Résumé
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.