Abstract:

Owing to its reactivity enhancing properties, quantum tunneling represents one of the most crucial effects to account for in order to achieve accurate prediction of rate constants for numerous chemical processes[1], even at ambient temperature[2]. Over the years, efficient methods emerged to accurately reproduce quantum tunneling in approximate atomistic simulations, with much progress being made on assessing the multidimensional character of the optimal tunneling path[3]. However resonant tunneling still proves to be a difficult phenomenon to characterize in the aforementioned methodological framework. In this talk, we present a purely trajectory based[4] approach of great accuracy and efficiency[5] applied to potential energy profiles subject to resonant tunneling. The working equations are a set of first order ODEs for a Hamiltonian in an extended phase space with respect to its classical analog. Trajectory propagation time enjoys a close relationship with collision lifetime, allowing to directly recover Smith's quantal time delay[6] at the energy of interest and thus giving further insight into resonant phenomena[7]. Trajectories describing scattering states with a reflection probability of nearly unity manifest strong destructive interference patterns, resulting in a very arduous numerical integration. This is reminiscent of pathologic numerical behavior encountered by the log-derivative approach in the deep tunneling regime[8] and constitutes a specific form of the well-known « node problem » encountered in Bohmian Dynamics[9]. To cope with the node problem, we propose an efficient semi-analytic scheme allowing trajectories to bypass nodes without significant loss of accuracy. As a result the method is a robust tool to analyse resonant reactive scattering.