We show that a nonstationary electron can be created in HD+ corresponding to partial electron transfer between H+ and D+. The electronic motion is introduced through nuclear motion, more specifically, through nonadiabatic curve crossing, and the electronic motion is here on the same time scale as the nuclear motion. We show that the branching ratio between the channels H + D+ and H+ + D depends on the electron distribution (i.e., where the electron “sits”) prior to the time where the bond is broken by an infrared femtosecond pulse. Thus, we controlin real-timewhich nucleus the electron will follow after the bond is broken.

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We study theoretically the electronic and nuclear dynamics in NaI. After a femtosecond pulse has prepared a wave packet in the first excited state, we consider the adiabatic and the nonadiabatic electronic dynamics and demonstrate explicitly that a nonstationary electron is created in NaI corresponding to electron transfer between Na and I. The electronic motion is introduced via nuclear motion, more specifically, through nonadiabatic curve crossing and the electronic motion is here on the same time scale as the nuclear motion. We show that the branching ratio between the channels NaϩI and Na ϩ ϩI Ϫ depends on the electron distribution ͑i.e., where the electron ''sits''͒ prior to the time where the bond is broken by a subpicosecond half-cycle unipolar electromagnetic pulse. Thus we control, in real time, which nucleus one of the valence electrons will follow after the bond is broken.

We consider electronic excitation induced with a continuous wave laser to an excited bound state which can predissociate due to a radiationless transition to a dissociative state. The conditions for a separation of the process into the preparation of a vibrational eigenstate which subsequently dissociates due to a radiationless transition are established. We point out that the probability of the radiationless transition can be calculated from a time-dependent nuclear autocorrelation function, an expression which nicely reflects the pictorial aspect of the Franck-Condon principle.

We derive an expression for a short-time phase space propagator. We use it in a new propagation scheme and demonstrate that it works for a Morse potential. The propagation scheme is used to propagate classical distributions which do not obey the Heisenberg uncertainty principle. It is shown that the simple classical deterministic motion breaks down surprisingly fast in an anharmonic potential. Finally, we discuss the possibility of using the scheme as a useful approach to quantum dynamics in many dimensions. To that end we present a Monte Carlo integration scheme using the norm of the propagator as a part of the sampling function.