Complex excited dynamics around a plateau on a retinal-like potential surface: chaos, multi-exponential decays and quantum/classical differences

We investigate the classical and quantum dynamics on the plateau of an excited potential energy surface (PES) whose shape mimics the PES where the photoisomerization of the protonated Schiff base of retinal (PSBR) takes place. We adopt a two-dimensional analytical model of the PES, and perform an extended study varying the potential parameters, revealing a scenario whose interest goes beyond the relevance for the specific case of PSBR. In fact we document cases with net differences among classical and quantum dynamical predictions, for barrierless PESs. Classical trajectories released on the PES display the signature of chaos and partial trapping on the plateau, whose origin is purely dynamical, since no barrier exists. At variance, on the same barrierless PESs, quantum dynamics does not predict any trapping, always showing a complete depletion of the excited population according to an approximate mono-exponential law. The plateau on the PES promotes complex and unusual dynamical features, and it is sufficient to introduce a very small barrier along the cis-trans torsional mode to give rise to a multi-exponential decay, also at quantum level. Our results are of general interest because plateaux are often found in Ĉ-systems excited states.