%0 Journal Article
%T Grid-based electronic structure calculations: the tensor decomposition approach
%A Maxim Rakhuba
%A Ivan Oseledets
%J Mathematics
%D 2015
%I arXiv
%X We present a fully grid-based approach for solving Hartree-Fock and all-electron Kohn-Sham equations based on low-rank approximation of three-dimensional electron orbitals. Due to the low-rank structure the total complexity of the algorithm depends linearly with respect to the one-dimensional grid size. Linear complexity allows for the usage of fine grids, e.g. $8192^3$ and, thus, cheap extrapolation procedure. We test the proposed approach on closed-shell atoms up to the argon, several molecules and clusters of hydrogen atoms. All tests show systematical convergence with the required accuracy.
%U http://arxiv.org/abs/1508.07632v1