L’effet tunnel est incontournable pour parfaire notre compréhension de la réactivité chimique. Permettant le passage de barrières de réaction cinétiquement infranchissables, son rôle primordial dans les réactions à basse température et pour l’échange d’éléments légers est bien connu. Cependant, l’assomption selon laquelle il serait sans impact hors de ces cas de figure a également été démentie ces dernières années: Ni l’échange d’éléments chimiques plus lourds que l’hélium[1], ni les réactions à température ambiante ne justifient de le négliger à priori[2]. Sa capacité à orienter la formation d’un produit de réaction l’élève au rang de troisième voie de contrôle de la réactivité, au même titre que les contrôles cinétique et thermodynamique[3]. De ce fait, il est nécessaire de disposer de méthodes numériques capables de reproduire cet effet purement quantique avec précision. Or, les méthodes approchées les plus couramment employées pour estimer la probabilité de transmission, comme WKB[4], ne garantissent pas un résultat fiable ( notamment en cas d’effet tunnel résonant, ou dans le régime deep tunneling ). L’utilisation de formules analytiques dérivées de potentiels approchés[5], une autre méthode répandue pour incorporer une estimation de l’effet tunnel, souffre également de son manque de précision. Si ces méthodes sont si largement utilisées, c’est avant tout pour leur simplicité et leur faible coût calculatoire. L’objet de cette contribution est de présenter une méthode efficace pour déterminer la probabilité de transmission le long d’un chemin de réaction de manière exacte[6,7]. Issue d’un formalisme rigoureusement équivalent à l’équation de Schrödinger stationnaire, cette approche remplace la détermination des états de diffusion par la propagation d’une trajectoire dans un espace des phases étendu[8,9]. La méthode et son efficacité seront illustrées sur des systèmes modèles ainsi qu’une réaction d’intérêt pour l’astrochimie[10].

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.

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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.

We report the detection and characterization of the transiting sub-Neptune TOI-1759 b, using photometric time series from the Transiting Exoplanet Survey Satellite (TESS) and near-infrared spectropolarimetric data from the Spectro-Polarimètre Infra Rouge (SPIRou) on the Canada-France-Hawaii Telescope. TOI-1759 b orbits a moderately active M0V star with an orbital period of 18.849975 ± 0.000006 days, and we measured a planetary radius and mass of 3.06 ± 0.22 R⊕ and 6.8 ± 2.0 M⊕. Radial velocities were extracted from the SPIRou spectra using both the cross-correlation function and the line-by-line methods, optimizing the velocity measurements in the near-infrared domain. We analyzed the broadband spectral energy distribution of the star and the high-resolution SPIRou spectra to constrain the stellar parameters and thus improve the accuracy of the derived planet parameters. A least squares deconvolution analysis of the SPIRou Stokes V polarized spectra detects Zeeman signatures in TOI-1759. We modeled the rotational modulation of the magnetic stellar activity using a Gaussian process regression with a quasi-periodic covariance function and find a rotation period of 35.65−0.15+0.17 days. We reconstructed the large-scale surface magnetic field of the star using Zeeman-Doppler imaging, which gives a predominantly poloidal field with a mean strength of 18 ± 4 G. Finally, we performed a joint Bayesian Markov chain Monte Carlo analysis of the TESS photometry and SPIRou radial velocities to optimally constrain the system parameters. At 0.1176 ± 0.0013 au from the star, the planet receives 6.4 times the bolometric flux incident on Earth, and its equilibrium temperature is estimated at 433 ± 14 K. TOI-1759 b is a likely gas-dominated sub-Neptune with an expected high rate of photoevaporation. Therefore, it is an interesting target to search for neutral hydrogen escape, which may provide important constraints on the planetary formation mechanisms responsible for the observed sub-Neptune radius desert.