Quantum dynamics through a handful of semiclassical trajectories

Abstract An accurate description of quantum dynamics is challenging from both a theoretical and computational point of view. We illustrate some representative calculations based on a handful of trajectories whereby the semiclassical initial value representation theory is able to produce approximate but accurate quantum dynamical results. The range of applicability of SCIVR is vast and includes, among others, spectroscopy in gas and condensed phase, wavefunction calculations, and non-adiabatic dynamics. Here, we present a few SCIVR applications of different complexity. They involve a vibrational study of an N 2 molecule adsorbed on a TiO 2 surface, the IR spectroscopy of a methane molecule, and the determination of the vibrational ground state wavefunction of the formic acid dimer. These calculations demonstrate that our semiclassical approaches are able not only to provide an effective approximation to nuclear quantum dynamics but also to slash computational costs, which is mandatory when dealing with large-dimensional systems or complex problems. Finally, as a perspective, we move to a non-adiabatic framework and, by means of a linearized semiclassical approach, we compute the electronic state populations in a non-adiabatic dynamical process integrating 10,000 trajectories. The very good agreement with split-operator results motivates us to perform future research in the field aiming at few-trajectory-based calculations of comparable accuracy.