Tensor decomposition in electronic structure calculations on 3D Cartesian grids

Modern problems of physical chemistry lead to computations of many-particle potentials and related integral transforms, involving quantities described by higher-order tensors. Conventional numerical treatment of these problems suffers from the so-called “curse of dimensionality”. Recently developed Tucker and canonical tensor approximation techniques provide structured data-sparse representation to higher-order tensors. We discuss the newly developed algorithms of multi-linear algebra (MLA) for the numerical treatment of multi-dimensional operators and functions. Applications to the electron density and to the Hartree potential in the Hartree-Fock equation are presented.