Sparse Grids For The Electronic Schrodinger Equation

Download or read book Sparse Grids for the Electronic Schrödinger Equation written by Jan Hamaekers and published by Sudwestdeutscher Verlag Fur Hochschulschriften AG. This book was released on 2010-05 with total page 172 pages. Available in PDF, EPUB and Kindle. Book excerpt: The successful numerical treatment of the electronic Schrodinger equation provides an effective predictive tool for new insights in several research areas like chemistry, biochemistry, molecular physics, material science and nanotechnology. However, any numerical solution of the electronic Schrodinger equation using conventional linear discretization schemes is not feasible due to its high dimensionality. Therefore, typically nonlinear model approximations like Hartree-Fock, coupled cluster or density functional theory are used. In this work we construct, study and apply novel sparse tensor product multiscale many-particle spaces with finite-order weights for the electronic Schodinger equation. This new variant of sparse grids combines the favorable properties of efficient Gaussian type orbitals basis sets and adaptive tensor product multiscale bases, which provide guaranteed convergence rates. In particular, the introduced formulation of the underlying particle-wise subspace splitting includes several decomposition schemes well known in different research fields. With the implementation of our approach, small atoms and molecules can be treated at very high accuracy."