Semiclassical Wigner approach to quantum effects in vibrational spectroscopy

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Rapid progress of the laser facilities and measuring techniques has made the vibrational spectroscopy an ubiquitous tool to probe dynamics of complex many-body systems. The measured spectra can yield an extremely accurate dynamical information on the atomistic level if supplemented by a theoretical simulation, that reveals the underlying microscopic mechanisms. Thus the demand to have theoretical methods that can cope with explaining such spectra and thus unravelling intricate phenomena in condensed phase becomes apparent. The Wigner function constitutes a one-to-one representation of the quantum mechanical density operator, including coherences. The state-of-the-art methods based on linear semiclassical initial value representation readily reproduce static quantum effects already present in the initial state, whereas truly dynamical quantum effects that arise during the time evolution in the presence of nonlinear potentials remain outside reach. Major progress could be achieved through the insight that even quantum coherences can be time-evolved faithfully if the propagation is not based on single but on pairs of classical trajectories. This allows one to construct a truly semiclassical Wigner propagator in closed form that includes quantum corrections of the phase up to fourth-order terms in the potential. It has proven itself as a powerful tool already in analyzing quantum spectra of classically chaotic systems in terms of time-dependent phase-space structures and has been applied successfully to numerical propagation tasks and linear time-correlation functions in the framework of a grid-based methodology. Here, we attempt to make an important step ahead by recasting the successful grid-based formulation, which is well-suited for low-dimensional problems, into a grid-free representation where all relevant dynamical quantities are evaluated directly as averages over trajectory ensembles. This requires to recast the formalism accordingly, which has been mostly achieved during the preliminary work stage. The main goal of this project is thus to achieve the proof-of-concept for the proposed methodology applied to realistic molecular systems with many degrees of freedom. We propose to start from linear spectroscopy of model low-dimensional systems and to gradually increase their complexity, systematically solving all emerging methodological problems. Finally, the concept will be tested on chemically relevant molecules. The non-linear spectroscopy as well as the extension for the ab initio molecular dynamics framework treating the surrounding either by means of a QM/MM or realistic system-bath partitioning is foreseen.