Grid-based electronic structure calculations: the tensor decomposition approach
This work provides a computationally efficient grid-based approach for electronic structure calculations, potentially enabling high-accuracy simulations for quantum chemistry.
The authors developed a grid-based method for Hartree-Fock and Kohn-Sham equations using low-rank tensor decomposition, achieving linear complexity with grid size and enabling fine grids up to 8192^3. Tests on atoms, molecules, and hydrogen clusters showed systematic convergence to required accuracy.
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.