The real-time simulation of light-induced dynamical processes in molecules not only provides important insights into their photochemistry and photophysics, but also allows one to obtain a deep molecular-level understanding of the mechanisms underlying e.g. laser control or the specific appearance of experimentally obtained spectroscopic signals. A crucial characteristic of processes driven or initiated by UV or visible light consists in the coupling of electronic and nuclear motion, both due the light-matter interaction itself as well as due to intrinsic non-adiabatic couplings caused by the breakdown of the Born-Oppenheimer approximation, e.g. in the vicinity of conical intersections between electronic states.
While for simple systems, purely quantum mechanical methods are applicable, this is no longer possible for molecules exhibiting a large number of nuclear degrees of freedom. In this case, mixed quantum-classical approaches are appropriate. In our group, we have developed the field-induced surface hopping method (FISH) , which is based on the propagation of classical nuclear trajectories in a manifold of electronic quantum states. The electronic population dynamics is accounted for by allowing the nuclear trajectories to switch the actual electronic state according to quantum mechanically calculated hopping probabilities, which in turn are obtained from solving the time-dependent electronic Schrödinger equation along the trajectories, including the light-induced and non-adiabatic couplings between the electronic states. The necessary energies, forces and coupling elements can be provided by any appropriate quantum chemical method.
We have employed this approach for the simulation of the photodynamics in a wide variety of molecular systems, both in isolated form [2,3] as well as in solvent environment [4,5]. Moreover, we have continuously advanced our methodology such as to include as well multiphoton processes  or magnetic-field-induced couplings .
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