Grid-based electronic structure calculations: The tensor decomposition approach

M. V. Rakhuba, I. V. Oseledets

    Research output: Contribution to journalArticlepeer-review

    15 Citations (Scopus)


    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.

    Original languageEnglish
    Pages (from-to)19-30
    Number of pages12
    JournalJournal of Computational Physics
    Publication statusPublished - 1 May 2016


    • Cross-approximation method
    • Hartree-Fock equation
    • Integral iteration
    • Kohn-Sham equation
    • Multidimensional convolution
    • Tensor decompositions


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