• azobenzene
• non-adiabatic dynamics
• quantum decoherence
• Surface Hopping

The study of many photochemical and photophysical problems requires that non-adiabatic effects are taken into account. Since non-adiabatic effects are fully quantum features, quantum methods would be the most suitable choice. Alas, due to the exponential scaling with the number of coordinates, quantum methods are not affordable to treat molecular systems with more than four or five atoms, and one has to resort to a semiclassical method.
Semiclassical methods are interesting in many ways. Many of them scale only linearly with the number of particles. Moreover semiclassical methods are naturally suited to be performed ``on the fly''.
The widest used semiclassical method for the non-adiabatic dynamics is probably Tully's Surface Hopping method. The nuclear motion is represented by a swarm of classical trajectories. Each trajectory runs on a single PES (the ``current'' state) and the probability of hopping on another potential energy surface is calculated with the ``Fewest Switches'' algorithm.
One of the main problems of Surface Hopping is the lack of quantum decoherence. This implies that the populations of different electronic states are not treated accurately, in particular when a trajectory gets far from the strong coupling regions.
We tried to correct the SH algorithm to account for the quantum decoherence without give up the independent trajectories approach. The developed method is not an ad hoc correction, but is rather based on a physically motivated model. Approximate trajectories are also computed on PES different from the ``current'' one, and gaussian wavepacket are associated with each trajectory. The decay of the overlap between wavepackets on different PES accounts for the main decoherence effects. In this way the computed results depend on a single parameter associated to the gaussian width.
The method has been tested on various two state models, with various dimensionalities (from 1 to 72 coordinates). The results of our method compare well with quantum results.
Many future developements are possible, from the application to other model systems to an improved description of the wavepacket time evolution.