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 (12D). The efficiency of this kind of grid is related to the replacement 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 for the calculation of large amplitude motion of confined molecule. 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.Preliminary results for the translation-rotation levels of (H2O)20H2 (hydrogen water clathrates) in a rigid or partially flexible water clathrate cage will be presented. This system has been investigated both experimentally [3] and theoretically [4, 5] as water cages are able to store efficiently molecular hydrogen clusters in various experimental conditions or other molecules in planetary atmospheres [6, 7].References[1] G. Avila and T. Carrington, J. Chem. Phys. 131, 174103 (2009). [2] D. Lauvergnat and A. Nauts, Spectrochim. Acta Part A. 119, 134114 (2013).[3] M. Celli, A. Powers, D. Colognesi, M. Xu, Z. Bacic, and L. Ulivi, J. Chem. Phys. 139, 164507 (2013).[4] M. Xu, L. Ulivi, M. Celli, D. Colognesi, and Z. Bacic, Chem. Phys. Lett. 563, 1-8 (2013).[5] A. Powers, Y. Scribano and Z. Bacic, in preparation.[6] E. Dartois, Molecular Physics 108, 2273-2278 (2010).[7] K. Shin et al., Proc. Nat. Acad. Sci. 109, 14785-14790, (2012).