title: Variational tensor approach for approximating the rare-event kinetics of macromolecular systems.
abstract: Essential information about the stationary and slow kinetic properties of macromolecules is contained in the eigenvalues and eigenfunctions of the dynamical operator of the molecular dynamics. A recent variational formulation allows to optimally approximate these eigenvalues and eigenfunctions when a basis set for the eigenfunctions is provided. In this study, we propose that a suitable choice of basis functions is given by products of one-coordinate basis functions, which describe changes along internal molecular coordinates, such as dihedral angles or distances. A sparse tensor product approach is employed in order to avoid a combinatorial explosion of products, i.e., of the basis set size. Our results suggest that the high-dimensional eigenfunctions can be well approximated with relatively small basis set sizes.
authors: Department of Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 6, 14195 Berlin, Germany.
authors: Feliks
authors: F
authors: Nüske
authors: Institut für Mathematik, Technische Universität Berlin, Straße des 17. Juni 136, 10623 Berlin, Germany.
authors: Reinhold
authors: R
authors: Schneider
authors: Department of Chemistry, Freie Universität Berlin, Takustr. 3, 14195 Berlin, Germany.
authors: Francesca
authors: F
authors: Vitalini
authors: Department of Mathematics and Computer Science, Freie Universität Berlin, Arnimallee 6, 14195 Berlin, Germany.
authors: Frank
authors: F
authors: Noé