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.

In this work, we present the efficient combination of Smolyak representations with time independent quantum mechanical approach using absorbing boundary conditions for the cumulative reaction probability calculations of a multidimensional reactive scattering problem. Our approach uses both kinds of Smolyak representations (finite basis and grid) which drastically reduces the size of the basis representation for the cumulative reaction operator. The cumulative reaction probability is thus obtained by solving the eigenvalue problem within the context of reaction path Hamiltonian using the compact Smolyak basis combined with an iterative Lanczos algorithm. Benchmark calculations are presented for reactive scattering models with a linear reaction coordinate and applied to a 25D model highlighting the efficiency of the present approach for multidimensional reactive processes.

We present a quantum dynamics method based on the propagation of interacting quan- tum trajectories to describe both adiabatic and nonadiabatic processes within the same formalism. The idea originates from the work of Poirier [Chem. Phys. 370 4–14 (2010)] and Schiff and Poirier [J. Chem. Phys. 136 031102 (2012)] on quantum dynamics with- out wavefunctions. It consists in determining the quantum force arising in the Bohmian hydrodynamic formulation of quantum dynamics using only information about quan- tum trajectories. The particular time-dependent propagation scheme proposed here results in very stable dynamics. Its performance is discussed by applying the method to analytical potentials in the adiabatic regime, and by combining it with the exact factorization method in the nonadiabatic regime.

A Smolyak algorithm adapted to system−bath separation is proposed for rigorous quantum simulations. This technique combines a sparse grid method with the system−bath concept in a specific configuration without limitations on the form of the Hamiltonian, thus achieving a highly efficient convergence of the excitation transitions for the “system” part. Our approach provides a general way to overcome the perennial convergence problem for the standard Smolyak algorithm and enables the simulation of floppy molecules with more than a hundred degrees of freedom. The efficiency of the present method is illustrated on the simulation of H2 caged in an sII clathrate hydrate including two kinds of cage modes. The transition energies are converged by increasing the number of normal modes of water molecules. Our results confirm the triplet splittings of both translational and rotational (j = 1) transitions of the H 2 molecule. Furthermore, they show a slight increase of the translational transitions with respect to the ones in a rigid cage.

The accurate description of quantum effects, particularly quantum tunneling[1], in bimolecular chemical reactions constitutes one of the major goals of theoretical chemistry. Due to an unfavorable scaling law, exact quantum scattering methods lead to expensive and often unfeasible simulations when considering chemical systems with a large number of degrees of freedom. Moreover, at low temperature quantum effects often do not represent a small correction to classical calculations, but contrariwise are essential to obtain quantitative results. In this talk, I will show the feasibility of accurate quantum stationary scattering simulations for high dimensional systems using hybrid quantum-classical trajectories[2]. The configuration space is partitioned in one reaction coordinate going from reactants to products along which trajectories reproduce quantum effects, and bath coordinates with small amplitude motion which are treated classically[3]. Quantization of bath modes by a semi-classical phase-space sampling approximation based on Wigner-Weyl mapping allows to accurately reproduce quantum structure effects such as reaction thresholds. As was acknowledged many years ago [4], when the motion along the reaction coordinate is sufficiently slow compared to perpendicular motion, both subsystems undergo adiabatic evolution. By taking advantage from the local character of trajectory dynamics, I will illustrate how on-the-fly conversion from position-momenta to action-angle representation for bath coordinates in specific regions of vibrational adiabaticity leads to a computationally efficient scheme[5].

Among the numerous concepts of time in quantum scattering, Smith’s dwell time [F. T. Smith, Phys. Rev. 118, 349–356 (1960)] and Eisenbud & Wigner’s time delay [E. P. Wigner, Phys. Rev. 98, 145 (1955)] are the most well established. The dwell time represents the amount of time spent by the particle inside a given coordinate range (typically a potential barrier interaction region), while the time delay measures the excess time spent in the interaction region because of the potential. In this paper, we use the exact trajectory-ensemble reformulation of quantum mechanics, recently proposed by one of the authors (Poirier), to study how tunneling and reflection unfold over time, in a one-dimensional rectangular potential barrier. Among other dynamical details, the quantum trajectory approach provides an extremely robust, accurate, and straightforward method for directly computing the dwell time and time delay, from a single quantum trajectory. The resultant numerical method is highly efficient, and in the case of the time delay, completely obviates the traditional need to energy-differentiate the scattering phase shift. In particular, the trajectory variables provide a simple expression for the time delay that disentangles the contribution of the self-interference delay. More generally, quantum trajectories provide interesting physical insight into the tunneling process.

In this work we propose an exact derivation of the Hamilton formulation of quantum mechanical stationary scattering in one-dimensional curved space.