure diabatic transitions as well as situations where the trajectory propagates in a `mixed stateʹ near the conical intersection before decay to the ground state.