We are interested in time dependent DFT, surface hopping and Franck-Condon factors, wavepacket methods, vibrational predissociation, and conical intersections in polyatomic systems.

For instance, we generalized the concept of Tully−Preston surface hopping to include larger *jumps* in the case that the surfaces do not cross. Instead of identifying a complex hopping point, we specified a jump between two locales in phase space. In particular, we applied this to find the propensity rules for the accepting vibrational mode(s) in a radiationless vibronic relaxation transition. For a model inspired by the S_{2} → S_{0} vibronic relaxation transition of the benzene molecule in which 30 modes of vibration compete for the electronic energy, we showed that almost all of the energy must go to a single C−H local stretching. The initial conditions for vibrations of this mode are a coordinate jump of the hydrogen atom toward the ring. All of the other modes undergo an almost vertical transition, in which the energy that they take is determined by their equilibrium displacement between the two surfaces. We observed that for a large energy gap the masses and frequencies become the defining parameters for choosing the accepting mode. Anharmonicities are very important when a competition between degenerate modes occurs. (J. Phys. Chem. A, 2002, 106 (25), pp 6006–6016)