## A quasiresonant smoothing algorithm for the fast analysis of selective vibrational excitation.

Please always quote using this URN: urn:nbn:de:0297-zib-1066
• One key problem in modern chemistry is the simulation of the dynamical reaction of a molecule subjected to external radiation. This is described by the Schrödinger equation, which, after eigenfunction expansion, can be written in form of a system of ordinary differential equations, whose solutions show a highly oscillatory behaviour. The oscillations with high frequencies and small amplitudes confine the stepsizes of any numerical integrator -- an effect, which, in turn, blows up the simulation time. Larger stepsizes can be expected by averaging these fast oscillations, thus smoothing the trajectories. This idea leads to the construction of a quasiresonant smoothing algorithm (QRS). In QRS, a natural and computationally available splitting parameter $\delta$ controls the smoothing properties. The performance of QRS is demonstrated in two applications treating the selective excitation of vibrational states by picosecond laser pulses. In comparison with standard methods a speedup factor of 60--100 is observed. A closer look to purely physically motivated quasiresonant approximations such as WFQRA shows some additional advantages of the above smoothing idea. Among these the possibility of an adaptive formulation of QRS via the parameter $\delta$ is of particular importance.