title: Quantum dynamics with sparse grids: a combination of Smolyak scheme and cubature. Application to methanol in full dimensionality.
abstract: Quantum dynamical approaches based on product-grids are limited to the studies of molecular systems with few degrees of freedom, typically less than ten. Recently, Avila et al. [G. Avila, T. Carrington, J. Chem. Phys., 131 (2009) 174103] have introduced the Smolyak scheme [S.A. Smolyak, Sov. Math. Dokl., 4 (1963) 240], which considerably reduces the size of the grids. This approach has pushed back the present calculation limits on the vibrational spectra of polyatomic molecules. In the present study, we have developed an extension of the standard Smolyak scheme in which this scheme is combined with multidimensional grids, such as cubatures, to obtain new sparse grids. This scheme has been applied to the study of the torsional energy levels of methanol in full dimensionality (12D).
authors.affiliation: Laboratoire de Chimie Physique, Bâtiment 349, CNRS, UMR8000, Univ Paris-Sud, Orsay F-91405, France. Electronic address: David.Lauvergnat@u-psud.fr.
authors.forename: David
authors.initials: D
authors.lastname: Lauvergnat
authors.forename: André
authors.initials: A
authors.lastname: Nauts
mesh_terms: D000465:Algorithms; D000432:Methanol / Q000737:chemistry*; D008958:Models, Molecular; D011789:Quantum Theory
chemical_list: D000432:Methanol
keywords: Cubature; Methanol; Smolyak; Sparse grid; Vibrational spectroscopy