Grid-based electronic structure calculations: The tensor decomposition approach

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. 81923 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.