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Cumulative reaction probability plays a central role in the calculation of reaction rate constant of any bimolecular chemical reaction of interest. In order to give meaningful results, these calculations should be performed for chemical systems with a large number of degrees of freedom leadingto expensive and often infeasible simulations. In this work, a new computational scheme is proposed to allow high dimensional quantum reactive simulations. This scheme is based on the Green’s function operator technics combined to absorbing boundary conditions, a powerful approach introduced by W.H. Miller, T. Seideman and U. Manthe many years ago [1,2]. The new implementation takes benefit that the initial quantum reactive scattering problem can be cast into an eigenvalue problem [2] and uses the high efficiency and accuracy of Smolyak algorithm [3] to build very compact basis for eigenvalue problems [4]. Using this new computational framework, it is now possible to perform quantum dynamics simulations for multidimensional systems pushing away the curse of dimensionality problem. Some preliminary results will be presented [5] using this new powerful scheme

National audience; We present recent progress on quantum trajectories method for one dimensional resonant reactive scattering processes.

The study of small/medium size molecules inside nanoscale cavities of diverse host material, e.g.,clathrates hydrates, cryogenic fluids (or superfluids), fullerenes, carbon nanotubes and zeolites, has receiveda great deal of attention over the past years due to their broad application domain (condensed matter physics,nanomaterial sciences, geoscience, quantum chemistry, astrophysical and planetary sciences, biophysics, ...).However the description of such systems is often far from complete. Indeed,in such nanoscale confinement, the motion of the encapsulated molecule is far from harmonic and is characterised by large amplitude motions. The translational center-of-mass motionsof the caged molecules are quantized and strongly coupled to themolecular rotations, which are quantized too.In this talk, I will present our recent progress in the Translation-Rotation (TR) and Vibration-Translation-Rotation (VRT) bound states calculation of guest molecules such as molecular hydrogen in a clathrate hydrate. Within this study, we have investigated the effect of a non-rigid description of a clathrate hydrate framework on the encapsulated molecular hydrogen eigenstates using an efficient sparse grid scheme which allow us to consider up to 65 degrees of freedom. Traditionally, the water cage structure is assumed to be rigid, thus ignoring the quantum nature of hydrogen nuclei in the water framework.

International audience; I present some recent work using sparse-grid technics for high dimensional molecular bound states calculations

we present new strategy to perform vibrational mean field and vibrational configuration interaction coalculations for large molecular systems. Thanks to an efficient pruning scheme based on the many body expansion of the potential energy surface, we show that variational bound state calculation is possible form large molecular systems

International audience; I present the recent results obtained for high dimensional eigenvalue problems involving large amplitude motions as ones meet in molecular spectroscopy and reaction dynmics

International audience; The quantum dynamics studies of molecular bound states are actually limited by the well known dimensionality problem. Indeed even for molecules of medium size, usual quadrature techniques have already reached their limit since a multidimensional direct-product grid can be very large. An alternative to avoid the direct-product grid is to use the Smolyak sparse-grid techniques, recently investigated by Avila and Carrington [1] for the calculation of vibrational bound states of semi-rigid molecules. Lauvergnat and Nauts [2] have proposed a new implementation of such sparse grid for the study of the torsional levels of methanol in full dimensionality in order to treat one large amplitude motion. The efficiency of this kind of grid is related to the substitution of a single large direct-product grid by a sum of small direct-product grids. We will present a recent adaptation of this kind of sparse grid scheme for the calculation of six-dimensional (6D) vibration-translation-rotation bound states of confined molecule such as H$_2$ (and its isotopologues) in water clathrate [3]. In particular, we are able to use a combination of 2D-grids associated to spherical harmonic basis functions and the usual 1D-gaussian quadrature grids to form the Smolyak sparse-grid [4]. We will discuss the efficiency of this approach for the calculation the intramolecular vibrational shift of H$_2$ as well as the effect of the condensed phase environment.[1] A. Avila and T. Carrington, J. Chem. Phys. 131 (2009), 174103.[2] D. Lauvergnat and A. Nauts, Spectrochim. Acta. Part A 119 (2014), 18.[3] D. Lauvergnat and P. Felker and Y. Scribano and D. Benoit and Z. Bacic, J. Chem. Phys.150 (2019), 154303.[4] A. Powers and Y. Scribano and D. Lauvergnat and E. Mebe and D. Benoit and Z. Bacic, J.Chem. Phys. 148 (2018), 144304.

International audience; The Langevin capture model is often used to describe barrierless reactive collisions. At very lowtemperatures, quantum effects may alter this simple capture image and dramatically affect the reactionprobability. In this paper, we use the trajectory-ensemble reformulation of quantum mechanics, asrecently proposed by one of the authors (Poirier) to compute adiabatic-channel capture probabilitiesand cross-sections for the highly exothermic reaction Li + CaH(v = 0, j = 0)!LiH + Ca, at low andultra-lowtemperatures. Each captured quantum trajectory takes full account of tunneling and quantumreflection along the radial collision coordinate. Our approach is found to be very fast and accurate,down to extremely low temperatures. Moreover, it provides an intuitive and practical procedurefor determining the capture distance (i.e., where the capture probability is evaluated), which wouldotherwise be arbitrary.

While direct reactions with activation barriers are now routinely calculated, reactions going through a longlivedintermediate complex are much more difficult to study[1, 2]. Complex-forming reactions are often barrierlessand are thus relevant to the field of cold and utra-cold chemistry [2]. With decreasing temperature, wave effectsbecome increasingly important and may dominate the collisional behavior at ultralow temperatures. Capture theories(close-coupling expansion with boundary conditions applied in the reactant channel) are often used to studycomplex-forming reactions [3, 4].The Langevin capture model is often used to describe barrierless reactive collisions. At very low temperature,quantum effects may alter this simple capture image and dramatically affect the reaction probability. In this talk,we use the trajectory-ensemble reformulation of quantum mechanics without wavefunctions recently proposed byPoirier and coworkers[5, 6] to compute adiabatic-channel capture probabilities and cross-sections for the reactionLi + CaH(v = 0; j = 0)!LiH + Ca at low and ultra-low temperatures. The captured quantum trajectory takes fullaccount of tunneling and quantum reflection along the radial collision coordinate. Our approach turns out to bevery fast and accurate, down to extremely low temperatures.

International audience; The study of small/medium size molecules inside nanoscale cavities of diverse host material, e.g., clathrates hydrates, cryogenic fluids (or superfluids), fullerenes, carbon nanotubes and zeolites, has received a great deal of attention over the past years due to their broad application domain (condensed matter physics, nanomaterial sciences, geoscience, quantum chemistry, astrophysical and planetary sciences, biophysics, \ldots).However the description of such systems is often far from complete. Indeed, in such nanoscale confinement, the translational center-of-mass motions of the caged molecules are quantized and strongly coupled to the molecular rotations, which are quantized too. To interpret experimental data, theoretical tools are useful but we need to go beyond the simple harmonic approximation as the guest molecule presents very large amplitude motions (translation and rotation) and its interaction with the nanoscale cavity can be far from harmonic. A rigorous quantum treatment of the intricate coupled translation-rotation (TR) dynamics of the caged diatomic molecules is far from a routine task.In this talk, I will present recent methodological development based on the concept of Smolyak sparse grid technic for the rigorous quantum treatment of the intricate coupled translation-rotation (TR) dynamics of the molecular hydrogen in water clathrates.

International audience; The Time Independant Quantum Method is the reference for the calculations of cold molecule-molecule collisions. This close-coupling (CC) approach is commonly used in the cold chemistry and molecular astrophysics communities. However, the numerical cost of the CC-method increases significantlywith the size of the target molecule and some new methods should be investigated. I will present the use of an adiabatic model (and its possible extension) in the context of the CC-method. I will present the results (inelastic cross sections and rate constants) for the water colliding with para-Hydrogen molecule. The internal rotational adiabatic decoupling scheme reduces dimensional dynamics from a 5D to a 3D problem and a good agreement is found between those two calcutaions. This adiabatic reduction of dimensionality seems very promising for scattering studies involving the excitation of a heavy target molecule by a light molecular projectile.

International audience; We present in this talk the efficiency of the smolyak sparse grids for the desciption of molecular large amplitude motion. The method is applied to the calculation of the coupled translation-rotation eigenstates of H2 in water clathrate.

The study of small/medium size molecules inside nanoscale cavities of diverse host material, e.g.,clathrates hydrates, cryogenic fluids (or superfluids), fullerenes, carbon nanotubes and zeolites, has receiveda great deal of attention over the past years due to their broad application domain (condensed matter physics,nanomaterial sciences, geoscience, quantum chemistry, astrophysical and planetary sciences, biophysics, ...).However the description of such systems is often far from complete. Indeed,in such nanoscale confinement, the translational center-of-mass motionsof the caged molecules are quantized and strongly coupled to themolecular rotations, which are quantized too. To interpret experimentaldata, theoretical tools are useful but we need to go beyond the simple harmonicapproximation as the guest molecule presents very large amplitudemotions (translation and rotation) and its interaction with the nanoscalecavity can be far from harmonic. A rigorous quantum treatment of the intricatecoupled translation-rotation (TR) dynamics of the caged diatomicmolecules is far from a routine task.

National audience; In this contribution, we expose a new mixed quantum-classical reaction dynamics method whosenovelty is that it is entirely based on trajectories. Our approach rests on the concept of quantumtrajectory, which has been long been considered a philosophical and interpretative tool for quantummechanics [1]. Recently, quantum trajectories have been “rediscovered” with the goal of developinga totally new and unconventional computational method for doing quantum reaction dynamics [2,3].The most recent formulation, due to Bill Poirier and coworkers [4-6], sums up as a system ofcoupled ordinary differential equations (ODEs), that can be propagated in an extremely stable andaccurate manner. Potential advantages of this method are easily seen: (i) accurate propagation canbe extended to very large internuclear distances at low temperature; (ii) the propagation of onequantum degree of freedom together with several—possibly many—classical degrees of freedomsimply amounts to solving a “cheap” classical-like ODE system.Here we elaborate on our companion communication “Quantum trajectory capture at low and ultralowtemperature”. The above quantum trajectory approach is introduced and its physical as well ascomputational advantages are detailed, with special emphasis on the capture process.

National audience; The classical capture model for chemical reactions assumes that all trajectories with enough energyto cross the (centrifugal) barrier in the effective potential actually do so, and then proceed to formthe products. However, wave effects (not accounted for in a classical approach, by definition)become increasingly important with decreasing temperature and may dominate the collisionalbehavior at ultra-low temperatures.In this contribution we propose a new approach that describes the capture process by evolvingquantum trajectories [1,2] in the reactant channel up to a given limit, the capture distance, on theinside of the centrifugal barrier. The quantum trajectories take full account of quantum effects alongthe reaction path direction in the entrance channel. In particular, tunneling and quantum reflection,which can change the reaction rate by orders of magnitude, are accurately computed. In addition,quantum trajectories give valuable physical insight into the quantum capture process all along theapproach of the reactants. They also provide a technical means to determine the optimum capturedistance.Moreover, quantum trajectories along the reactant approach can easily be coupled with classicaltrajectories that drive the rest of the degrees of freedom of the system [3]. Apart from the captureprocess, which is guided by a quantum trajectory, all other coordinates are treated classically [3].This mixed quantum-classical capture approach is thus highly “classical-like” [3] and is aimed atlarge system reactions with quantum effects, still out of reach for current quantum scattering codes.Preliminary results will be presented at the conference.The authors are very grateful to Bill Poirier for his ongoing encouragement.[1] B. Poirier, “Bohmian mechanics without pilot waves”, Chem. Phys. 370, 4 (2010)[2] J. Schiff and B. Poirier, “Quantum mechanics without wavefunctions”, J. Chem. Phys. 136